Professor Igor Shparlinski

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More information is available from http://web.maths.unsw.edu.au/~igorshparlinski/

E-mail

igor.shparlinski@unsw.edu.au

Books | 2006

Abe M; Aoki K; Ateniese G; Avanzi R; Beerliová Z; Billet O; Biryukov A; Blake I; Boyd C; Brier E; Castiglione A; Cha J; Chan A; Chen L; Cho K; Contini S; D'Arco P; Ding J; Doche C; Dunkelman O; Fitzi M; Fouque PA; Fournier JJA; Fujisaki K; Fujisaki E; Furukawa J; Galindo D; Halevi S; Handschuh H; Heneghan C; Holenstein T; Hoshino F; Hwang YH; Isshiki T; Jochemsz E; Joux A; Juels A; Jutla C; Kiayias A; Kikuchi H; Kobayashi T; Kohno T; Krawczyk H; Kumar S; Lange T; Lee JW; Masucci B; May A; Mihaljevic M; Minematsu K; Monrose F; Montague P; Myers S; Naccache D; Nicolosi A; Obana S; Okazaki S; Okeya K; Olivier F; Oyono R; Page D; Park JH; Peng K; Pietrzak K; Raub D; Sakai Y; Sakurai K; Schindler W; Seo JW; Shin JH; Shparlinski I; Steinfeld R; Szydlo M; Kalai YT; Teranishi I; Tokita T; Tunstall M; Vercauteren F; Villegas K; Walfish S; Wang H; Wang X; Warinschi B; De Weger B; Wolf C; Yampolskiy A; Yang YH; Yin YL; Yoon J; Pointcheval D, 2006, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

Books | 2003

Everest G; van der Poorten A; Shparlinski I; Ward T, 2003, Recurrence Sequences, American Mathematical Society, http://dx.doi.org/10.1090/surv/104

Books | 2001

Boztaş S; Shparlinski IE, 2001, Preface

Books | 1999

Konyagin S; Shparlinski I, 1999, Character Sums with Exponential Functions and their Applications, Cambridge University Press, http://dx.doi.org/10.1017/cbo9780511542930

Books | 1999

Shparlinski I, 1999, Number Theoretic Methods in Cryptography, Birkhäuser Basel, http://dx.doi.org/10.1007/978-3-0348-8664-2

Books | 1999

Shparlinski IE, 1999, Finite Fields: Theory and Computation, Springer Netherlands, http://dx.doi.org/10.1007/978-94-015-9239-0

Books | 1992

Shparlinski IE, 1992, Computational and Algorithmic Problems in Finite Fields, Springer Netherlands, http://dx.doi.org/10.1007/978-94-011-1806-4
Book Chapters | 2022

Konyagin SV; Shparlinski IE; Vyugin IV, 2022, 'Polynomial equations in subgroups and applications', in Analysis at Large: Dedicated to the Life and Work of Jean Bourgain, Springer International Publishing, pp. 273 - 297, http://dx.doi.org/10.1007/978-3-031-05331-3_12

Book Chapters | 2020

Cools R; Kuo FY; Sloan IH; Nuyens D, 2020, 'Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters', in Brenner SC; Shparlinski I; Shu C-W; Szyld D (ed.), 75 Years of Mathematics of Computation, American Mathematical Society, pp. 93 - 113, http://dx.doi.org/10.1090/conm/754/15150

Book Chapters | 2018

Kaszian J; Moree P; Shparlinski I, 2018, 'Periodic structure of the exponential pseudorandom number generator', in Larcher G; Pillichshammer F; Winterhof A; Xing C (ed.), Applied Algebra and Number Theory, Cambridge University Press, pp. 190 - 203, http://dx.doi.org/10.1017/CCO9781139696456.011

Book Chapters | 2017

Ostafe A; Shparlinski IE, 2017, 'Orbits of algebraic dynamical systems in subgroups and subfields', in Elsholtz C; Grabner P (ed.), Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer, pp. 347 - 368, http://dx.doi.org/10.1007/978-3-319-55357-3_18

Book Chapters | 2014

Kaszián J; Moree P; Shparlinski IE, 2014, 'Periodic structure of the exponential pseudorandom number generator', in Applied Algebra and Number Theory, Cambridge University Press, pp. 190 - 203, http://dx.doi.org/10.1017/cbo9781139696456.012

Book Chapters | 2013

Shparlinski IE, 2013, 'Additive Combinatorics over Finite Fields: New Results and Applications', in Finite Fields and Their Applications, DE GRUYTER, pp. 233 - 272, http://dx.doi.org/10.1515/9783110283600.233

Book Chapters | 2011

Cillerueloa J; Lucab F; Shparlinskic IE, 2011, 'Power values of palindromes', in Frontiers of Combinatorics and Number Theory, pp. 103 - 110

Book Chapters | 2011

Shparlinski I, 2011, 'Computational Diffie-Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 240 - 244, http://dx.doi.org/10.1007/978-1-4419-5906-5_882

Book Chapters | 2007

Murty R; Shparlinski I, 2007, 'GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS', in Garcia A; Stichtenoth H (ed.), TOPICS IN GEOMETRY, CODING THEORY AND CRYPTOGRAPHY, SPRINGER, pp. 167 - 198, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267348300005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Book Chapters | 2003

Shparlinski I, 2003, '1/M Generator', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 279 - 282, http://dx.doi.org/10.1007/978-3-0348-8037-4_26

Book Chapters | 2003

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p — 1', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 123 - 128, http://dx.doi.org/10.1007/978-3-0348-8037-4_10

Book Chapters | 2003

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 109 - 122, http://dx.doi.org/10.1007/978-3-0348-8037-4_9

Book Chapters | 2003

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 129 - 141, http://dx.doi.org/10.1007/978-3-0348-8037-4_11

Book Chapters | 2003

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Real Polynomials', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 143 - 156, http://dx.doi.org/10.1007/978-3-0348-8037-4_12

Book Chapters | 2003

Shparlinski I, 2003, 'Arithmetic Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 67 - 81, http://dx.doi.org/10.1007/978-3-0348-8037-4_6

Book Chapters | 2003

Shparlinski I, 2003, 'Basic Notation and Definitions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 17 - 26, http://dx.doi.org/10.1007/978-3-0348-8037-4_2

Book Chapters | 2003

Shparlinski I, 2003, 'Bit Security of NTRU', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 223 - 229, http://dx.doi.org/10.1007/978-3-0348-8037-4_21

Book Chapters | 2003

Shparlinski I, 2003, 'Bit Security of the Diffie—Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 189 - 194, http://dx.doi.org/10.1007/978-3-0348-8037-4_15

Book Chapters | 2003

Shparlinski I, 2003, 'Bit Security of the RSA Encryption and the Shamir Message Passing Scheme', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 211 - 215, http://dx.doi.org/10.1007/978-3-0348-8037-4_19

Book Chapters | 2003

Shparlinski I, 2003, 'Bit Security of the XTR and LUC Secret Keys', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 217 - 221, http://dx.doi.org/10.1007/978-3-0348-8037-4_20

Book Chapters | 2003

Shparlinski I, 2003, 'Boolean Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 179 - 188, http://dx.doi.org/10.1007/978-3-0348-8037-4_14

Book Chapters | 2003

Shparlinski I, 2003, 'Complexity Theory', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 103 - 106, http://dx.doi.org/10.1007/978-3-0348-8037-4_8

Book Chapters | 2003

Shparlinski I, 2003, 'Concluding Remarks and Open Questions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 341 - 365, http://dx.doi.org/10.1007/978-3-0348-8037-4_33

Book Chapters | 2003

Shparlinski I, 2003, 'Distribution and Discrepancy', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 61 - 65, http://dx.doi.org/10.1007/978-3-0348-8037-4_5

Book Chapters | 2003

Shparlinski I, 2003, 'Distribution of the ElGamal Signature', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 207 - 210, http://dx.doi.org/10.1007/978-3-0348-8037-4_18

Book Chapters | 2003

Shparlinski I, 2003, 'Distribution of the RSA and Exponential Pairs', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 231 - 237, http://dx.doi.org/10.1007/978-3-0348-8037-4_22

Book Chapters | 2003

Shparlinski I, 2003, 'Exponential Sums', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 37 - 60, http://dx.doi.org/10.1007/978-3-0348-8037-4_4

Book Chapters | 2003

Shparlinski I, 2003, 'Exponentiation and Inversion with Precomputation', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 239 - 245, http://dx.doi.org/10.1007/978-3-0348-8037-4_23

Book Chapters | 2003

Shparlinski I, 2003, 'Introduction', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 1 - 14, http://dx.doi.org/10.1007/978-3-0348-8037-4_1

Book Chapters | 2003

Shparlinski I, 2003, 'Inversive, Polynomial and Quadratic Exponential Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 283 - 294, http://dx.doi.org/10.1007/978-3-0348-8037-4_27

Book Chapters | 2003

Shparlinski I, 2003, 'Lattices and the Hidden Number Problem', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 83 - 102, http://dx.doi.org/10.1007/978-3-0348-8037-4_7

Book Chapters | 2003

Shparlinski I, 2003, 'Naor—Reingold Function', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 271 - 277, http://dx.doi.org/10.1007/978-3-0348-8037-4_25

Book Chapters | 2003

Shparlinski I, 2003, 'Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 159 - 177, http://dx.doi.org/10.1007/978-3-0348-8037-4_13

Book Chapters | 2003

Shparlinski I, 2003, 'Polynomial Approximation, Permanents and Noisy Exponentiation in Finite Fields', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 325 - 332, http://dx.doi.org/10.1007/978-3-0348-8037-4_31

Book Chapters | 2003

Shparlinski I, 2003, 'Polynomials and Recurrence Sequences', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 27 - 36, http://dx.doi.org/10.1007/978-3-0348-8037-4_3

Book Chapters | 2003

Shparlinski I, 2003, 'RSA and Blum—Blum—Shub Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 249 - 270, http://dx.doi.org/10.1007/978-3-0348-8037-4_24

Book Chapters | 2003

Shparlinski I, 2003, 'Security Against the Cycling Attack on the RSA and Timed-release Crypto', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 197 - 200, http://dx.doi.org/10.1007/978-3-0348-8037-4_16

Book Chapters | 2003

Shparlinski I, 2003, 'Special Polynomials and Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 333 - 339, http://dx.doi.org/10.1007/978-3-0348-8037-4_32

Book Chapters | 2003

Shparlinski I, 2003, 'Square-Freeness Testing and Other Number-Theoretic Problems', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 303 - 308, http://dx.doi.org/10.1007/978-3-0348-8037-4_29

Book Chapters | 2003

Shparlinski I, 2003, 'Subset Sum Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 295 - 299, http://dx.doi.org/10.1007/978-3-0348-8037-4_28

Book Chapters | 2003

Shparlinski I, 2003, 'The Insecurity of the Digital Signature Algorithm with Partially Known Nonces', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 201 - 206, http://dx.doi.org/10.1007/978-3-0348-8037-4_17

Book Chapters | 2003

Shparlinski I, 2003, 'Trade-off Between the Boolean and Arithmetic Depths of Modulo p Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 309 - 323, http://dx.doi.org/10.1007/978-3-0348-8037-4_30

Book Chapters | 2002

Shparlinski IE, 2002, 'EXPONENTIAL SUMS IN CODING THEORY, CRYPTOLOGY AND ALGORITHMS', in Coding Theory and Cryptology, CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, pp. 323 - 383, http://dx.doi.org/10.1142/9789812388841_0009

Book Chapters | 2001

von zur Gathen J; Shparlinski I, 2001, 'Gauß Periods in Finite Fields', in Finite Fields and Applications, Springer Berlin Heidelberg, pp. 162 - 177, http://dx.doi.org/10.1007/978-3-642-56755-1_14

Book Chapters | 1999

Friedlander JB; Lieman D; Shparlinski IE, 1999, 'On the Distribution of the RSA Generator', in Sequences and their Applications, Springer London, pp. 205 - 212, http://dx.doi.org/10.1007/978-1-4471-0551-0_14

Book Chapters | 1996

Mullen GL; Shparlinski I, 1996, 'Open problems and conjectures in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 243 - 268, http://dx.doi.org/10.1017/cbo9780511525988.021

Book Chapters | 1996

Shparlinski I, 1996, 'Approximate constructions in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 313 - 332, http://dx.doi.org/10.1017/cbo9780511525988.024

Book Chapters | 1995

Shparlinski IE, 1995, 'On Some Characteristics of Uniformity of Distribution and Their Applications', in Computational Algebra and Number Theory, Springer Netherlands, pp. 227 - 241, http://dx.doi.org/10.1007/978-94-017-1108-1_16

Book Chapters |

Shparlinski IE, 'Diffie–Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 154 - 158, http://dx.doi.org/10.1007/0-387-23483-7_112
Edited Books | 2020

Shparlinski I; Brenner SC; Shu C-W; Szyld DB, (eds.), 2020, 75 Years of Mathematics of Computation, American Mathematical Society, https://bookstore.ams.org/conm-754
Journal articles | 2023

Abdalaoui E; Shparlinski IE; Steiner RS, 2023, 'Chowla and Sarnak conjectures for Kloosterman sums', Mathematische Nachrichten, http://dx.doi.org/10.1002/mana.202200480

Journal articles | 2023

Bag N; Shparlinski IE, 2023, 'Bounds on bilinear sums of Kloosterman sums', Journal of Number Theory, 242, pp. 102 - 111, http://dx.doi.org/10.1016/j.jnt.2022.07.006

Journal articles | 2023

Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, 385, pp. 309 - 355, http://dx.doi.org/10.1007/s00208-021-02352-x

Journal articles | 2023

Chen C; Shparlinski IE, 2023, 'Hybrid Bounds on Two-Parametric Families of Weyl Sums Along Smooth Curves', Michigan Mathematical Journal, 73, pp. 123 - 139, http://dx.doi.org/10.1307/MMJ/20205904

Journal articles | 2023

Dąbrowski A; Pomykała J; Shparlinski IE, 2023, 'On oracle factoring of integers', Journal of Complexity, 76, pp. 101741 - 101741, http://dx.doi.org/10.1016/j.jco.2023.101741

Journal articles | 2023

Fouvry É; Shparlinski IE, 2023, 'On character sums with determinants', Science China Mathematics, http://dx.doi.org/10.1007/s11425-022-2122-0

Journal articles | 2023

Hauck M; Shparlinski IE, 2023, 'Smooth numbers with few non-zero binary digits', Canadian Mathematical Bulletin, pp. 1 - 16, http://dx.doi.org/10.4153/S0008439523000504

Journal articles | 2023

Kaminski M; Shparlinski IE; Waldschmidt M, 2023, 'On sets of linear forms of maximal complexity', Computational Complexity, 32, http://dx.doi.org/10.1007/s00037-022-00234-5

Journal articles | 2023

Kerr B; Mello J; Shparlinski IE, 2023, 'An effective local-global principle and additive combinatorics in finite fields', Journal d'Analyse Mathematique, pp. 1 - 27, http://dx.doi.org/10.1007/s11854-023-0291-2

Journal articles | 2023

Kerr B; Shparlinski IE; Wu X; Xi P, 2023, 'Bounds on bilinear forms with Kloosterman sums', Journal of the London Mathematical Society, 108, pp. 578 - 621, http://dx.doi.org/10.1112/jlms.12753

Journal articles | 2023

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2023, 'FUNCTIONAL GRAPHS OF FAMILIES OF QUADRATIC POLYNOMIALS', Mathematics of Computation, 92, pp. 2307 - 2331, http://dx.doi.org/10.1090/mcom/3838

Journal articles | 2023

Ostafe A; Shparlinski IE; Voloch JF, 2023, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', International Mathematics Research Notices, 2023, pp. 14196 - 14238, http://dx.doi.org/10.1093/imrn/rnac226

Journal articles | 2023

Ostafe ALINA; Shparlinski IE; Voloch JF, 2023, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, pp. 1 - 15, http://dx.doi.org/10.1017/S0305004123000415

Journal articles | 2023

Shparlinski IE; Thuswaldner JM, 2023, 'Weyl Sums over Integers with Digital Restrictions', Michigan Mathematical Journal, -1, http://dx.doi.org/10.1307/mmj/20216094

Journal articles | 2023

Shparlinski IE, 2023, 'Fixed points of the subset sum pseudorandom number generators', Designs, Codes, and Cryptography, 91, pp. 2473 - 2479, http://dx.doi.org/10.1007/s10623-023-01209-5

Journal articles | 2023

Shparlinski IE, 2023, 'On Quadratic Fields Generated by Polynomials', Bulletin of the Australian Mathematical Society, pp. 1 - 10, http://dx.doi.org/10.1017/S0004972723000606

Journal articles | 2023

Shparlinski IE, 2023, 'On the Glasner property for matrices with polynomial entries', Journal of Number Theory, 242, pp. 522 - 531, http://dx.doi.org/10.1016/j.jnt.2022.04.015

Journal articles | 2023

Shparlinski IE, 2023, 'On the number of Diophantine m-tuples in finite fields', Finite Fields and their Applications, 90, http://dx.doi.org/10.1016/j.ffa.2023.102241

Journal articles | 2022

Bagshaw C; Shparlinski IE, 2022, 'Energy bounds, bilinear forms and their applications in function fields', Finite Fields and their Applications, 82, pp. 102048 - 102048, http://dx.doi.org/10.1016/j.ffa.2022.102048

Journal articles | 2022

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 1 - 46, http://dx.doi.org/10.1016/j.jmaa.2022.126030

Journal articles | 2022

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, 510, pp. 126030 - 126030, http://dx.doi.org/10.1016/j.jmaa.2022.126030

Journal articles | 2022

Baker RC; Munsch M; Shparlinski IE, 2022, 'Additive energy and a large sieve inequality for sparse sequences', Mathematika, 68, pp. 362 - 399, http://dx.doi.org/10.1112/mtk.12140

Journal articles | 2022

Banks W; Shparlinski I, 2022, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, 54, pp. 301 - 317, http://dx.doi.org/10.1112/blms.12524

Journal articles | 2022

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2022, 'On sparsity of representations of polynomials as linear combinations of exponential functions', Journal of the London Mathematical Society, http://dx.doi.org/10.1112/jlms.12554

Journal articles | 2022

Ghioca D; Shparlinski IE, 2022, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, 233, pp. 112 - 125, http://dx.doi.org/10.1016/j.jnt.2021.06.006

Journal articles | 2022

Kerr B; Mérai L; Shparlinski IE, 2022, 'On digits of Mersenne numbers', Revista Matematica Iberoamericana, 38, pp. 1901 - 1925, http://dx.doi.org/10.4171/RMI/1316

Journal articles | 2022

Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics

Journal articles | 2022

Ostafe A; Shparlinski IE, 2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, 74, pp. 773 - 792, http://dx.doi.org/10.4153/S0008414X21000080

Journal articles | 2022

Shkredov ID; Shparlinski IE; Zaharescu A, 2022, 'Bilinear Forms with Modular Square Roots and Twisted Second Moments of Half Integral Weight Dirichlet Series', International Mathematics Research Notices, 2022, pp. 17431 - 17474, http://dx.doi.org/10.1093/imrn/rnab220

Journal articles | 2022

Shparlinski IE, 2022, 'Bilinear sums of Gauss sums', Acta Arithmetica, 202, pp. 379 - 388, http://dx.doi.org/10.4064/aa210523-3-2

Journal articles | 2022

Shparlinski IE, 2022, 'MULTIPLICATIVE PROPERTIES of HILBERT CUBES', SIAM Journal on Discrete Mathematics, 36, pp. 1064 - 1070, http://dx.doi.org/10.1137/22M1470396

Journal articles | 2021

Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, 219, pp. 228 - 236, http://dx.doi.org/10.1016/j.jnt.2020.09.020

Journal articles | 2021

Baker RC; Chen C; Shparlinski IE, 2021, 'Bounds on the Norms of Maximal Operators on Weyl Sums', , http://arxiv.org/abs/2107.13674v1

Journal articles | 2021

Baker RC; Munsch M; Shparlinski IE, 2021, 'Additive energy and a large sieve inequality for sparse sequences', , http://arxiv.org/abs/2103.12659v2

Journal articles | 2021

Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743

Journal articles | 2021

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, 104, pp. 381 - 390, http://dx.doi.org/10.1017/S0004972721000083

Journal articles | 2021

Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, 64, http://dx.doi.org/10.1016/j.jco.2020.101542

Journal articles | 2021

Kerr B; Mello J; Shparlinski IE, 2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478

Journal articles | 2021

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, 'Energy bounds for modular roots and their applications', , http://arxiv.org/abs/2103.09405v1

Journal articles | 2021

Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5

Journal articles | 2021

Mérai L; Shparlinski IE, 2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, 8, http://dx.doi.org/10.1007/s40687-021-00249-4

Journal articles | 2021

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, 27, pp. 903 - 917, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2021

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', New York Journal of Mathematics, 27, pp. 903 - 917

Journal articles | 2021

Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2

Journal articles | 2021

Sha M; Shparlinski IE, 2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363

Journal articles | 2021

Shparlinski IE; Stewart CL, 2021, 'Counting solvable s-unit equations', Proceedings of the American Mathematical Society, 149, pp. 5119 - 5129, http://dx.doi.org/10.1090/proc/15674

Journal articles | 2021

Shparlinski IE; Thuswaldner JM, 2021, 'Weyl sums over integers with digital restrictions', , http://arxiv.org/abs/2105.04835v1

Journal articles | 2021

Shparlinski IE; Voloch JF, 2021, 'Erratum: Value sets of sparse polynomials (Canadian Mathematical Bulletin (2020) 63 (187-196) DOI: 10.4153/xxxx)', Canadian Mathematical Bulletin, pp. 1 - 3, http://dx.doi.org/10.4153/S0008439521000928

Journal articles | 2021

Shparlinski IE; Wang Q, 2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, 35, pp. 976 - 987, http://dx.doi.org/10.1137/20M1357731

Journal articles | 2021

Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv der Mathematik, 117, pp. 261 - 266, http://dx.doi.org/10.1007/s00013-021-01623-y

Journal articles | 2021

Shparlinski IE, 2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386

Journal articles | 2020

Banks W; Shparlinski I, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7

Journal articles | 2020

Brandes J; Shparlinski IE, 2020, 'Two-dimensional Weyl sums failing square-root cancellation along lines', , http://arxiv.org/abs/2012.08877v1

Journal articles | 2020

Chen C; Kerr B; Maynard J; Shparlinski I, 2020, 'Metric theory of Weyl sums', , http://arxiv.org/abs/2011.09306v1

Journal articles | 2020

Chen C; Kerr B; Shparlinski I, 2020, 'Metric theory of lower bounds on Weyl sums', , http://arxiv.org/abs/2004.02539v3

Journal articles | 2020

Chen C; Shparlinski IE, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, 214, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Journal articles | 2020

Chen C; Shparlinski IE, 2020, 'Hybrid bounds on two-parametric family Weyl sums along smooth curves', , http://arxiv.org/abs/2003.02419v1

Journal articles | 2020

Chen C; Shparlinski IE, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, http://dx.doi.org/10.1016/j.aim.2020.107216

Journal articles | 2020

Di Benedetto D; Garaev MZ; Garcia VC; Gonzalez-Sanchez D; Shparlinski IE; Trujillo CA, 2020, 'New estimates for exponential sums over multiplicative subgroups and intervals in prime fields', Journal of Number Theory, 215, pp. 261 - 274, http://dx.doi.org/10.1016/j.jnt.2020.02.004

Journal articles | 2020

Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, http://dx.doi.org/10.1016/j.aim.2020.107369

Journal articles | 2020

Gómez-Pérez D; Mérai L; Shparlinski IE, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001

Journal articles | 2020

Kerr B; Mello J; Shparlinski I, 2020, 'An effective local-global principle for algebraic varieties and the sum product problem in finite fields', , http://arxiv.org/abs/2005.02923v3

Journal articles | 2020

Kerr B; Mérai L; Shparlinski IE, 2020, 'On digits of Mersenne numbers', , http://arxiv.org/abs/2001.03380v4

Journal articles | 2020

Kerr B; Shparlinski IE, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, 6, http://dx.doi.org/10.1007/s40993-020-0191-9

Journal articles | 2020

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, 71, pp. 637 - 648, http://dx.doi.org/10.1093/qmathj/haz055

Journal articles | 2020

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, 'Polynomial Equations in Subgroups and Applications', , http://arxiv.org/abs/2005.05315v1

Journal articles | 2020

Korolev M; Shparlinski I, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions', Pacific Journal of Mathematics, 304, pp. 505 - 522, http://dx.doi.org/10.2140/pjm.2020.304.505

Journal articles | 2020

Li R; Shparlinski IE, 2020, 'Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers', , http://arxiv.org/abs/2001.09721v1

Journal articles | 2020

Liu K; Shparlinski IE; Zhang T, 2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, 293, pp. 1505 - 1514, http://dx.doi.org/10.1002/mana.201900006

Journal articles | 2020

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, 34, pp. 2124 - 2136, http://dx.doi.org/10.1137/20M1325502

Journal articles | 2020

Munsch M; Shparlinski IE, 2020, 'Smooth squarefree and square-full integers in arithmetic progressions', Journal of the London Mathematical Society, 101, pp. 1941 - 1067, http://dx.doi.org/10.1112/jlms.12297

Journal articles | 2020

Mérai L; Shparlinski IE, 2020, 'Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$', Mathematics of Computation, 322, pp. 911 - 922, http://dx.doi.org/10.1090/mcom/3467

Journal articles | 2020

Mérai L; Shparlinski IE, 2020, 'Unlikely intersections over finite fields: Polynomial orbits in small subgroups', Discrete and Continuous Dynamical Systems- Series A, 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070

Journal articles | 2020

Pakovich F; Shparlinski IE, 2020, 'Level curves of rational functions nd unimodular points on rational curves', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Journal articles | 2020

Ricotta G; Royer E; Shparlinski I, 2020, 'Kloosterman paths of prime powers moduli, II', Bulletin de la Societe Mathematique de France, 148, pp. 173 - 188, http://dx.doi.org/10.24033/bsmf.2802

Journal articles | 2020

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, 'On the distribution of modular square roots of primes', , http://arxiv.org/abs/2009.03460v1

Journal articles | 2020

Shparlinski I; Banks W, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7

Journal articles | 2020

Shparlinski I; Banks W, 2020, 'Sums with the Mobius function twisted by characters with powerful moduli', Trans. Amer. Math. Soc., pp. 249 - 272, http://dx.doi.org/10.1090/tran/7914

Journal articles | 2020

Shparlinski I; Chen C, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Journal articles | 2020

Shparlinski I; Chen C, 2020, 'On large values of Weyl sums', Advances in Mathematics, 370, pp. 1 - 48, http://dx.doi.org/10.1016/j.aim.2020.107216

Journal articles | 2020

Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369

Journal articles | 2020

Shparlinski I; Gomez-Perez D; Merai L, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001

Journal articles | 2020

Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737

Journal articles | 2020

Shparlinski I; Kerr B, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, pp. 1 - 21, http://dx.doi.org/10.1007/s40993-020-0191-9

Journal articles | 2020

Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., 304, pp. 505 - 18, http://dx.doi.org/10.2140/pjm.2020.304.505

Journal articles | 2020

Shparlinski I; Pakovich F, 2020, 'Level curves of rational functions and unimodular points on rational curves.', Proceedings of the American Mathematical Society, 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Journal articles | 2020

Shparlinski I; Voloch F, 2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, 21, pp. 931 - 941, http://dx.doi.org/10.2422/2036-2145.201811_007

Journal articles | 2020

Shparlinski I; Voloch F, 2020, 'Value sets of sparse polynomials', Canad. Math. Bull., 63, pp. . 187 - 196, http://dx.doi.org/10.4153/S0008439519000316

Journal articles | 2020

Shparlinski I, 2020, 'Lower bounds for periods of Ducci sequences', Bulletin of the Australian Mathematical Society, 102, pp. 31 - 38, http://dx.doi.org/10.1017/S0004972719001187

Journal articles | 2020

Shparlinski I, 2020, 'Unlikely intersections over finite fields: polynomial orbits in small subgroups', DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS., Ser.A, 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070

Journal articles | 2020

Shparlinski IE; Stewart CL, 2020, 'Counting solvable $S$-unit equations', , http://arxiv.org/abs/2007.15170v1

Journal articles | 2020

Shparlinski IE; Technau M, 2020, 'Kloosterman sums with twice-differentiable functions', Functiones et Approximatio Commentarii Mathematici, 63, pp. 113 - 124, http://dx.doi.org/10.7169/facm/1845

Journal articles | 2020

Shparlinski IE; Voloch JF, 2020, 'Value Sets of Sparse Polynomials', Canadian Mathematical Bulletin, 63, pp. 187 - 196, http://dx.doi.org/10.4153/S0008439519000316

Journal articles | 2020

Shparlinski IE, 2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, 68, http://dx.doi.org/10.1016/j.ffa.2020.101747

Journal articles | 2020

Shparlinski IE, 2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, 148, pp. 2371 - 2377, http://dx.doi.org/10.1090/proc/14901

Journal articles | 2019

Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2019, 'Counting integers with a smooth totient', The Quarterly Journal of Mathematics, pp. 1371 - 1386, http://dx.doi.org/10.1093/qmathj/haz026

Journal articles | 2019

Banks WD; Shparlinski IE, 2019, 'Bounds on short character sums and L-functions with characters to a powerful modulus', Journal d'Analyse Mathematique, 139, pp. 239 - 263, http://dx.doi.org/10.1007/s11854-019-0060-4

Journal articles | 2019

Bordellès O; Dai L; Heyman R; Pan H; Shparlinski IE, 2019, 'On a sum involving the Euler function', Journal of Number Theory, 202, pp. 278 - 297, http://dx.doi.org/10.1016/j.jnt.2019.01.006

Journal articles | 2019

Bretèche RDL; Kurlberg P; Shparlinski IE, 2019, 'On the number of products which form perfect powers and discriminants of multiquadratic extensions', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz316

Journal articles | 2019

Breuer F; Shparlinski IE, 2019, 'Lower bounds for periods of Ducci sequences', Bull. Aust. Math. Soc., http://dx.doi.org/10.1017/S0004972719001187

Journal articles | 2019

Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2019, 'Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz091

Journal articles | 2019

Chen C; Shparlinski IE, 2019, 'New bounds of Weyl sums', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz293

Journal articles | 2019

Dietmann R; Ostafe A; Shparlinski IE, 2019, 'Discriminants of Fields Generated by Polynomials of Given Height', , http://arxiv.org/abs/1909.00135v2

Journal articles | 2019

El Abdalaoui EH; Shparlinski IE, 2019, 'Disjointness of the Möbius Transformation and Möbius Function', Research in the Mathematical Sciences, 6, http://dx.doi.org/10.1007/s40687-019-0180-6

Journal articles | 2019

Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2019, 'On the distribution of multiplicatively dependent vectors', , http://arxiv.org/abs/1903.09796v4

Journal articles | 2019

Liu K; Shparlinski IE; Zhang T, 2019, 'CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS', Mathematika, 65, pp. 475 - 487, http://dx.doi.org/10.1112/s0025579318000554

Journal articles | 2019

Macourt S; Shparlinski IE, 2019, 'Double sums of Kloosterman sums in finite fields', Finite Fields and their Applications, 60, http://dx.doi.org/10.1016/j.ffa.2019.101575

Journal articles | 2019

Mérai L; Shparlinski IE, 2019, 'Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields', Acta Arithmetica, 188, pp. 401 - 411, http://dx.doi.org/10.4064/aa180307-20-8

Journal articles | 2019

Ostafe A, 2019, 'Polynomial Values in Affine Subspaces of Finite Fields', Journal d'Analyse Mathematique, pp. 49 - 81, http://dx.doi.org/10.1007/s11854-019-0021-y

Journal articles | 2019

Petridis G; Shparlinski IE, 2019, 'Bounds on trilinear and quadrilinear exponential sums', Journal d'Analyse Mathématique, http://arxiv.org/abs/1604.08469v4

Journal articles | 2019

Roche-Newton O; Shparlinski IE; Winterhof A, 2019, 'Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions', Annals of Combinatorics, http://dx.doi.org/10.1007/s00026-019-00420-3

Journal articles | 2019

SHPARLINSKI IGORE, 2019, 'ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES', Bulletin of the Australian Mathematical Society, pp. 1 - 4, http://dx.doi.org/10.1017/s0004972718001302

Journal articles | 2019

Sha M; Shparlinski IE, 2019, 'Möbius Randomness Law for Frobenius Traces', , http://arxiv.org/abs/1909.00969v3

Journal articles | 2019

Shparlinski I; Zannier U, 2019, 'Arithmetic properties of quadratic exponential polynomials', New York Journal of Mathematics, 25, pp. 207 - 218, https://www.emis.de/journals/NYJM/nyjm/j/2019/25-12p.pdf

Journal articles | 2019

Shparlinski I, 2019, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, 15, pp. 469 - 477, http://dx.doi.org/10.1142/S1793042119500246

Journal articles | 2019

Shparlinski IE; Voloch JF, 2019, 'Binomial exponential sums', ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE, pp. 1 - 1, http://dx.doi.org/10.2422/2036-2145.201811_007

Journal articles | 2019

Shparlinski IE, 2019, 'Bilinear Forms with Kloosterman and Gauss Sums', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, http://dx.doi.org/10.1090/tran/7506

Journal articles | 2019

Shparlinski IE, 2019, 'Bounds on average values of double incomplete Kloosterman sums', Journal of Number Theory, 203, pp. 1 - 11, http://dx.doi.org/10.1016/j.jnt.2019.03.009

Journal articles | 2019

Shparlinski IE, 2019, 'ON SHORT PRODUCTS OF PRIMES IN ARITHMETIC PROGRESSIONS', Proceedings of the American Mathematical Society, 147, pp. 977 - 986, http://dx.doi.org/10.1090/proc/14289

Journal articles | 2018

Banks WD; Guo VZ; Shparlinski IE, 2018, 'Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$', Indagationes Mathematicae, 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002

Journal articles | 2018

Bordellès O; Luca F; Moree P; Shparlinski IE, 2018, 'DENOMINATORS of BERNOULLI POLYNOMIALS', Mathematika, 64, pp. 519 - 541, http://dx.doi.org/10.1112/S0025579318000153

Journal articles | 2018

Bordellès O; Luca F; Shparlinski IE, 2018, 'On the error term of a lattice counting problem', Journal of Number Theory, 182, pp. 19 - 36, http://dx.doi.org/10.1016/j.jnt.2017.07.019

Journal articles | 2018

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2018, 'Multiplicative congruences with variables from short intervals', Journal d'Analyse Mathematique, 124, pp. 117 - 147, http://dx.doi.org/10.1007/s11854-014-0029-2

Journal articles | 2018

Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Orbits of Polynomial Dynamical Systems Modulo Primes', Proceedings of the American Mathematical Society, 146, pp. 2015 - 2025, http://dx.doi.org/10.1090/proc/13904

Journal articles | 2018

Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, 459, pp. 53 - 81, http://dx.doi.org/10.1016/j.jmaa.2017.10.070

Journal articles | 2018

D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437

Journal articles | 2018

D’Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437

Journal articles | 2018

Gómez-Pérez D; Shparlinski IE, 2018, 'Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions', Experimental Mathematics, 27, pp. 184 - 192, http://dx.doi.org/10.1080/10586458.2016.1239146

Journal articles | 2018

Heyman R; Shparlinski IE, 2018, 'On shifted Eisenstein polynomials', Periodica Mathematica Hungarica, 69, pp. 170 - 181, http://dx.doi.org/10.1007/s10998-014-0061-0

Journal articles | 2018

Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski IE, 2018, 'Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields', Algorithmica, 80, pp. 560 - 575, http://dx.doi.org/10.1007/s00453-016-0273-1

Journal articles | 2018

Karpinski M; Mérai L; Shparlinski IE, 2018, 'Identity testing and interpolation from high powers of polynomials of large degree over finite fields', Journal of Complexity, 49, pp. 74 - 84, http://dx.doi.org/10.1016/j.jco.2018.07.006

Journal articles | 2018

LUCA F; RADZIWIŁŁ M; SHPARLINSKI IE, 2018, 'On the typical size and cancellations among the coefficients of some modular forms', Mathematical Proceedings of the Cambridge Philosophical Society, 166, pp. 173 - 189, http://dx.doi.org/10.1017/S0305004117000780

Journal articles | 2018

Liu K; Shparlinski IE; Zhang T, 2018, 'Bilinear forms with exponential sums with binomials', Journal of Number Theory, 188, pp. 172 - 185, http://dx.doi.org/10.1016/j.jnt.2017.12.011

Journal articles | 2018

Liu K; Shparlinski IE; Zhang T, 2018, 'Divisor problem in arithmetic progressions modulo a prime power', Advances in Mathematics, 325, pp. 459 - 481, http://dx.doi.org/10.1016/j.aim.2017.12.006

Journal articles | 2018

Macourt S; Shkredov ID; Shparlinski IE, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2

Journal articles | 2018

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On abelian multiplicatively dependent points on a curve in a torus', The Quarterly Journal of Mathematics, 69, pp. 391 - 401, http://dx.doi.org/10.1093/qmath/hax045

Journal articles | 2018

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem', MICHIGAN MATHEMATICAL JOURNAL, 5, https://arxiv.org/abs/1706.05874

Journal articles | 2018

Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2018, 'On multiplicatively dependent vectors of algebraic numbers', Transactions of the American Mathematical Society, 370, pp. 6221 - 6244, http://dx.doi.org/10.1090/tran/7115

Journal articles | 2018

Pomerance C; Shparlinski I, 2018, 'CONNECTED COMPONENTS OF THE GRAPH GENERATED BY POWER MAPS IN PRIME FINITE FIELDS', Integers : Electronic Journal of Combinatorial Number Theory, 18A, pp. 1 - 8, http://math.colgate.edu/~integers/vol18a.html

Journal articles | 2018

Sha M; Shparlinski IE, 2018, 'Effective results on linear dependence for elliptic curves', Pacific Journal of Mathematics, 295, pp. 123 - 144, http://dx.doi.org/10.2140/pjm.2018.295.123

Journal articles | 2018

Sha M; Shparlinski IE, 2018, 'The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height', Indagationes Mathematicae, 28, pp. 306 - 320, http://dx.doi.org/10.1016/j.indag.2016.07.004

Journal articles | 2018

Shkredov ID; Shparlinski IE, 2018, 'Double Character Sums with Intervals and Arbitrary Sets', Proceedings of the Steklov Institute of Mathematics, 303, pp. 239 - 258, http://dx.doi.org/10.1134/S0081543818080199

Journal articles | 2018

Shparlinski I; Voloch JF, 2018, 'Generators of Elliptic Curves over Finite Fields', Bulletin of the Institute of Mathematics Academia Sinica, 9, pp. 657 - 670, https://web.ma.utexas.edu/users/voloch/Preprints/EC-Generators.pdf

Journal articles | 2018

Shparlinski IE; Sutherland AV, 2018, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, 14, pp. 285 - 297, http://dx.doi.org/10.1007/s10208-013-9181-9

Journal articles | 2018

Shparlinski IE; Winterhof A, 2018, 'Codes correcting restricted errors', Designs, Codes, and Cryptography, http://dx.doi.org/10.1007/s10623-018-0585-z

Journal articles | 2018

Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, 191, pp. 194 - 212, http://dx.doi.org/10.1016/j.jnt.2018.04.017

Journal articles | 2018

Shparlinski IE; Zumalacárregui A, 2018, 'Sums of inverses in thin sets of finite fields', Proceedings of the American Mathematical Society, 146, pp. 1377 - 1388, http://dx.doi.org/10.1090/proc/13915

Journal articles | 2018

Shparlinski IE, 2018, 'Character sums with smooth numbers', Archiv der Mathematik, 110, pp. 467 - 476, http://dx.doi.org/10.1007/s00013-018-1168-y

Journal articles | 2018

Shparlinski IE, 2018, 'Constructing Dominating Sets in Circulant Graphs', Annals of Combinatorics, 22, pp. 201 - 211, http://dx.doi.org/10.1007/s00026-018-0377-1

Journal articles | 2018

Shparlinski IE, 2018, 'Linear equations with rational fractions of bounded height and stochastic matrices', Quarterly Journal of Mathematics, 69, pp. 487 - 499, http://dx.doi.org/10.1093/qmath/hax049

Journal articles | 2018

Shparlinski IE, 2018, 'Multiplicative orders in orbits of polynomials over finite fields', Glasgow Mathematical Journal, 60, pp. 487 - 493, http://dx.doi.org/10.1017/S0017089517000222

Journal articles | 2018

Shparlinski IE, 2018, 'On Constructing Primitive Roots in Finite Fields With Advice', IEEE Transactions on Information Theory, 64, pp. 7132 - 7136, http://dx.doi.org/10.1109/TIT.2018.2810938

Journal articles | 2018

Shparlinski IE, 2018, 'On the Győry-Sárközy-Stewart conjecture in function fields', Czechoslovak Mathematical Journal, 68, pp. 1067 - 1077, http://dx.doi.org/10.21136/CMJ.2018.0085-17

Journal articles | 2018

Shparlinski IE, 2018, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, pp. 1 - 9, http://dx.doi.org/10.1142/S1793042119500246

Journal articles | 2018

Shparlinski IE, 2018, 'Trilinear forms with double Kloosterman sums', International Journal of Number Theory, 14, pp. 2195 - 2203, http://dx.doi.org/10.1142/S1793042118501312

Journal articles | 2018

Simon M; Shkredov I; Shparlinski I, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2

Journal articles | 2017

Banks WD; Shparlinski IE, 2017, 'On coincidences among quadratic fields generated by the shanks sequence', Quarterly Journal of Mathematics, 68, pp. 465 - 484, http://dx.doi.org/10.1093/qmath/haw054

Journal articles | 2017

Bell J; Shparlinski IE, 2017, 'Power series approximations to Fekete polynomials', Journal of Approximation Theory, 222, pp. 132 - 142, http://dx.doi.org/10.1016/j.jat.2017.07.002

Journal articles | 2017

Dietmann R; Elsholtz C; Shparlinski IE, 2017, 'Prescribing the binary digits of squarefree numbers and quadratic residues', Transactions of the American Mathematical Society, 369, pp. 8369 - 8388, http://dx.doi.org/10.1090/tran/6903

Journal articles | 2017

Dubickas A; Sha M; Shparlinski IE, 2017, 'On distances in lattices from algebraic number fields', Moscow Mathematical Journal, 17, pp. 239 - 268, http://dx.doi.org/10.17323/1609-4514-2017-17-2-239-268

Journal articles | 2017

Liu K; Shparlinski IE; Zhang T, 2017, 'Squares in Piatetski-Shapiro sequences', Acta Arithmetica, 181, pp. 239 - 252, http://dx.doi.org/10.4064/aa8644-8-2017

Journal articles | 2017

Luca F; Sha M; Shparlinski IE, 2017, 'On two functions arising in the study of the euler and carmichael quotients', Colloquium Mathematicum, 149, pp. 179 - 192, http://dx.doi.org/10.4064/cm6910-3-2017

Journal articles | 2017

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2017, 'On Functional Graphs of Quadratic Polynomials', Experimental Mathematics, pp. 1 - 9, http://dx.doi.org/10.1080/10586458.2017.1391725

Journal articles | 2017

Pomerance C; Shparlinski IE, 2017, 'Connected components of the graph generated by power maps in prime finite fields', Connected components of the graph generated by power maps in prime finite fields, http://arxiv.org/abs/1703.09292v2

Journal articles | 2017

Shkredov ID; Shparlinski IE, 2017, 'ON SOME MULTIPLE CHARACTER SUMS', Mathematika, 63, pp. 553 - 560, http://dx.doi.org/10.1112/S0025579317000055

Journal articles | 2017

Shparlinski IE; Sutherland AV, 2017, 'Finding elliptic curves with a subgroup of prescribed size', International Journal of Number Theory, 13, pp. 133 - 152, http://dx.doi.org/10.1142/S1793042117500099

Journal articles | 2017

Shparlinski IE; Weingartner AJ, 2017, 'An explicit polynomial analogue of Romanoff's theorem', Finite Fields and their Applications, 44, pp. 22 - 33, http://dx.doi.org/10.1016/j.ffa.2016.11.002

Journal articles | 2017

Shparlinski IE; Yau KH, 2017, 'Double exponential sums with exponential functions', International Journal of Number Theory, 13, pp. 2531 - 2543, http://dx.doi.org/10.1142/S179304211750141X

Journal articles | 2017

Shparlinski IE, 2017, 'On the convex hull of the points on multivariate modular hyperbolas', Journal of Number Theory, 171, pp. 71 - 78, http://dx.doi.org/10.1016/j.jnt.2016.07.011

Journal articles | 2016

Banks WD; Guo VZ; Shparlinski IE, 2016, 'Almost primes of the form ⌊p^c⌋', Indagationes Mathematicae, 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002

Journal articles | 2016

Banks WD; Shparlinski IE, 2016, 'Fractional parts of Dedekind sums', International Journal of Number Theory, 12, pp. 1137 - 1147, http://dx.doi.org/10.1142/S179304211650069X

Journal articles | 2016

Banks WD; Shparlinski IE, 2016, 'On Gauss sums and the evaluation of Stechkin's constant', Mathematics of Computation, 85, pp. 2569 - 2581, http://dx.doi.org/10.1090/mcom3056

Journal articles | 2016

Banks WD; Shparlinski IE, 2016, 'On the number of distinct quadratic fields generated by the Shanks sequence', On the number of distinct quadratic fields generated by the Shanks sequence, http://arxiv.org/abs/1602.06473v1

Journal articles | 2016

Camburu OM; Ciolan EA; Luca F; Moree P; Shparlinski IE, 2016, 'Cyclotomic coefficients: Gaps and jumps', Journal of Number Theory, 163, pp. 211 - 237, http://dx.doi.org/10.1016/j.jnt.2015.11.020

Journal articles | 2016

Chang MC; Shparlinski IE, 2016, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, 282, pp. 935 - 954, http://dx.doi.org/10.1007/s00209-015-1571-z

Journal articles | 2016

Fité F; Shparlinski IE, 2016, 'On the singularity of the demjanenko matrix of quotients of fermat curves', Proceedings of the American Mathematical Society, 144, pp. 55 - 63, http://dx.doi.org/10.1090/proc12717

Journal articles | 2016

Harman G; Shparlinski IE, 2016, 'Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients', International Mathematics Research Notices, 2016, pp. 1424 - 1446, http://dx.doi.org/10.1093/imrn/rnv182

Journal articles | 2016

Heyman R; Shparlinski IE, 2016, 'Counting irreducible binomials over finite fields', Finite Fields and their Applications, 38, pp. 1 - 12, http://dx.doi.org/10.1016/j.ffa.2015.12.001

Journal articles | 2016

Koh D; Shen CY; Shparlinski I, 2016, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, 26, pp. 1415 - 1441, http://dx.doi.org/10.1007/s12220-015-9595-5

Journal articles | 2016

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2016, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, 116, pp. 87 - 122, http://dx.doi.org/10.1016/j.jctb.2015.07.003

Journal articles | 2016

Nguyen PQ; Shparlinski IE, 2016, 'Counting Co-cyclic lattices', SIAM Journal on Discrete Mathematics, 30, pp. 1358 - 1370, http://dx.doi.org/10.1137/15M103950X

Journal articles | 2016

Rivat J; Shparlinski IE, 2016, 'Multiples of squares in short intervals', Functiones et Approximatio, Commentarii Mathematici, 54, pp. 57 - 63, http://dx.doi.org/10.7169/facm/2016.54.1.5

Journal articles | 2016

Shparlinski IE; Yau KH, 2016, 'Bounds of double multiplicative character sums and gaps between residues of exponential functions', Journal of Number Theory, 167, pp. 304 - 316, http://dx.doi.org/10.1016/j.jnt.2016.03.022

Journal articles | 2016

Shparlinski IE; Zhang T, 2016, 'Cancellations amongst Kloosterman sums', Acta Arithmetica, 176, pp. 201 - 210, http://dx.doi.org/10.4064/aa8365-6-2016

Journal articles | 2016

Shparlinski IE, 2016, 'Groups generated by iterations of polynomials over finite fields', Proceedings of the Edinburgh Mathematical Society, 59, pp. 235 - 245, http://dx.doi.org/10.1017/S0013091515000097

Journal articles | 2016

Shparlinski IE, 2016, 'Linear congruences with ratios', Proceedings of the American Mathematical Society, 144, pp. 2837 - 2846, http://dx.doi.org/10.1090/proc/12949

Journal articles | 2016

Shparlinski IE, 2016, 'On bilinear exponential and character sums with reciprocals of polynomials', Mathematika, 62, pp. 842 - 859, http://dx.doi.org/10.1112/S0025579316000036

Journal articles | 2016

Shparlinski IE, 2016, 'On small gaps between the elements of multiplicative subgroups of finite fields', Designs, Codes, and Cryptography, 80, pp. 63 - 71, http://dx.doi.org/10.1007/s10623-015-0063-9

Journal articles | 2016

Shparlinski IE, 2016, 'On the additive energy of the distance set in finite fields', Finite Fields and their Applications, 42, pp. 187 - 199, http://dx.doi.org/10.1016/j.ffa.2016.08.001

Journal articles | 2016

Shparlinski IE, 2016, 'Polynomial values in small subgroups of finite fields', Revista Matematica Iberoamericana, 32, pp. 1127 - 1136, http://dx.doi.org/10.4171/RMI/909

Journal articles | 2016

Shparlinski IE, 2016, 'Ratios of Small Integers in Multiplicative Subgroups of Residue Rings', Experimental Mathematics, 25, pp. 273 - 280, http://dx.doi.org/10.1080/10586458.2015.1091754

Journal articles | 2016

Shparlinski IE, 2016, 'SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS', Bulletin of the Australian Mathematical Society, 93, pp. 364 - 371, http://dx.doi.org/10.1017/S0004972715001240

Journal articles | 2015

Blackburn SR; Konyagin SV; Shparlinski IE, 2015, 'Counting additive decompositions of quadratic residues in finite fields', Functiones et Approximatio, Commentarii Mathematici, 52, pp. 223 - 227, http://dx.doi.org/10.7169/facm/2015.52.2.3

Journal articles | 2015

Bourgain J; Konyagin SV; Shparlinski IE, 2015, 'Character sums and deterministic polynomial root finding in finite fields', Mathematics of Computation, 84, pp. 2969 - 2977, http://dx.doi.org/10.1090/mcom/2946

Journal articles | 2015

Bretèche RDL; Sha M; Shparlinski IE; Voloch JF, 2015, 'The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves', Mathematische Zeitschrift, 290, pp. 831 - 855, http://dx.doi.org/10.1007/s00209-018-2042-0

Journal articles | 2015

Chang MC; Shparlinski IE, 2015, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, http://dx.doi.org/10.1007/s00209-015-1571-z

Journal articles | 2015

Dubickas A; Sha M; Shparlinski I, 2015, 'Explicit form of Cassels' p-adic Embedding Theorem for Number Fields', Canadian Journal of Mathematics, 67, pp. 1046 - 1064, http://dx.doi.org/10.4153/CJM-2015-021-2

Journal articles | 2015

Gómez-Pérez D; Shparlinski IE, 2015, 'Subgroups generated by rational functions in finite fields', Monatshefte fur Mathematik, 176, pp. 241 - 253, http://dx.doi.org/10.1007/s00605-014-0697-0

Journal articles | 2015

Heyman R; Shparlinski IE, 2015, 'On the greatest common divisor of shifted sets', Journal of Number Theory, 154, pp. 63 - 73, http://dx.doi.org/10.1016/j.jnt.2015.02.012

Journal articles | 2015

Koh D; Shen CY; Shparlinski I, 2015, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, http://dx.doi.org/10.1007/s12220-015-9595-5

Journal articles | 2015

Konyagin SV; Shparlinski IE, 2015, 'Quadratic non-residues in short intervals', Proceedings of the American Mathematical Society, 143, pp. 4261 - 4269, http://dx.doi.org/10.1090/S0002-9939-2015-12584-1

Journal articles | 2015

Kurlberg P; Luca F; Shparlinski IE, 2015, 'On the fixed points of the map x→x^x modulo a prime', Mathematical Research Letters, 22, pp. 141 - 168, http://dx.doi.org/10.4310/MRL.2015.v22.n1.a8

Journal articles | 2015

Munsch M; Shparlinski IE, 2015, 'Congruences with intervals and subgroups modulo a prime', Michigan Mathematical Journal, 64, pp. 655 - 672, http://dx.doi.org/10.1307/mmj/1441116662

Journal articles | 2015

Roche-Newton O; Shparlinski IE, 2015, 'Polynomial values in subfields and affine subspaces of finite fields', Quarterly Journal of Mathematics, 66, pp. 693 - 706, http://dx.doi.org/10.1093/qmath/hau032

Journal articles | 2015

Sha M; Shparlinski IE, 2015, 'Lang-trotter and sato-tate distributions in single and double parametric families of elliptic curves', Acta Arithmetica, 170, pp. 299 - 325, http://dx.doi.org/10.4064/aa170-4-1

Journal articles | 2015

Shparlinski I, 2015, 'Points on Varieties over Finite Fields in Small Boxes', Contemporary Mathematics, 655, pp. 209 - 233, http://dx.doi.org/10.1090/conm/655/13235

Journal articles | 2015

Shparlinski IE; Sutherland AV, 2015, 'On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average', LMS Journal of Computation and Mathematics, 18, pp. 308 - 322, http://dx.doi.org/10.1112/S1461157015000017

Journal articles | 2015

Shparlinski IE, 2015, 'Cayley graphs generated by small degree polynomials over finite fields', SIAM Journal on Discrete Mathematics, 29, pp. 376 - 381, http://dx.doi.org/10.1137/14095813X

Journal articles | 2015

Shparlinski IE, 2015, 'Close values of shifted modular inversions and the decisional modular inversion hidden number problem', Advances in Mathematics of Communications, 9, pp. 169 - 176, http://dx.doi.org/10.3934/amc.2015.9.169

Journal articles | 2015

Shparlinski IE, 2015, 'Distribution of polynomial discriminants modulo a prime', Archiv der Mathematik, 105, pp. 251 - 259, http://dx.doi.org/10.1007/s00013-015-0806-x

Journal articles | 2015

Shparlinski IE, 2015, 'On the product of small Elkies primes', Proceedings of the American Mathematical Society, 143, pp. 1441 - 1448, http://dx.doi.org/10.1090/S0002-9939-2014-12345-8

Journal articles | 2015

Shparlinski IE, 2015, 'Small discriminants of complex multiplication fields of elliptic curves over finite fields', Czechoslovak Mathematical Journal, 65, pp. 381 - 388, http://dx.doi.org/10.1007/s10587-015-0183-4

Journal articles | 2015

Von Zur Gathen J; Shparlinski IE, 2015, 'Circulant graphs and GCD and LCM of subsets', Information Processing Letters, 115, pp. 134 - 138, http://dx.doi.org/10.1016/j.ipl.2014.07.014

Journal articles | 2014

Ahmadi O; Shparlinski IE, 2014, 'Exponential sums over points of elliptic curves', Journal of Number Theory, 140, pp. 299 - 313, http://dx.doi.org/10.1016/j.jnt.2014.01.016

Journal articles | 2014

Blake IF; Luca F; Shparlinski IE, 2014, 'VSH and multiplicative modular relations between small primes with polynomial exponents', Applicable Algebra in Engineering, Communications and Computing, 25, pp. 181 - 188, http://dx.doi.org/10.1007/s00200-014-0219-2

Journal articles | 2014

Chang MC; Cilleruelo J; Garaev MZ; Hernández J; Shparlinski IE; Zumalacárregui A, 2014, 'Points on curves in small boxes and applications', Michigan Mathematical Journal, 63, pp. 503 - 534, http://dx.doi.org/10.1307/mmj/1409932631

Journal articles | 2014

Chang MC; Kerr B; Shparlinski IE; Zannier U, 2014, 'Elements of large order on varieties over prime finite fields', Journal de Theorie des Nombres de Bordeaux, 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880

Journal articles | 2014

Chang MC; Shparlinski IE, 2014, 'Double character sums over subgroups and intervals', Bulletin of the Australian Mathematical Society, 90, pp. 376 - 390, http://dx.doi.org/10.1017/S0004972714000227

Journal articles | 2014

Chen Z; Shparlinski IE; Winterhof A, 2014, 'Covering sets for limited-magnitude errors', IEEE Transactions on Information Theory, 60, pp. 5315 - 5321, http://dx.doi.org/10.1109/TIT.2014.2338078

Journal articles | 2014

Friedlander JB; Shparlinski IE, 2014, 'Enumeration of certain varieties over a finite field', Proceedings of the American Mathematical Society, 142, pp. 2615 - 2623, http://dx.doi.org/10.1090/S0002-9939-2014-11999-X

Journal articles | 2014

Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, 'Interpolation and approximation of polynomials in finite fields over a short interval from noisy values', Experimental Mathematics, 23, pp. 241 - 260, http://dx.doi.org/10.1080/10586458.2014.890918

Journal articles | 2014

Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9

Journal articles | 2014

Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809

Journal articles | 2014

Ling S; Shparlinski I; Wang H, 2014, 'On the multidimensional distribution of the Naor-Reingold pseudo-random function', Mathematics of Computation, 83, pp. 2429 - 2434, http://dx.doi.org/10.1090/S0025-5718-2014-02794-4

Journal articles | 2014

Luca F; Shparlinski IE, 2014, 'On the counting function of elliptic carmichael numbers', Canadian Mathematical Bulletin, 57, pp. 105 - 112, http://dx.doi.org/10.4153/CMB-2012-037-4

Journal articles | 2014

Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, 70, pp. 301 - 325, http://dx.doi.org/10.1007/s00453-013-9810-3

Journal articles | 2014

Munsch M; Shparlinski IE, 2014, 'Upper and Lower Bounds for Higher Moments of Theta Functions', Quarterly Journal of Mathematics, 67, pp. 53 - 73, http://dx.doi.org/10.1093/qmath/hav039

Journal articles | 2014

Shparlinski IE; Sutantyo D, 2014, 'Distribution of elliptic twin primes in isogeny and isomorphism classes', Journal of Number Theory, 137, pp. 1 - 15, http://dx.doi.org/10.1016/j.jnt.2013.10.018

Journal articles | 2014

Shparlinski IE; Sutherland AV, 2014, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, pp. 1 - 13, http://dx.doi.org/10.1007/s10208-013-9181-9

Journal articles | 2014

Shparlinski IE, 2014, 'Distribution of exponential functions modulo a prime power', Journal of Number Theory, 143, pp. 224 - 231, http://dx.doi.org/10.1016/j.jnt.2014.04.010

Journal articles | 2014

Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, 547, pp. 117 - 121, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Journal articles | 2014

Shparlinski IE, 2014, 'Multiple exponential and character sums with monomials', Mathematika, 60, pp. 363 - 373, http://dx.doi.org/10.1112/S0025579314000084

Journal articles | 2014

Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, 89, pp. 300 - 307, http://dx.doi.org/10.1017/S0004972713000671

Journal articles | 2014

Shparlinski IE, 2014, 'On the distribution of points on the generalized markoff-hurwitz and dwork hypersurfaces', International Journal of Number Theory, 10, pp. 151 - 160, http://dx.doi.org/10.1142/S1793042113500863

Journal articles | 2014

Shparlinski IE, 2014, 'Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields', Journal of Symbolic Computation, 64, pp. 35 - 41, http://dx.doi.org/10.1016/j.jsc.2013.12.005

Journal articles | 2014

Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv der Mathematik, 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0

Journal articles | 2013

Baker RC; Banks WD; Brüdern J; Shparlinski IE; Weingartner AJ, 2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3

Journal articles | 2013

Borwein JM; Shparlinski I; Zudilin W, 2013, 'Number Theory and Related Fields: In Memory of Alf van der Poorten', Springer Proceedings in Mathematics and Statistics, 43, http://dx.doi.org/10.1007/978-1-4614-6642-0

Journal articles | 2013

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2013, 'On congruences with products of variables from short intervals and applications', Proceedings of the Steklov Institute of Mathematics, 280, pp. 61 - 90, http://dx.doi.org/10.1134/S0081543813010057

Journal articles | 2013

Cilleruelo J; Kumchev A; Luca F; Rué J; Shparlinski IE, 2013, 'On the fractional parts of aⁿ/n', Bulletin of the London Mathematical Society, 45, pp. 249 - 256, http://dx.doi.org/10.1112/blms/bds084

Journal articles | 2013

Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte fur Mathematik, 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x

Journal articles | 2013

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022

Journal articles | 2013

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, 24, pp. 930 - 938, http://dx.doi.org/10.1016/j.indag.2013.02.005

Journal articles | 2013

Farashahi RR; Fouque PA; Shparlinski IE; Tibouchi M; Voloch JF, 2013, 'Indifferentiable deterministic hashing to elliptic and hyperelliptic curves', Mathematics of Computation, 82, pp. 491 - 512, http://dx.doi.org/10.1090/S0025-5718-2012-02606-8

Journal articles | 2013

Gutierrez J; Ibeas A; Gómez-Pérez D; Shparlinski IE, 2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs, Codes, and Cryptography, 67, pp. 395 - 402, http://dx.doi.org/10.1007/s10623-012-9615-4

Journal articles | 2013

Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201

Journal articles | 2013

Heyman R; Shparlinski IE, 2013, 'On the number of Eisenstein polynomials of bounded height', Applicable Algebra in Engineering, Communications and Computing, 24, pp. 149 - 156, http://dx.doi.org/10.1007/s00200-013-0187-y

Journal articles | 2013

Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012

Journal articles | 2013

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2013, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, http://dx.doi.org/10.1016/j.jctb.2015.07.003

Journal articles | 2013

Shparlinski I, 2013, 'Erratum: Sum-product estimates and multiplicative orders ofΓ and Γ + Γ^-1 in finite fields (Bulletin of the Australian Mathematical Society)', Bulletin of the Australian Mathematical Society, 87, pp. 527 - 528, http://dx.doi.org/10.1017/S0004972712001062

Journal articles | 2013

Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027

Journal articles | 2013

Shparlinski IE; Winterhof A, 2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, 19, pp. 93 - 104, http://dx.doi.org/10.1016/j.ffa.2012.10.004

Journal articles | 2013

Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470

Journal articles | 2013

Shparlinski IE, 2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, 113, pp. 414 - 417, http://dx.doi.org/10.1016/j.ipl.2013.03.016

Journal articles | 2013

Shparlinski IE, 2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, 66, pp. 65 - 90, http://dx.doi.org/10.1007/978-1-4614-5389-5_4

Journal articles | 2013

Shparlinski IE, 2013, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Journal articles | 2013

Shparlinski IE, 2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, 67, pp. 55 - 61, http://dx.doi.org/10.1007/s10998-013-2736-3

Journal articles | 2013

Shparlinski IE, 2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, 43, pp. 361 - 371, http://dx.doi.org/10.1216/RMJ-2013-43-1-361

Journal articles | 2013

Shparlinski IE, 2013, 'On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves', Michigan Mathematical Journal, 62, pp. 491 - 505, http://dx.doi.org/10.1307/mmj/1378757885

Journal articles | 2013

Shparlinski IE, 2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, 25, pp. 647 - 664, http://dx.doi.org/10.1515/FORM.2011.141

Journal articles | 2013

Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8

Journal articles | 2013

Shparlinski IE, 2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, 36, pp. 99 - 108, http://dx.doi.org/10.2996/kmj/1364562722

Journal articles | 2013

Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011

Journal articles | 2012

Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X

Journal articles | 2012

Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, 12, http://dx.doi.org/10.1515/integers-2012-0012

Journal articles | 2012

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2012, 'Exponential and character sums with mersenne numbers', Journal of the Australian Mathematical Society, 92, pp. 1 - 13, http://dx.doi.org/10.1017/S1446788712000109

Journal articles | 2012

Banks WD; Pappalardi F; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, 21, pp. 11 - 25, http://dx.doi.org/10.1080/10586458.2011.606075

Journal articles | 2012

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, 'On the hidden shifted power problem', SIAM Journal on Computing, 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414

Journal articles | 2012

Bourgain J; Konyagin SV; Shparlinski IE, 2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, 2012, pp. 1968 - 2009, http://dx.doi.org/10.1093/imrn/rnr097

Journal articles | 2012

Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7

Journal articles | 2012

Cilleruelo J; Shparlinski IE; Zumalacárregui A, 2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, 19, pp. 335 - 343, http://dx.doi.org/10.4310/MRL.2012.v19.n2.a6

Journal articles | 2012

Cojocaru AC; Luca F; Shparlinski IE, 2012, 'Erratum: Pseudoprime reductions of elliptic curves (Mathematical Proceedings of the Cambridge Philosophical Society (2009) 146 (513-522))', Mathematical Proceedings of the Cambridge Philosophical Society, 152, pp. 571, http://dx.doi.org/10.1017/S0305004111000399

Journal articles | 2012

Farashahi RR; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, 21, pp. 1 - 10, http://dx.doi.org/10.1080/10586458.2012.632754

Journal articles | 2012

Farashahi RR; Shparlinski IE, 2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, 58, pp. 1242 - 1247, http://dx.doi.org/10.1109/TIT.2011.2170054

Journal articles | 2012

González JJA; Luca F; Pomerance C; Shparlinski IE, 2012, 'On numbers n dividing the nth term of a linear recurrence', Proceedings of the Edinburgh Mathematical Society, 55, pp. 271 - 289, http://dx.doi.org/10.1017/S0013091510001355

Journal articles | 2012

Konyagin SV; Shparlinski IE, 2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, 58, pp. 11 - 20, http://dx.doi.org/10.1112/S0025579311002117

Journal articles | 2012

Ling S; Shparlinski IE; Steinfeld R; Wang H, 2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, 47, pp. 358 - 367, http://dx.doi.org/10.1016/j.jsc.2011.09.002

Journal articles | 2012

Mans B; Shparlinski IE, 2012, 'Random walks and bisections in random circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7256 LNCS, pp. 542 - 555, http://dx.doi.org/10.1007/978-3-642-29344-3_46

Journal articles | 2012

Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426

Journal articles | 2012

Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719

Journal articles | 2012

Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2

Journal articles | 2012

Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010

Journal articles | 2012

Shparlinski I, 2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ ^-1 in finite fields', Bulletin of the Australian Mathematical Society, 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887

Journal articles | 2012

Shparlinski IE; Stange KE, 2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x

Journal articles | 2012

Shparlinski IE, 2012, 'Modular hyperbolas', Japanese Journal of Mathematics, 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8

Journal articles | 2012

Shparlinski IE, 2012, 'On the convex hull of solutions to polynomial congruences', Journal of Number Theory, 132, pp. 254 - 257, http://dx.doi.org/10.1016/j.jnt.2011.06.016

Journal articles | 2012

Shparlinski IE, 2012, 'On the distribution of solutions to polynomial congruences', Archiv der Mathematik, 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5

Journal articles | 2012

Shparlinski IE, 2012, 'On the restricted divisor function in arithmetic progressions', Revista Matematica Iberoamericana, 28, pp. 231 - 238, http://dx.doi.org/10.4171/rmi/675

Journal articles | 2012

Shparlinski IE, 2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, 140, pp. 1199 - 1206, http://dx.doi.org/10.1090/S0002-9939-2011-11203-6

Journal articles | 2012

Urroz JJ; Luca F; Shparlinski IE, 2012, 'On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves', Mathematics of Computation, 81, pp. 1093 - 1110, http://dx.doi.org/10.1090/S0025-5718-2011-02543-3

Journal articles | 2011

Balog A; Broughan KA; Shparlinski IE, 2011, 'On the number of solutions of exponential congruences', Acta Arithmetica, 148, pp. 93 - 103, http://dx.doi.org/10.4064/aa148-1-7

Journal articles | 2011

Bibak K; Shparlinski IE, 2011, 'On Fully Split Lacunary Polynomials in Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, 59, pp. 197 - 202, http://dx.doi.org/10.4064/ba59-3-1

Journal articles | 2011

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, http://arxiv.org/abs/1102.1053v1

Journal articles | 2011

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, abs/1102.1053

Journal articles | 2011

Fouvry E; Luca F; Pappalardi F; Shparlinski IE, 2011, 'Counting dihedral and quaternionic extensions', Transactions of the American Mathematical Society, 363, pp. 3233 - 3253, http://dx.doi.org/10.1090/S0002-9947-2011-05233-5

Journal articles | 2011

Fouvry E; Shparlinski IE, 2011, 'On a ternary quadratic form over primes', Acta Arithmetica, 150, pp. 285 - 314, http://dx.doi.org/10.4064/aa150-3-5

Journal articles | 2011

Fouvry E; Shparlinski IE, 2011, 'Smooth shifted monomial products', Publicationes Mathematicae Debrecen, 79, pp. 423 - 432, http://dx.doi.org/10.5486/PMD.2011.5089

Journal articles | 2011

Konyagin SV; Shparlinski IE, 2011, 'On convex hull of points on modular hyperbolas', Moscow Journal of Combinatorics and Number Theory, 1, pp. 43 - 51

Journal articles | 2011

Křížek M; Luca F; Shparlinski IE; Somer L, 2011, 'On the complexity of testing elite primes', Journal of Integer Sequences, 14, pp. 1 - 5

Journal articles | 2011

Luca F; Shparlinski IE, 2011, 'On the g-Ary expansions of middle binomial coefficients and catalan numbers', Rocky Mountain Journal of Mathematics, 41, pp. 1291 - 1301, http://dx.doi.org/10.1216/RMJ-2011-41-4-1291

Journal articles | 2011

Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, 7, pp. 1557 - 1571, http://dx.doi.org/10.1142/S1793042111004484

Journal articles | 2011

Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, 139, pp. 3815 - 3820, http://dx.doi.org/10.1090/S0002-9939-2011-10843-8

Journal articles | 2011

Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, 25, pp. 50 - 71, http://dx.doi.org/10.1137/100798466

Journal articles | 2011

Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, 148, pp. 77 - 92, http://dx.doi.org/10.4064/aa148-1-6

Journal articles | 2011

Shparlinski IE, 2011, 'Bounds of multiplicative character sums with Fermat quotients of primes', Bulletin of the Australian Mathematical Society, 83, pp. 456 - 462, http://dx.doi.org/10.1017/S000497271000198X

Journal articles | 2011

Shparlinski IE, 2011, 'Character sums with fermat quotients', Quarterly Journal of Mathematics, 62, pp. 1031 - 1043, http://dx.doi.org/10.1093/qmath/haq028

Journal articles | 2011

Shparlinski IE, 2011, 'Exponential sums with consecutive modular roots of an integer', Quarterly Journal of Mathematics, 62, pp. 207 - 213, http://dx.doi.org/10.1093/qmath/hap023

Journal articles | 2011

Shparlinski IE, 2011, 'Fermat quotients: Exponential sums, value set and primitive roots', Bulletin of the London Mathematical Society, 43, pp. 1228 - 1238, http://dx.doi.org/10.1112/blms/bdr058

Journal articles | 2011

Shparlinski IE, 2011, 'On small solutions to quadratic congruences', Journal of Number Theory, 131, pp. 1105 - 1111, http://dx.doi.org/10.1016/j.jnt.2010.12.002

Journal articles | 2011

Shparlinski IE, 2011, 'On the average distribution of pseudorandom numbers generated by nonlinear permutations', Mathematics of Computation, 80, pp. 1053 - 1061, http://dx.doi.org/10.1090/S0025-5718-2010-02408-1

Journal articles | 2011

Shparlinski IE, 2011, 'On the distribution of irreducible trinomials', Canadian Mathematical Bulletin, 54, pp. 748 - 756, http://dx.doi.org/10.4153/CMB-2011-053-0

Journal articles | 2010

Ahmadi O; Shparlinski I, 2010, 'Bilinear character sums and sum-product problems on elliptic curves', Proceedings of the Edinburgh Mathematical Society, 53, pp. 1 - 12, http://dx.doi.org/10.1017/S0013091508000771

Journal articles | 2010

Ahmadi O; Shparlinski IE; Voloch JF, 2010, 'Multiplicative order of gauss periods', International Journal of Number Theory, 6, pp. 877 - 882, http://dx.doi.org/10.1142/S1793042110003290

Journal articles | 2010

Ahmadi O; Shparlinski IE, 2010, 'On the distribution of the number of points on algebraic curves in extensions of finite fields', Mathematical Research Letters, 17, pp. 689 - 699, http://dx.doi.org/10.4310/MRL.2010.v17.n4.a9

Journal articles | 2010

Banks WD; Shparlinski IE, 2010, 'Sums with convolutions of Dirichlet characters', Manuscripta Mathematica, 133, pp. 105 - 114, http://dx.doi.org/10.1007/s00229-010-0364-2

Journal articles | 2010

Bourgain J; Ford K; Konyagin SV; Shparlinski IE, 2010, 'On the divisibility of Fermat quotients', Michigan Mathematical Journal, 59, pp. 313 - 328, http://dx.doi.org/10.1307/mmj/1281531459

Journal articles | 2010

Broughan KA; Luca F; Shparlinski IE, 2010, 'Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem', Integers, 10, http://dx.doi.org/10.1515/integ.2010.041

Journal articles | 2010

Chan TH; Shparlinski IE, 2010, 'On the concentration of points on modular hyperbolas and exponential curves', Acta Arithmetica, 142, pp. 59 - 66, http://dx.doi.org/10.4064/aa142-1-5

Journal articles | 2010

Chan TH; Shparlinski IE, 2010, 'Visible Points on Modular Exponential Curves', Bulletin of the Polish Academy of Sciences Mathematics, 58, pp. 17 - 22, http://dx.doi.org/10.4064/ba58-1-2

Journal articles | 2010

Cilleruelo J; Luca F; Quirós A; Shparlinski IE, 2010, 'On squares in polynomial products', Monatshefte fur Mathematik, 159, pp. 215 - 223, http://dx.doi.org/10.1007/s00605-008-0066-y

Journal articles | 2010

Farashahi RR; Shparlinski IE, 2010, 'On pseudopoints of algebraic curves', Archiv der Mathematik, 95, pp. 529 - 537, http://dx.doi.org/10.1007/s00013-010-0200-7

Journal articles | 2010

Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, 23, pp. 501 - 513, http://dx.doi.org/10.1007/s13163-010-0029-4

Journal articles | 2010

Ford K; Khan MR; Shparlinski IE, 2010, 'Geometric properties of points on modular hyperbolas', Proceedings of the American Mathematical Society, 138, pp. 4177 - 4185, http://dx.doi.org/10.1090/S0002-9939-2010-10561-0

Journal articles | 2010

Friedlander JB; Gong K; Shparlinskii IE, 2010, 'Character sums over shifted primes', Mathematical Notes, 88, pp. 585 - 598, http://dx.doi.org/10.1134/S0001434610090312

Journal articles | 2010

Glebsky L; Shparlinski IE, 2010, 'Short cycles in repeated exponentiation modulo a prime', Designs, Codes, and Cryptography, 56, pp. 35 - 42, http://dx.doi.org/10.1007/s10623-009-9339-2

Journal articles | 2010

Gutierrez J; Shparlinski IE, 2010, 'Expansion of orbits of some dynamical systems over finite fields', Bulletin of the Australian Mathematical Society, 82, pp. 232 - 239, http://dx.doi.org/10.1017/S0004972709001270

Journal articles | 2010

Iosevich A; Shparlinski IE; Xiong M, 2010, 'SETS WITH INTEGRAL DISTANCES IN FINITE FIELDS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 362, pp. 2189 - 2204, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000275819200020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2010

Iosevich A; Shparlinski IE; Xiong M, 2010, 'Sets with integral distances in finite fields', Transactions of the American Mathematical Society, 362, pp. 2189 - 2204, http://dx.doi.org/10.1090/S0002-9947-09-05004-1

Journal articles | 2010

Karabina K; Menezes A; Pomerance C; Shparlinski IE, 2010, 'On the asymptotic effectiveness of Weil descent attacks', Journal of Mathematical Cryptology, 4, pp. 175 - 191, http://dx.doi.org/10.1515/JMC.2010.007

Journal articles | 2010

Konyagin SV; Pomerance C; Shparlinski IE, 2010, 'On the distribution of pseudopowers', Canadian Journal of Mathematics, 62, pp. 582 - 594, http://dx.doi.org/10.4153/CJM-2010-020-4

Journal articles | 2010

Konyagin SV; Shparlinski IE, 2010, 'On the Convex Hull of the Points on Modular Hyperbolas', On the Convex Hull of the Points on Modular Hyperbolas, http://arxiv.org/abs/1012.1444v2

Journal articles | 2010

Loiperdinger SS; Shparlinski IE, 2010, 'ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS', COLLOQUIUM MATHEMATICUM, 120, pp. 139 - 148, http://dx.doi.org/10.4064/cm120-1-10

Journal articles | 2010

Luca F; Shparlinski IE, 2010, 'On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers', Annals of Combinatorics, 14, pp. 507 - 524, http://dx.doi.org/10.1007/s00026-011-0074-9

Journal articles | 2010

Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, 16, pp. 320 - 328, http://dx.doi.org/10.1016/j.ffa.2010.05.002

Journal articles | 2010

Ostafe A; Shparlinski IE; Winterhof A, 2010, 'On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences', Advances in Mathematics of Communications, 4, pp. 369 - 379, http://dx.doi.org/10.3934/amc.2010.4.369

Journal articles | 2010

Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, 79, pp. 501 - 511, http://dx.doi.org/10.1090/S0025-5718-09-02271-6

Journal articles | 2010

Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, 138, pp. 2653 - 2656, http://dx.doi.org/10.1090/S0002-9939-10-10404-3

Journal articles | 2010

Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0

Journal articles | 2010

Pomerance C; Shparlinski IE, 2010, 'Rank statistics for a family of elliptic curves over a function field', Pure and Applied Mathematics Quarterly, 6, pp. 21 - 40, http://dx.doi.org/10.4310/PAMQ.2010.v6.n1.a2

Journal articles | 2010

Rezaeian Farashahi R; Shparlinski IE, 2010, 'On the number of distinct elliptic curves in some families', Designs, Codes, and Cryptography, 54, pp. 83 - 99, http://dx.doi.org/10.1007/s10623-009-9310-2

Journal articles | 2010

Shparlinski IE; Winterhof A, 2010, 'Partitions into two Lehmer numbers', Monatshefte fur Mathematik, 160, pp. 429 - 441, http://dx.doi.org/10.1007/s00605-009-0130-2

Journal articles | 2010

Shparlinski IE, 2010, 'Numbers at work and play', Notices of the American Mathematical Society, 57, pp. 334 - 342

Journal articles | 2010

Shparlinski IE, 2010, 'On point sets in vector spaces over finite fields that determine only acute angle triangles', Bulletin of the Australian Mathematical Society, 81, pp. 114 - 120, http://dx.doi.org/10.1017/S0004972709000719

Journal articles | 2010

Shparlinski IE, 2010, 'On quadratic fields generated by discriminants of irreducible trinomials', Proceedings of the American Mathematical Society, 138, pp. 125 - 132, http://dx.doi.org/10.1090/S0002-9939-09-10074-6

Journal articles | 2010

Shparlinski IE, 2010, 'On the size of the Gelfond exponent', Journal of Number Theory, 130, pp. 1056 - 1060, http://dx.doi.org/10.1016/j.jnt.2009.09.005

Journal articles | 2010

Shparlinski IE, 2010, 'Some counting questions for matrices with restricted entries', Linear Algebra and Its Applications, 432, pp. 155 - 160, http://dx.doi.org/10.1016/j.laa.2009.07.036

Journal articles | 2010

Shparlinski IE, 2010, 'Tate-shafarevich groups and frobenius fields of reductions of elliptic curves', Quarterly Journal of Mathematics, 61, pp. 255 - 263, http://dx.doi.org/10.1093/qmath/hap001

Journal articles | 2010

von zur Gathen J; Mignotte M; Shparlinski IE, 2010, 'Approximate polynomial gcd: Small degree and small height perturbations', Journal of Symbolic Computation, 45, pp. 879 - 886, http://dx.doi.org/10.1016/j.jsc.2010.04.001

Journal articles | 2010

Фридландер ДБ; Friedlander JB; Гонг K; Gong K; Шпарлинский ИЕ; Shparlinski IE, 2010, 'Суммы значений характеров на сдвинутых простых числах', Matematicheskie Zametki, 88, pp. 605 - 619, http://dx.doi.org/10.4213/mzm8692

Journal articles | 2009

Abercrombie AG; Banks WD; Shparlinski IE, 2009, 'Arithmetic functions on Beatty sequences', Acta Arithmetica, 136, pp. 81 - 89, http://dx.doi.org/10.4064/aa136-1-6

Journal articles | 2009

Ahmadi O; Alon N; Blake IF; Shparlinski IE, 2009, 'Graphs with integral spectrum', Linear Algebra and Its Applications, 430, pp. 547 - 552, http://dx.doi.org/10.1016/j.laa.2008.08.020

Journal articles | 2009

Balasuriya S; Shparlinski IE; Sutantyo D, 2009, 'Multiplicative character sums with the Euler function', Studia Scientiarum Mathematicarum Hungarica, 46, pp. 223 - 229, http://dx.doi.org/10.1556/SScMath.46.2009.2.1087

Journal articles | 2009

Balasuriya S; Winterhof A; Shparlinski IE, 2009, 'An average bound for character sums with some counter-dependent recurrence sequences', Rocky Mountain Journal of Mathematics, 39, pp. 1403 - 1409, http://dx.doi.org/10.1216/RMJ-2009-39-5-1403

Journal articles | 2009

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2009, 'Uniform Distribution of Fractional Parts Related to Pseudoprimes', Canadian Journal of Mathematics, 61, pp. 481 - 502, http://dx.doi.org/10.4153/CJM-2009-025-2

Journal articles | 2009

Banks WD; Shparlinski IE, 2009, 'Multiplicative character sums with twice-differentiable functions', Quarterly Journal of Mathematics, 60, pp. 401 - 411, http://dx.doi.org/10.1093/qmath/han023

Journal articles | 2009

Banks WD; Shparlinski IE, 2009, 'Prime numbers with beatty sequences', Colloquium Mathematicum, 115, pp. 147 - 157, http://dx.doi.org/10.4064/cm115-2-1

Journal articles | 2009

Banks WD; Shparlinski IE, 2009, 'Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height', Israel Journal of Mathematics, 173, pp. 253 - 277, http://dx.doi.org/10.1007/s11856-009-0091-0

Journal articles | 2009

Bourgain J; Konyagin SV; Pomerance C; Shparlinski IE, 2009, 'On the smallest pseudopower', Acta Arithmetica, 140, pp. 43 - 55, http://dx.doi.org/10.4064/aa140-1-3

Journal articles | 2009

Bourgain J; Konyagin SV; Shparlinski IE, 2009, 'Erratum: Product sets of rationals, multiplicative translates of subgroups in residue rings and fixed points of the discrete logarithm (International Mathematics Research Notices)', International Mathematics Research Notices, 2009, pp. 3146 - 3147, http://dx.doi.org/10.1093/imrn/rnp041

Journal articles | 2009

Cojocaru AC; Luca F; Shparlinski IE, 2009, 'Pseudoprime reductions of elliptic curves', Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 513 - 522, http://dx.doi.org/10.1017/S0305004108001758

Journal articles | 2009

Cojocaru AC; Shparlinski IE, 2009, 'On the embedding degree of reductions of an elliptic curve', Information Processing Letters, 109, pp. 652 - 654, http://dx.doi.org/10.1016/j.ipl.2009.02.018

Journal articles | 2009

Farashahi RR; Shparlinski IE; Voloch JF, 2009, 'On hashing into elliptic curves', Journal of Mathematical Cryptology, 3, pp. 353 - 360, http://dx.doi.org/10.1515/JMC.2009.022

Journal articles | 2009

Ford K; Luca F; Shparlinski IE, 2009, 'On the largest prime factor of the mersenne numbers', Bulletin of the Australian Mathematical Society, 79, pp. 455 - 463, http://dx.doi.org/10.1017/S0004972709000033

Journal articles | 2009

Friedlander JB; Shparlinski IE, 2009, 'Elliptic twin prime conjecture', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5557 LNCS, pp. 77 - 81, http://dx.doi.org/10.1007/978-3-642-01877-0_8

Journal articles | 2009

Friedlander JB; Shparlinski IE, 2009, 'On the density of some special primes', Journal of Mathematical Cryptology, 3, pp. 265 - 271, http://dx.doi.org/10.1515/JMC.2009.016

Journal articles | 2009

Igor S, 2009, 'Some special character sums over elliptic curves', Boletin de la Sociedad Matematica Mexicana, 15, pp. 37 - 40

Journal articles | 2009

Katz NM; Shparlinski IE; Xiong M, 2009, 'On character sums with distances on the upper half plane over a finite field', Finite Fields and their Applications, 15, pp. 738 - 747, http://dx.doi.org/10.1016/j.ffa.2009.08.002

Journal articles | 2009

Luca F; Shparlinski IE, 2009, 'On quadratic fields generated by the Shanks sequence', Proceedings of the Edinburgh Mathematical Society, 52, pp. 719 - 729, http://dx.doi.org/10.1017/S001309150700123X

Journal articles | 2009

Pomerance C; Shparlinski IE, 2009, 'On Pseudosquares and Pseudopowers', COMBINATORIAL NUMBER THEORY, pp. 171 - +, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000269082400013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2009

Shparlinski IE, 2009, 'Bilinear sums with exponential functions', Proceedings of the American Mathematical Society, 137, pp. 2217 - 2224, http://dx.doi.org/10.1090/S0002-9939-09-09882-7

Journal articles | 2009

Shparlinski IE, 2009, 'EXPONENTS OF MODULAR REDUCTIONS OF FAMILIES OF ELLIPTIC CURVES', REVISTA DE LA UNION MATEMATICA ARGENTINA, 50, pp. 69 - 74, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000268682800008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2009

Shparlinski IE, 2009, 'Exponential Sums with Farey Fractions', Bulletin of the Polish Academy of Sciences Mathematics, 57, pp. 101 - 107, http://dx.doi.org/10.4064/ba57-2-2

Journal articles | 2009

Shparlinski IE, 2009, 'On a generalisation of a Lehmer problem', Mathematische Zeitschrift, 263, pp. 619 - 631, http://dx.doi.org/10.1007/s00209-008-0434-2

Journal articles | 2009

Shparlinski IE, 2009, 'On some weighted average values of l-functions', Bulletin of the Australian Mathematical Society, 79, pp. 183 - 186, http://dx.doi.org/10.1017/S0004972708001020

Journal articles | 2009

Shparlinski IE, 2009, 'On the distribution of arguments of gauss sums', Kodai Mathematical Journal, 32, pp. 172 - 177, http://dx.doi.org/10.2996/kmj/1238594554

Journal articles | 2009

Shparlinski IE, 2009, 'On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture', SIAM Journal on Discrete Mathematics, 23, pp. 2093 - 2099, http://dx.doi.org/10.1137/090770746

Journal articles | 2009

Shparlinski IE, 2009, 'On the distribution of solutions to linear equations', Glasnik Matematicki, 44, pp. 7 - 10, http://dx.doi.org/10.3336/gm.44.1.02

Journal articles | 2009

Shparlinski IE, 2009, 'On the values of Kloosterman sums', IEEE Transactions on Information Theory, 55, pp. 2599 - 2601, http://dx.doi.org/10.1109/TIT.2009.2018320

Journal articles | 2009

Von Zur Gathen J; Shparlinski IE, 2009, 'Subset sum pseudorandom numbers: Fast generation and distribution', Journal of Mathematical Cryptology, 3, pp. 149 - 163, http://dx.doi.org/10.1515/JMC.2009.007

Journal articles | 2008

Balasuriya S; Banks WD; Shparlinski IE, 2008, 'Congruences and exponential sums with the sum of aliquot divisors function', International Journal of Number Theory, 4, pp. 903 - 909, http://dx.doi.org/10.1142/S179304210800178X

Journal articles | 2008

Banks WD; Garaev MZ; Heath-Brown DR; Shparlinski IE, 2008, 'Density of non-residues in Burgess-type intervals and applications', Bulletin of the London Mathematical Society, 40, pp. 88 - 96, http://dx.doi.org/10.1112/blms/bdm111

Journal articles | 2008

Blackburn SR; Shparlinski IE, 2008, 'On the average energy of circulant graphs', Linear Algebra and Its Applications, 428, pp. 1956 - 1963, http://dx.doi.org/10.1016/j.laa.2007.11.003

Journal articles | 2008

Bourgain J; Konyagin SV; Shparlinski IE, 2008, 'Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm', International Mathematics Research Notices, 2008, http://dx.doi.org/10.1093/imrn/rnn090

Journal articles | 2008

Bourgain J; Shparlinski IE, 2008, 'Distribution of consecutive modular roots of an integer', Acta Arithmetica, 134, pp. 83 - 91, http://dx.doi.org/10.4064/aa134-1-6

Journal articles | 2008

Cojocaru AC; Shparlinski IE, 2008, 'Distribution of farey fractions in residue classes and lang-trotter conjectures on average', Proceedings of the American Mathematical Society, 136, pp. 1977 - 1986, http://dx.doi.org/10.1090/S0002-9939-08-09324-6

Journal articles | 2008

Ford K; Shparlinski I, 2008, 'On curves over finite fields with Jacobians of small exponent', International Journal of Number Theory, 4, pp. 819 - 826, http://dx.doi.org/10.1142/S1793042108001687

Journal articles | 2008

Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'PRODUCTS IN RESIDUE CLASSES', MATHEMATICAL RESEARCH LETTERS, 15, pp. 1133 - 1147, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000262382600023&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2008

Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'Products in residue classes', Mathematical Research Letters, 15, pp. 1133 - 1147, http://dx.doi.org/10.4310/mrl.2008.v15.n6.a6

Journal articles | 2008

Friedlander JB; Shparlinski IE, 2008, 'Erratum: Least totient in a residue class (Bulletin of the London Mathematical Society (2007) 39 (425-432))', Bulletin of the London Mathematical Society, 40, pp. 532, http://dx.doi.org/10.1112/blms/bdn037

Journal articles | 2008

Graham SW; Shparlinski IE, 2008, 'On RSA moduli with almost half of the bits prescribed', Discrete Applied Mathematics, 156, pp. 3150 - 3154, http://dx.doi.org/10.1016/j.dam.2007.12.012

Journal articles | 2008

Khan MR; Shparlinski IE; Yankov CL, 2008, 'On the convex closure of the graph of modular inversions', Experimental Mathematics, 17, pp. 91 - 104, http://dx.doi.org/10.1080/10586458.2008.10129021

Journal articles | 2008

Kohnen W; Lau YK; Shparlinski IE, 2008, 'On the number of sign changes of hecke eigenvalues of newforms', Journal of the Australian Mathematical Society, 85, pp. 87 - 94, http://dx.doi.org/10.1017/S1446788708000323

Journal articles | 2008

Luca F; Shparlinski IE; Thangadurai R, 2008, 'Quadratic non-residues versus primitive roots modulo p', Journal of the Ramanujan Mathematical Society, 23, pp. 97 - 104

Journal articles | 2008

Luca F; Shparlinski IE, 2008, 'Arithmetic properties of Apéry numbers', Journal of the London Mathematical Society, 78, pp. 545 - 562, http://dx.doi.org/10.1112/jlms/jdn031

Journal articles | 2008

Luca F; Shparlinski IE, 2008, 'On quadratic fields generated by polynomials', Archiv der Mathematik, 91, pp. 399 - 408, http://dx.doi.org/10.1007/s00013-008-2656-2

Journal articles | 2008

Luca F; Shparlinski IE, 2008, 'On the values of the divisor function', Monatshefte fur Mathematik, 154, pp. 59 - 69, http://dx.doi.org/10.1007/s00605-007-0511-3

Journal articles | 2008

Naccache D; Shparlinski IE, 2008, 'Divisibility, Smoothness and Cryptographic Applications', Divisibility, Smoothness and Cryptographic Applications, http://arxiv.org/abs/0810.2067v3

Journal articles | 2008

Shparlinski I, 2008, 'Bilinear character sums over elliptic curves', Finite Fields and their Applications, 14, pp. 132 - 141, http://dx.doi.org/10.1016/j.ffa.2006.12.005

Journal articles | 2008

Shparlinski I, 2008, 'On the elliptic curve analogue of the sum-product problem', Finite Fields and their Applications, 14, pp. 721 - 726, http://dx.doi.org/10.1016/j.ffa.2007.12.002

Journal articles | 2008

Shparlinski I, 2008, 'On the exponential sum-product problem', Indagationes Mathematicae, 19, pp. 325 - 331, http://dx.doi.org/10.1016/S0019-3577(08)80006-7

Journal articles | 2008

Shparlinski I, 2008, 'On the size of the Jacobians of curves over finite fields', Bulletin of the Brazilian Mathematical Society, 39, pp. 587 - 595, http://dx.doi.org/10.1007/s00574-008-0006-4

Journal articles | 2008

Shparlinski IE; Voloch JF, 2008, 'Average distribution of prime ideals in families of number fields', Bulletin of the Brazilian Mathematical Society, 39, pp. 417 - 425, http://dx.doi.org/10.1007/s00574-008-0014-4

Journal articles | 2008

Shparlinski IE; Winterhof A, 2008, 'On the number of distances between the coordinates of points on modular hyperbolas', Journal of Number Theory, 128, pp. 1224 - 1230, http://dx.doi.org/10.1016/j.jnt.2007.04.016

Journal articles | 2008

Shparlinski IE; Winterhof A, 2008, 'Visible points on multidimensional modular hyperbolas', Journal of Number Theory, 128, pp. 2695 - 2703, http://dx.doi.org/10.1016/j.jnt.2008.02.011

Journal articles | 2008

Shparlinski IE, 2008, 'Approximation by several rationals', Bulletin of the Australian Mathematical Society, 77, pp. 325 - 329, http://dx.doi.org/10.1017/S0004972708000373

Journal articles | 2008

Shparlinski IE, 2008, 'Arithmetic and geometric progressions in product sets over finite fields', Bulletin of the Australian Mathematical Society, 78, pp. 357 - 364, http://dx.doi.org/10.1017/S0004972708000695

Journal articles | 2008

Shparlinski IE, 2008, 'Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average', Michigan Mathematical Journal, 56, pp. 99 - 111, http://dx.doi.org/10.1307/mmj/1213972400

Journal articles | 2008

Shparlinski IE, 2008, 'Exponential sums and prime divisors of sparse integers', Periodica Mathematica Hungarica, 57, pp. 93 - 99, http://dx.doi.org/10.1007/s10998-008-7093-3

Journal articles | 2008

Shparlinski IE, 2008, 'Infinite hilbert class field towers over cyclotomic fields', Glasgow Mathematical Journal, 50, pp. 27 - 32, http://dx.doi.org/10.1017/S0017089507003977

Journal articles | 2008

Shparlinski IE, 2008, 'On a Generalised Lehmer Problem for Arbitrary Powers', On a Generalised Lehmer Problem for Arbitrary Powers, http://arxiv.org/abs/0803.3487v2

Journal articles | 2008

Shparlinski IE, 2008, 'On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas', Bulletin of the Polish Academy of Sciences Mathematics, 56, pp. 1 - 7, http://dx.doi.org/10.4064/ba56-1-1

Journal articles | 2008

Shparlinski IE, 2008, 'On the distribution of Kloosterman sums', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136, pp. 419 - 425, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000251536800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2008

Shparlinski IE, 2008, 'On the distribution of kloosterman sums', Proceedings of the American Mathematical Society, 136, pp. 419 - 425, http://dx.doi.org/10.1090/S0002-9939-07-08943-5

Journal articles | 2008

Shparlinski IE, 2008, 'On the solvability of bilinear equations in finite fields', Glasgow Mathematical Journal, 50, pp. 523 - 529, http://dx.doi.org/10.1017/S0017089508004382

Journal articles | 2008

Shparlinski IE, 2008, 'Pseudorandom graphs from elliptic curves', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4957 LNCS, pp. 284 - 292, http://dx.doi.org/10.1007/978-3-540-78773-0_25

Journal articles | 2008

Van Dam W; Shparlinski IE, 2008, 'Classical and quantum algorithms for exponential congruences', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5106 LNCS, pp. 1 - 10, http://dx.doi.org/10.1007/978-3-540-89304-2_1

Journal articles | 2008

Von Zur Gathen J; Shparlinski IE, 2008, 'Approximate polynomial gcd: Small degree and small height perturbations', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4957 LNCS, pp. 276 - 283, http://dx.doi.org/10.1007/978-3-540-78773-0_24

Journal articles | 2007

Ahmadi O; Shparlinski IE, 2007, 'Distribution of matrices with restricted entries over finite fields', Indagationes Mathematicae, 18, pp. 327 - 337, http://dx.doi.org/10.1016/S0019-3577(07)00013-4

Journal articles | 2007

Ahmadi O; Shparlinski IE, 2007, 'Geometric progressions in sumsets over finite fields', Monatshefte fur Mathematik, 152, pp. 177 - 185, http://dx.doi.org/10.1007/s00605-007-0471-7

Journal articles | 2007

Balasuriya S; Luca F; Shparlinski IE, 2007, 'Prime Divisors Of Some Recurrence Sequence', Periodica Mathematica Hungarica, 54, pp. 215 - 227, http://dx.doi.org/10.1007/s-10998-007-2215-z

Journal articles | 2007

Balasuriya S; Shparlinski IE, 2007, 'Character sums with subsequence sums', Periodica Mathematica Hungarica, 55, pp. 215 - 221, http://dx.doi.org/10.1007/s10998-007-4215-4

Journal articles | 2007

Banks WD; Luca F; Shparlinski IE, 2007, 'Estimates for Wieferich numbers', Ramanujan Journal, 14, pp. 361 - 378, http://dx.doi.org/10.1007/s11139-007-9030-z

Journal articles | 2007

Banks WD; Luca F; Shparlinski IE, 2007, 'On rough and smooth neighbors', REVISTA MATEMATICA COMPLUTENSE, 20, pp. 109 - 118, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254910400002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2007

Banks WD; Shparlinski IE, 2007, 'On values taken by the largest prime factor of shifted primes', Journal of the Australian Mathematical Society, 82, pp. 133 - 147, http://dx.doi.org/10.1017/s1446788700017511

Journal articles | 2007

Banks WD; Shparlinski IE, 2007, 'Prime divisors in Beatty sequences', Journal of Number Theory, 123, pp. 413 - 425, http://dx.doi.org/10.1016/j.jnt.2006.07.011

Journal articles | 2007

Becheanu M; Luca F; Shparlinski IE, 2007, 'On the sums of complementary divisors', INTERNATIONAL JOURNAL OF NUMBER THEORY, 3, pp. 635 - 648, http://dx.doi.org/10.1142/S1793042107001152

Journal articles | 2007

Blackburn SR; Shparlinski IE, 2007, 'Erratum to "Character sums and nonlinear recurrence sequences". [Discrete Math. 306 (2006) 1126-1131] (DOI:10.1016/j.disc.2006.02.012)', Discrete Mathematics, 307, pp. 1218 - 1219, http://dx.doi.org/10.1016/j.disc.2006.10.009

Journal articles | 2007

Blake IF; Shparlinski IE, 2007, 'Statistical distribution and collisions of VSH', JOURNAL OF MATHEMATICAL CRYPTOLOGY, 1, pp. 329 - 349, http://dx.doi.org/10.1515/JMC.2007.016

Journal articles | 2007

Friedlander JB; Shparlinski IE, 2007, 'Least totient in a residue class', Bulletin of the London Mathematical Society, 39, pp. 425 - 432, http://dx.doi.org/10.1112/blms/bdm027

Journal articles | 2007

Garaev MZ; Luca F; Shparlinski IE, 2007, 'Exponential sums with Catalan numbers and middle binomial coefficients', Indagationes Mathematicae, 18, pp. 23 - 37, http://dx.doi.org/10.1016/S0019-3577(07)80004-8

Journal articles | 2007

Lange T; Shparlinski IE, 2007, 'Distribution of some sequences of points on elliptic curves', Journal of Mathematical Cryptology, 1, pp. 1 - 11, http://dx.doi.org/10.1515/JMC.2007.001

Journal articles | 2007

Luca F; Shparlinski IE, 2007, 'Arithmetic functions with linear recurrence sequences', Journal of Number Theory, 125, pp. 459 - 472, http://dx.doi.org/10.1016/j.jnt.2006.12.006

Journal articles | 2007

Luca F; Shparlinski IE, 2007, 'Discriminants of complex multiplication fields of elliptic curves over finite fields', Canadian Mathematical Bulletin, 50, pp. 409 - 417, http://dx.doi.org/10.4153/CMB-2007-039-2

Journal articles | 2007

Luca F; Shparlinski IE, 2007, 'On finite fields for pairing based cryptography', ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 1, pp. 281 - 286, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254707500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2007

Luca F; Shparlinski IE, 2007, 'On the square-free parts of ⌊en!⌋', Glasgow Mathematical Journal, 49, pp. 391 - 403, http://dx.doi.org/10.1017/S0017089507003734

Journal articles | 2007

Luca F; Shparlinski IE, 2007, 'Pseudoprime Cullen and Woodall numbers', Colloquium Mathematicum, 107, pp. 35 - 43, http://dx.doi.org/10.4064/cm107-1-5

Journal articles | 2007

Saxena N; Severini S; Shparlinski I, 2007, 'Parameters of integral circulant graphs and periodic quantum dynamics', International Journal of Quantum Information, 5, pp. 417 - 430, http://dx.doi.org/10.1142/S0219749907002918

Journal articles | 2007

Shparlinski I, 2007, 'A computational introduction to number theory and algebra', MATHEMATICS OF COMPUTATION, 76, pp. 1697 - 1698, http://dx.doi.org/10.1090/S0025-5718-07-01995-3

Journal articles | 2007

Shparlinski IE; Steinfeld R, 2007, 'Chinese remaindering with multiplicative noise', Theory of Computing Systems, 40, pp. 33 - 41, http://dx.doi.org/10.1007/s00224-005-1272-9

Journal articles | 2007

Shparlinski IE; Sutantyo D, 2007, 'On the set of the largest prime divisors', Publicationes Mathematicae Debrecen, 71, pp. 95 - 100

Journal articles | 2007

Shparlinski IE; Voloch JF, 2007, 'Visible Points on Curves over Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, 55, pp. 193 - 199, http://dx.doi.org/10.4064/ba55-3-1

Journal articles | 2007

Shparlinski IE; Winterhof A, 2007, 'Quantum period reconstruction of approximate sequences', Information Processing Letters, 103, pp. 211 - 215, http://dx.doi.org/10.1016/j.ipl.2007.02.019

Journal articles | 2007

Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', JOURNAL OF NUMBER THEORY, 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003

Journal articles | 2007

Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', Journal of Number Theory, 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003

Journal articles | 2007

Shparlinski IE, 2007, 'Bounds on the Fourier coefficients of the weighted sum function', Information Processing Letters, 103, pp. 83 - 87, http://dx.doi.org/10.1016/j.ipl.2007.02.011

Journal articles | 2007

Shparlinski IE, 2007, 'Character sums over shifted smooth numbers', Proceedings of the American Mathematical Society, 135, pp. 2699 - 2705, http://dx.doi.org/10.1090/S0002-9939-07-08785-0

Journal articles | 2007

Shparlinski IE, 2007, 'Communication complexity of some number theoretic functions', Applied Mathematics Letters, 20, pp. 872 - 875, http://dx.doi.org/10.1016/j.aml.2006.05.024

Journal articles | 2007

Shparlinski IE, 2007, 'Distribution of roots of polynomial congruences', International Journal of Mathematics and Mathematical Sciences, 2007, http://dx.doi.org/10.1155/2007/37853

Journal articles | 2007

Shparlinski IE, 2007, 'On some dynamical systems in finite fields and residue rings', Discrete and Continuous Dynamical Systems, 17, pp. 901 - 917, http://dx.doi.org/10.3934/dcds.2007.17.901

Journal articles | 2007

Shparlinski IE, 2007, 'On the distribution of angles of the salié sums', Bulletin of the Australian Mathematical Society, 75, pp. 221 - 227, http://dx.doi.org/10.1017/s0004972700039150

Journal articles | 2007

Shparlinski IE, 2007, 'On the distribution of points on multidimensional modular hyperbolas', Proceedings of the Japan Academy Series A: Mathematical Sciences, 83, pp. 5 - 9, http://dx.doi.org/10.3792/pjaa.83.5

Journal articles | 2006

Banks MK, 2006, 'Editor’s Note', Journal of Environmental Engineering, 132, pp. 157 - 157, http://dx.doi.org/10.1061/(asce)0733-9372(2006)132:2(157)

Journal articles | 2006

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Character sums with exponential functions over smooth numbers', Indagationes Mathematicae, 17, pp. 157 - 168, http://dx.doi.org/10.1061/(ASCE)0733-9372(2006)132:2(157)

Journal articles | 2006

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Double character sums over elliptic curves and finite fields', PURE AND APPLIED MATHEMATICS QUARTERLY, 2, pp. 179 - 197, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000241377300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2006

Banks WD; Friedlander JB; Konyagin SV; Shparlinski IE, 2006, 'Incomplete exponential sums and Diffie-Hellman triples', Mathematical Proceedings of the Cambridge Philosophical Society, 140, pp. 193 - 206, http://dx.doi.org/10.1017/S0305004105008947

Journal articles | 2006

Banks WD; Friedlander JB; Luca F; Pappalardi F; Shparlinski IE, 2006, 'Coincidences in the values of the Euler and Carmichael functions', Acta Arithmetica, 122, pp. 207 - 234, http://dx.doi.org/10.4064/aa122-3-1

Journal articles | 2006

Banks WD; Luca F; Shparlinski IE, 2006, 'Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n', Commentarii Mathematici Helvetici, 81, pp. 1 - 22, http://dx.doi.org/10.4171/CMH/40

Journal articles | 2006

Banks WD; Luca F; Shparlinski IE, 2006, 'Common divisors of the Euler function at related arguments', ACTA SCIENTIARUM MATHEMATICARUM, 72, pp. 525 - 536, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000216758800005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Average Value of the Euler Function on Binary Palindromes', Bulletin of the Polish Academy of Sciences Mathematics, 54, pp. 95 - 101, http://dx.doi.org/10.4064/ba54-2-1

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Character sums with Beatty sequences on Burgess-type intervals', Character sums with Beatty sequences on Burgess-type intervals, http://arxiv.org/abs/math/0608042v1

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Congruences and rational exponential sums with the euler function', Rocky Mountain Journal of Mathematics, 36, pp. 1415 - 1426, http://dx.doi.org/10.1216/rmjm/1181069373

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Integers with a large smooth divisor', Integers with a large smooth divisor, http://arxiv.org/abs/math/0601460v1

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Multiplicative character sums with the sum of g-ary digits function', Ramanujan Journal, 11, pp. 215 - 219, http://dx.doi.org/10.1007/s11139-006-6508-z

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Non-residues and primitive roots in beatty sequences', Bulletin of the Australian Mathematical Society, 73, pp. 433 - 443, http://dx.doi.org/10.1017/s0004972700035449

Journal articles | 2006

Banks WD; Shparlinski IE, 2006, 'Short character sums with beatty sequences', Mathematical Research Letters, 13, pp. 539 - 547, http://dx.doi.org/10.4310/MRL.2006.v13.n4.a4

Journal articles | 2006

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', JOURNAL OF ALGORITHMS-COGNITION INFORMATICS AND LOGIC, 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002

Journal articles | 2006

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', Journal of Algorithms, 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002

Journal articles | 2006

Blackburn SR; Shparlinski IE, 2006, 'Character sums and nonlinear recurrence sequences', Discrete Mathematics, 306, pp. 1126 - 1131, http://dx.doi.org/10.1016/j.disc.2006.02.012

Journal articles | 2006

Blake IF; Garefalakis T; Shparlinski IE, 2006, 'On the bit security of the Diffie-Hellman key', Applicable Algebra in Engineering, Communications and Computing, 16, pp. 397 - 404, http://dx.doi.org/10.1007/s00200-005-0184-x

Journal articles | 2006

Contini S; Croot E; Shparlinski IE, 2006, 'Complexity of inverting the Euler function', Mathematics of Computation, 75, pp. 983 - 996, http://dx.doi.org/10.1090/S0025-5718-06-01826-6

Journal articles | 2006

Coppersmith D; Howgrave-Graham N; Nguyễn PQ; Shparlinski IE, 2006, 'Testing set proportionality and the Ádám isomorphism of circulant graphs', Journal of Discrete Algorithms, 4, pp. 324 - 335, http://dx.doi.org/10.1016/j.jda.2005.06.003

Journal articles | 2006

El-Mahassni ED; Shparlinski IE; Winterhof A, 2006, 'Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers', Monatshefte fur Mathematik, 148, pp. 297 - 307, http://dx.doi.org/10.1007/s00605-005-0355-7

Journal articles | 2006

Garaev MZ; Luca F; Shparlinski IE; Winterhof A, 2006, 'On the lower bound of the linear complexity over Fp of Sidelnikov sequences', IEEE Transactions on Information Theory, 52, pp. 3299 - 3304, http://dx.doi.org/10.1109/TIT.2006.876352

Journal articles | 2006

Garaev MZ; Luca F; Shparlinski IE, 2006, 'Catalan and Apéry numbers in residue classes', Journal of Combinatorial Theory. Series A, 113, pp. 851 - 865, http://dx.doi.org/10.1016/j.jcta.2005.08.003

Journal articles | 2006

Garaev MZ; Luca F; Shparlinski IE, 2006, 'Distribution of harmonic sums and Bernoulli polynomials modulo a prime', Mathematische Zeitschrift, 253, pp. 855 - 865, http://dx.doi.org/10.1007/s00209-006-0939-5

Journal articles | 2006

Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Exponential sums with Dickson polynomials', Finite Fields and their Applications, 12, pp. 16 - 25, http://dx.doi.org/10.1016/j.ffa.2004.08.001

Journal articles | 2006

Luca F; McKee J; Shparlinsk IE, 2006, 'Small exponent point groups on elliptic curves', Journal de Theorie des Nombres de Bordeaux, 18, pp. 471 - 476, http://dx.doi.org/10.5802/jtnb.554

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'Arithmetic properties of the Ramanujan function', Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 116, pp. 1 - 8, http://dx.doi.org/10.1007/BF02829735

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'Elliptic curves with low embedding degree', Journal of Cryptology, 19, pp. 553 - 562, http://dx.doi.org/10.1007/s00145-006-0544-0

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'ON THE NUMBER OF POLYNOMIAL MAPS INTO Z(n)', TSUKUBA JOURNAL OF MATHEMATICS, 30, pp. 431 - 441, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000219852100011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'On the number of polynomial maps into $\mathbb{Z}_{n}$', Tsukuba Journal of Mathematics, 30, http://dx.doi.org/10.21099/tkbjm/1496165073

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function', Indagationes Mathematicae, 17, pp. 611 - 625, http://dx.doi.org/10.1016/S0019-3577(06)81037-2

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'Some divisibilities amongst the terms of linear recurrences', Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 76, pp. 143 - 156, http://dx.doi.org/10.1007/BF02960862

Journal articles | 2006

Luca F; Shparlinski IE, 2006, 'Uniformity of distribution modulo 1 of the geometric mean prime divisor', Boletin de la Sociedad Matematica Mexicana, 12, pp. 155 - 163

Journal articles | 2006

Shparlinski I, 2006, 'On the energy of some circulant graphs', Linear Algebra and Its Applications, 414, pp. 378 - 382, http://dx.doi.org/10.1016/j.laa.2005.10.020

Journal articles | 2006

Shparlinski I, 2006, 'On the set of distances between two sets over finite fields', International Journal of Mathematics and Mathematical Sciences, 2006, http://dx.doi.org/10.1155/IJMMS/2006/59482

Journal articles | 2006

Shparlinski IE; Winterhof A, 2006, 'Constructions of approximately mutually unbiased bases', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3887 LNCS, pp. 793 - 799, http://dx.doi.org/10.1007/11682462_72

Journal articles | 2006

Shparlinski IE; Winterhof A, 2006, 'On the discrepancy and linear complexity of some counter-dependent recurrence sequences', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4086 LNCS, pp. 295 - 303, http://dx.doi.org/10.1007/11863854_25

Journal articles | 2006

Shparlinski IE; Winterhof A, 2006, 'On the nonlinearity of linear recurrence sequences', Applied Mathematics Letters, 19, pp. 340 - 344, http://dx.doi.org/10.1016/j.aml.2005.04.015

Journal articles | 2006

Shparlinski IE, 2006, 'On RSA moduli with prescribed bit patterns', Designs, Codes, and Cryptography, 39, pp. 113 - 122, http://dx.doi.org/10.1007/s10623-005-3137-2

Journal articles | 2006

Shparlinski IE, 2006, 'On some generalisations of the Erdos distance problem over finite fields', Bulletin of the Australian Mathematical Society, 73, pp. 285 - 292, http://dx.doi.org/10.1017/S0004972700038867

Journal articles | 2006

Shparlinski IE, 2006, 'On the sum of iterations of the Euler function', Journal of Integer Sequences, 9, pp. 1 - 5

Journal articles | 2006

Shparlinski IE, 2006, 'Primitive Points on a Modular Hyperbola', Bulletin of the Polish Academy of Sciences Mathematics, 54, pp. 193 - 200, http://dx.doi.org/10.4064/ba54-3-1

Journal articles | 2006

Shparlinski IE, 2006, 'Truncations of L-functions in residue classes', Glasgow Mathematical Journal, 48, pp. 347 - 350, http://dx.doi.org/10.1017/S0017089506003120

Journal articles | 2006

Von Zur Gathen J; Shparlinski IE, 2006, 'GCD of random linear combinations', Algorithmica (New York), 46, pp. 137 - 148, http://dx.doi.org/10.1007/s00453-006-0072-1

Journal articles | 2005

Banks WD; Ford K; Luca F; Pappalardi F; Shparlinski IE, 2005, 'Values of the Euler function in various sequences', Monatshefte fur Mathematik, 146, pp. 1 - 19, http://dx.doi.org/10.1007/s00605-005-0302-7

Journal articles | 2005

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, 'Uniform Distribution of the Fractional Part of the Average Prime Divisor', Forum Mathematicum, 17, pp. 885 - 901, http://dx.doi.org/10.1515/form.2005.17.6.885

Journal articles | 2005

Banks WD; Harman G; Shparlinski IE, 2005, 'Distributional properties of the largest prime factor', Michigan Mathematical Journal, 53, pp. 665 - 681, http://dx.doi.org/10.1307/mmj/1133894172

Journal articles | 2005

Banks WD; Heath-Brown R; Shparlinski IE, 2005, 'On the average value of divisor sums in arithmetic progressions', International Mathematics Research Notices, pp. 1 - 25, http://dx.doi.org/10.1155/imrn.2005.1

Journal articles | 2005

Banks WD; Luca F; Saidak F; Shparlinski IE, 2005, 'Values of arithmetical functions equal to a sum of two squares', Quarterly Journal of Mathematics, 56, pp. 123 - 139, http://dx.doi.org/10.1093/qmath/hah039

Journal articles | 2005

Banks WD; Luca F; Shparlinski IE, 2005, 'Irrationality of power series for various number theoretic functions', Manuscripta Mathematica, 117, pp. 183 - 197, http://dx.doi.org/10.1007/s00229-005-0564-3

Journal articles | 2005

Banks WD; Luca F; Shparlinski IE, 2005, 'Some divisibility properties of the Euler function', Glasgow Mathematical Journal, 47, pp. 517 - 528, http://dx.doi.org/10.1017/S0017089505002752

Journal articles | 2005

Banks WD; Shparlinski IE, 2005, 'Prime divisors of palindromes', Periodica Mathematica Hungarica, 51, pp. 1 - 10, http://dx.doi.org/10.1007/s10998-005-0016-6

Journal articles | 2005

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2005, 'Predicting nonlinear pseudorandom number generators', Mathematics of Computation, 74, pp. 1471 - 1494, http://dx.doi.org/10.1090/S0025-5718-04-01698-9

Journal articles | 2005

Cohen SD; Dewar M; Friedlander JB; Panario D; Shparlinski IE, 2005, 'Polynomial gauss sums', Proceedings of the American Mathematical Society, 133, pp. 2225 - 2231, http://dx.doi.org/10.1090/S0002-9939-05-08004-4

Journal articles | 2005

Contini S; Shparlinski IE, 2005, 'On Stern's attack against secret truncated linear congruential generators', Lecture Notes in Computer Science, 3574, pp. 52 - 60, http://dx.doi.org/10.1007/11506157_5

Journal articles | 2005

De Koninck JM; Luca F; Shparlinski IE, 2005, 'Powerful numbers in short intervals', Bulletin of the Australian Mathematical Society, 71, pp. 11 - 16, http://dx.doi.org/10.1017/s0004972700037953

Journal articles | 2005

Everest G; Shparlinski IE, 2005, 'Prime divisors of sequences associated to elliptic curves', Glasgow Mathematical Journal, 47, pp. 115 - 122, http://dx.doi.org/10.1017/S0017089504002113

Journal articles | 2005

Ford K; Khan MR; Shparlinski IE; Yankov CL, 2005, 'On the maximal difference between an element and its inverse in residue rings', Proceedings of the American Mathematical Society, 133, pp. 3463 - 3468, http://dx.doi.org/10.1090/S0002-9939-05-07962-1

Journal articles | 2005

Friedlander JB; Pomerance C; Shparlinski IE, 2005, 'Finding the group structure of elliptic curves over finite fields', Bulletin of the Australian Mathematical Society, 72, pp. 251 - 263, http://dx.doi.org/10.1017/s0004972700035048

Journal articles | 2005

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Exponential sums and congruences with factorials', Journal fur die Reine und Angewandte Mathematik, pp. 29 - 44, http://dx.doi.org/10.1515/crll.2005.2005.584.29

Journal articles | 2005

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Waring problem with factorials', Bulletin of the Australian Mathematical Society, 71, pp. 259 - 264, http://dx.doi.org/10.1017/s0004972700038223

Journal articles | 2005

Garaev MZ; Shparlinski IE, 2005, 'The large sieve inequality with exponential functions and the distribution of mersenne numbers modulo primes', International Mathematics Research Notices, pp. 2391 - 2403, http://dx.doi.org/10.1155/imrn.2005.2391

Journal articles | 2005

Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over F-P and residue races', JOURNAL OF NUMBER THEORY, 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

Journal articles | 2005

Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over Fp and residue races', Journal of Number Theory, 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

Journal articles | 2005

Hallgren S; Russell A; Shparlinski IE, 2005, 'Quantum noisy rational function reconstruction', Lecture Notes in Computer Science, 3595, pp. 420 - 429, http://dx.doi.org/10.1007/11533719_43

Journal articles | 2005

Hess F; Shparlinski IE, 2005, 'On the linear complexity and multidimensional distribution of congruential generators over elliptic curves', Designs, Codes, and Cryptography, 35, pp. 111 - 117, http://dx.doi.org/10.1007/s10623-003-6153-0

Journal articles | 2005

Klappenecker A; Rötteler M; Shparlinski IE; Winterhof A, 2005, 'On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states', Journal of Mathematical Physics, 46, http://dx.doi.org/10.1063/1.1998831

Journal articles | 2005

Lange T; Shparlinski I, 2005, 'Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves', Applicable Algebra in Engineering, Communications and Computing, 15, pp. 329 - 337, http://dx.doi.org/10.1007/s00200-004-0161-9

Journal articles | 2005

Lange T; Shparlinski IE, 2005, 'Certain exponential sums and random walks on elliptic curves', Canadian Journal of Mathematics, 57, pp. 338 - 350, http://dx.doi.org/10.4153/CJM-2005-015-8

Journal articles | 2005

Levieil E; Luca F; Shparlinski IE, 2005, 'Bounding the number of solutions of some congruences', Boletin de la Sociedad Matematica Mexicana, 11, pp. 175 - 180

Journal articles | 2005

Levieil E; Luca F; Shparlinski IE, 2005, 'Prime divisors of some shifted products', International Journal of Mathematics and Mathematical Sciences, 2005, pp. 3057 - 3073, http://dx.doi.org/10.1155/IJMMS.2005.3057

Journal articles | 2005

Luca F; Shparlinski IE, 2005, 'On the exponent of the group of points on elliptic curves in extension fields', International Mathematics Research Notices, pp. 1391 - 1409, http://dx.doi.org/10.1155/imrn.2005.1391

Journal articles | 2005

Luca F; Shparlinski IE, 2005, 'On the largest prime factor of n! + 2ⁿ − 1', Journal de Theorie des Nombres de Bordeaux, 17, pp. 859 - 870, http://dx.doi.org/10.5802/jtnb.524

Journal articles | 2005

Luca F; Shparlinski IE, 2005, 'Prime divisors of shifted factorials', Bulletin of the London Mathematical Society, 37, pp. 809 - 817, http://dx.doi.org/10.1112/S0024609305004923

Journal articles | 2005

Shparlinski I; Winterhof A, 2005, 'A hidden number problem in small subgroups', Mathematics of Computation, 74, pp. 2073 - 2080, http://dx.doi.org/10.1090/S0025-5718-05-01797-7

Journal articles | 2005

Shparlinski I; Winterhof A, 2005, 'Noisy interpolation of sparse polynomials in finite fields', Applicable Algebra in Engineering, Communications and Computing, 16, pp. 307 - 317, http://dx.doi.org/10.1007/s00200-005-0180-1

Journal articles | 2005

Shparlinski I, 2005, 'Book Review: Report on global methods for combinatorial isoperimetric problems', Mathematics of Computation, 74, pp. 1033 - 1052, http://dx.doi.org/10.1090/s0025-5718-04-01757-0

Journal articles | 2005

Shparlinski IE; Winterhof A, 2005, 'On the linear complexity of bounded integer sequences over different moduli', Information Processing Letters, 96, pp. 175 - 177, http://dx.doi.org/10.1016/j.ipl.2005.08.004

Journal articles | 2005

Shparlinski IE, 2005, 'On the nonlinearity of the sequence of signs of Kloosterman sums', Bulletin of the Australian Mathematical Society, 71, pp. 405 - 409, http://dx.doi.org/10.1017/s0004972700038405

Journal articles | 2005

Shparlinski IE, 2005, 'On the singularity of generalised Vandermonde matrices over finite fields', Finite Fields and their Applications, 11, pp. 193 - 199, http://dx.doi.org/10.1016/j.ffa.2004.11.001

Journal articles | 2005

Shparlinski IE, 2005, 'On the value set of the Ramanujan function', Archiv der Mathematik, 85, pp. 508 - 513, http://dx.doi.org/10.1007/s00013-005-1322-1

Journal articles | 2004

Banks WD; Conflitti A; Friedlander JB; Shparlinski IE, 2004, 'Exponential sums over Mersenne numbers', Compositio Mathematica, 140, pp. 15 - 30, http://dx.doi.org/10.1112/S0010437X03000022

Journal articles | 2004

Banks WD; Conflitti A; Shparlinski IE, 2004, 'Number theoretic designs for directed regular graphs of small diameter', SIAM Journal on Discrete Mathematics, 17, pp. 377 - 383, http://dx.doi.org/10.1137/S0895480101396676

Journal articles | 2004

Banks WD; Harcharras A; Shparlinski IE, 2004, 'Smooth values of shifted primes in arithmetic progressions', Michigan Mathematical Journal, 52, pp. 603 - 618, http://dx.doi.org/10.1307/mmj/1100623415

Journal articles | 2004

Banks WD; Shparlinski IE, 2004, 'Arithmetic properties of numbers with restricted digits', Acta Arithmetica, 112, pp. 313 - 332, http://dx.doi.org/10.4064/aa112-4-1

Journal articles | 2004

Chou WS; Shparlinski IE, 2004, 'On the cycle structure of repeated exponentiation modulo a prime', Journal of Number Theory, 107, pp. 345 - 356, http://dx.doi.org/10.1016/j.jnt.2004.04.005

Journal articles | 2004

Conflitti A; Shparlinski IE, 2004, 'On the multidimensional distribution of the subset sum generator of pseudorandom numbers', Mathematics of Computation, 73, pp. 1005 - 1011, http://dx.doi.org/10.1090/S0025-5718-03-01563-1

Journal articles | 2004

Dewar M; Panario D; Shparlinski IE, 2004, 'Distribution of exponential functions with k-full exponent modulo a prime', Indagationes Mathematicae, 15, pp. 497 - 503, http://dx.doi.org/10.1016/S0019-3577(04)80014-4

Journal articles | 2004

Frandsen GS; Shparlinski IE, 2004, 'On Reducing a System of Equations to a Single Equation', BRICS Report Series, 11, http://dx.doi.org/10.7146/brics.v11i6.21831

Journal articles | 2004

Frandsen GS; Shparlinski IE, 2004, 'On reducing a system of equations to a single equation', Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 163 - 166, http://dx.doi.org/10.1145/1005285.1005310

Journal articles | 2004

Galbraith SD; Hopkins HJ; Shparlinski IE, 2004, 'Secure bilinear Diffie-Hellman bits', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3108, pp. 370 - 378, http://dx.doi.org/10.1007/978-3-540-27800-9_32

Journal articles | 2004

Garaev MZ; Luca F; Shparlinski IE, 2004, 'Character sums and congruences with n!', Transactions of the American Mathematical Society, 356, pp. 5089 - 5102, http://dx.doi.org/10.1090/S0002-9947-04-03612-8

Journal articles | 2004

Goresky M; Klapper A; Murty R; Shparlinski I, 2004, 'On decimations of ℓ-sequences', SIAM Journal on Discrete Mathematics, 18, pp. 130 - 140, http://dx.doi.org/10.1137/S0895480102403428

Journal articles | 2004

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Florianptic curves', Illinois Journal of Mathematics, 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

Journal articles | 2004

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Mov attack in various subgroups on elliptic curves', ILLINOIS JOURNAL OF MATHEMATICS, 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

Journal articles | 2004

Mans B; Shparlinski I, 2004, 'Bisecting and gossiping in circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2976, pp. 589 - 598, http://dx.doi.org/10.1007/978-3-540-24698-5_61

Journal articles | 2004

Russell A; Shparlinski IE, 2004, 'Classical and quantum function reconstruction via character evaluation', Journal of Complexity, 20, pp. 404 - 422, http://dx.doi.org/10.1016/j.jco.2003.08.019

Journal articles | 2004

Shparlinski IE; Steinfield R, 2004, 'Noisy Chinese remaindering in the Lee norm', Journal of Complexity, 20, pp. 423 - 437, http://dx.doi.org/10.1016/j.jco.2003.08.020

Journal articles | 2004

Shparlinski IE; Winterhof A, 2004, 'A nonuniform algorithm for the hidden number problem in subgroups', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2947, pp. 416 - 424, http://dx.doi.org/10.1007/978-3-540-24632-9_30

Journal articles | 2004

Shparlinski IE, 2004, 'Bounds of Gauss sums in finite fields', Proceedings of the American Mathematical Society, 132, pp. 2817 - 2824, http://dx.doi.org/10.1090/S0002-9939-04-07133-3

Journal articles | 2004

Shparlinski IE, 2004, 'Distribution of exponential functions with squarefull exponent in residue rings', Indagationes Mathematicae, 15, pp. 283 - 289, http://dx.doi.org/10.1016/S0019-3577(04)90020-1

Journal articles | 2004

Shparlinski IE, 2004, 'Exponential function analogue of kloosterman sums', Rocky Mountain Journal of Mathematics, 34, pp. 1497 - 1502, http://dx.doi.org/10.1216/rmjm/1181069811

Journal articles | 2004

Shparlinski IE, 2004, 'On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA', Information Processing Letters, 92, pp. 143 - 147, http://dx.doi.org/10.1016/j.ipl.2004.07.004

Journal articles | 2004

Shparlinski IE, 2004, 'Security of polynomial transformations of the Diffie-Hellman key', Finite Fields and their Applications, 10, pp. 123 - 131, http://dx.doi.org/10.1016/S1071-5797(03)00048-0

Journal articles | 2004

Vasco MIG; Näslund M; Shparlinski IE, 2004, 'New results on the hardness of diffie-hellman bits', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2947, pp. 159 - 172

Journal articles | 2004

Von Gathen JZ; Shparlinski IE, 2004, 'GCD of random linear forms', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3341, pp. 464 - 469

Journal articles | 2004

Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3357, pp. 241 - 251

Journal articles | 2004

Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3357, pp. 241 - 251

Journal articles | 2004

Von Zur Gathen J; Shparlinski IE, 2004, 'Polynomial Interpolation from Multiples', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 15, pp. 1125 - 1130

Journal articles | 2004

von zur Gathen J; Knopfmacher A; Luca F; Lucht LG; Shparlinski IE, 2004, 'Average order in cyclic groups', Journal de Theorie des Nombres de Bordeaux, 16, pp. 107 - 123, http://dx.doi.org/10.5802/jtnb.436

Journal articles | 2004

von zur Gathen J; Shparlinski I; Stichtenoth H, 2004, 'Finite Fields: Theory and Applications', Oberwolfach Reports, pp. 2913 - 2970, http://dx.doi.org/10.4171/owr/2004/54

Journal articles | 2003

Allender E; Bernasconi A; Damm C; Von Zur Gathen J; Saks M; Shparlinski I, 2003, 'Complexity of some arithmetic problems for binary polynomials', Computational Complexity, 12, pp. 23 - 47, http://dx.doi.org/10.1007/s00037-003-0176-9

Journal articles | 2003

Banks WD; Harcharras A; Shparlinski IE, 2003, 'Short Kloosterman sums for polynomials over finite fields', Canadian Journal of Mathematics, 55, pp. 225 - 246, http://dx.doi.org/10.4153/CJM-2003-010-0

Journal articles | 2003

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2003, 'Predicting the Inversive Generator', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2898, pp. 264 - 275, http://dx.doi.org/10.1007/978-3-540-40974-8_21

Journal articles | 2003

Guruswami V; Shparlinski I, 2003, 'Unconditional proof of tightness of Johnson bound', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 754 - 755

Journal articles | 2003

Gutierrez J; Shparlinski IE; Winterhof A, 2003, 'On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators', IEEE Transactions on Information Theory, 49, pp. 60 - 64, http://dx.doi.org/10.1109/TIT.2002.806144

Journal articles | 2003

Howgrave-Graham NA; Nguyen PQ; Shparlinski IE, 2003, 'Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation', Mathematics of Computation, 72, pp. 1473 - 1485, http://dx.doi.org/10.1090/S0025-5718-03-01495-9

Journal articles | 2003

Khan MR; Shparlinski IE, 2003, 'On the maximal difference between an element and its inverse modulo n', Periodica Mathematica Hungarica, 47, pp. 111 - 117, http://dx.doi.org/10.1023/b:mahu.0000010815.14847.96

Journal articles | 2003

Konyagin S; Lange T; Shparlinski I, 2003, 'Linear complexity of the discrete logarithm', Designs, Codes, and Cryptography, 28, pp. 135 - 146, http://dx.doi.org/10.1023/A:1022584306676

Journal articles | 2003

Luca F; Shparlinski IE, 2003, 'Average multiplicative orders of elements modulo n', Acta Arithmetica, 109, pp. 387 - 411, http://dx.doi.org/10.4064/aa109-4-7

Journal articles | 2003

Nguyen PQ; Shparlinski IE, 2003, 'The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces', Designs, Codes, and Cryptography, 30, pp. 201 - 217, http://dx.doi.org/10.1023/A:1025436905711

Journal articles | 2003

Nguyen PQ; Shparlinski IE, 2003, 'The insecurity of the digital signature algorithm with partially known nonces', Journal of Cryptology, 15, pp. 151 - 176, http://dx.doi.org/10.1007/s00145-002-0021-3

Journal articles | 2003

Niederreiter H; Shparlinski IE, 2003, 'Dynamical systems generated by rational functions', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2643, pp. 6 - 17, http://dx.doi.org/10.1007/3-540-44828-4_2

Journal articles | 2003

Niederreiter H; Shparlinski IE, 2003, 'On the distribution of power residues and primitive elements in some nonlinear recurring sequences', Bulletin of the London Mathematical Society, 35, pp. 522 - 528, http://dx.doi.org/10.1112/S002460930300198X

Journal articles | 2003

Niederreiter H; Shparlinski IE, 2003, 'Periodic sequences with maximal linear complexity and almost maximal k-rrror linear complexity', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2898, pp. 183 - 189, http://dx.doi.org/10.1007/978-3-540-40974-8_15

Journal articles | 2003

Näslund M; Shparlinski IE; Whyte W, 2003, 'On the bit security of NTRUEncrypt', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2567, pp. 62 - 70, http://dx.doi.org/10.1007/3-540-36288-6_5

Journal articles | 2003

Pappalardi F; Saidak F; Shparlinski IE, 2003, 'Square-free values of the Carmichael function', Journal of Number Theory, 103, pp. 122 - 131, http://dx.doi.org/10.1016/S0022-314X(03)00110-0

Journal articles | 2003

Shparlinski IE, 2003, 'Prime divisors of sparse integers', Periodica Mathematica Hungarica, 46, pp. 215 - 222, http://dx.doi.org/10.1023/A:1025996312037

Journal articles | 2003

Von Zur Gathen J; Shparlinski I; Sinclair A, 2003, 'Finding points on curves over finite fields', SIAM Journal on Computing, 32, pp. 1436 - 1448, http://dx.doi.org/10.1137/S0097539799351018

Journal articles | 2002

Banks WD; Conflitti A; Shparlinski IE, 2002, 'Character sums over integers with restricted g-ary digits', Illinois Journal of Mathematics, 46, pp. 819 - 836, http://dx.doi.org/10.1215/ijm/1258130986

Journal articles | 2002

Banks WD; Shparlinski IE, 2002, 'Average normalisations of elliptic curves', Bulletin of the Australian Mathematical Society, 66, pp. 353 - 358, http://dx.doi.org/10.1017/s0004972700040211

Journal articles | 2002

Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', JOURNAL OF NUMBER THEORY, 95, pp. 340 - 350, http://dx.doi.org/10.1006/jnth.2001.2775

Journal articles | 2002

Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', Journal of Number Theory, 95, pp. 340 - 350, http://dx.doi.org/10.1016/S0022-314X(01)92775-1

Journal articles | 2002

Codenotti B; Shparlinski IE; Winterhof A, 2002, 'On the hardness of approximating the permanent of structured matrices', Computational Complexity, 11, pp. 158 - 170, http://dx.doi.org/10.1007/s00037-002-0174-3

Journal articles | 2002

El Mahassni E; Shparlinski I, 2002, 'On the Uniformity of Distribution of the Elliptic Curve ElGamal Signature', Finite Fields and Their Applications, 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366

Journal articles | 2002

El Mahassni E; Shparlinski I, 2002, 'On the uniformity of distribution of the elliptic curve ElGamal signature', Finite Fields and their Applications, 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366

Journal articles | 2002

Friedlander JB; Konyagin S; Shparllnski IE, 2002, 'Some doubly exponential sums over ℤm', Acta Arithmetica, 105, pp. 349 - 370, http://dx.doi.org/10.4064/aa105-4-4

Journal articles | 2002

Friedlander JB; Pomerance C; Shparlinski IE, 2002, 'Erratum: Period of the power generator and small values of Carmichael's function (Mathematics of Computation)', Mathematics of Computation, 71, pp. 1803 - 1806, http://dx.doi.org/10.1090/S0025-5718-02-01519-3

Journal articles | 2002

Mans B; Pappalardi F; Shparlinski I, 2002, 'On the spectral Ádám property for circulant graphs', Discrete Mathematics, 254, pp. 309 - 329, http://dx.doi.org/10.1016/S0012-365X(01)00374-0

Journal articles | 2002

Niederreiter H; Shparlinski IE, 2002, 'On the Average Distribution of Inversive Pseudorandom Numbers', Finite Fields and Their Applications, 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358

Journal articles | 2002

Niederreiter H; Shparlinski IE, 2002, 'On the average distribution of inversive pseudorandom numbers', Finite Fields and their Applications, 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358

Journal articles | 2002

Shparlinski IE, 2002, 'On a question of Erdos and Graham', Archiv der Mathematik, 78, pp. 445 - 448, http://dx.doi.org/10.1007/s00013-002-8269-2

Journal articles | 2002

Shparlinski IE, 2002, 'On the distribution of the Diffie-Hellman pairs', Finite Fields and their Applications, 8, pp. 131 - 141, http://dx.doi.org/10.1006/ffta.2000.0321

Journal articles | 2002

Shparlinski IE, 2002, 'On the uniformity of distribution of the EIGamal signature', Applicable Algebra in Engineering, Communications and Computing, 13, pp. 9 - 16, http://dx.doi.org/10.1007/s002000100087

Journal articles | 2002

Shparlinski IE, 2002, 'Security of most significant bits of g^x(2)', Information Processing Letters, 83, pp. 109 - 113, http://dx.doi.org/10.1016/S0020-0190(01)00315-5

Journal articles | 2002

Vasco MIG; Shparlinski IE, 2002, 'Security of the most significant bits of the Shamir message passing scheme', Mathematics of Computation, 71, pp. 333 - 342, http://dx.doi.org/10.1090/S0025-5718-01-01358-8

Journal articles | 2001

Banks WD; Shparlinski IE, 2001, 'Distribution of inverses in polynomial rings', Indagationes Mathematicae, 12, pp. 303 - 315, http://dx.doi.org/10.1016/S0019-3577(01)80012-4

Journal articles | 2001

Bernasconi A; Damm C; Shparlinski I, 2001, 'Circuit and decision tree complexity of some number theoretic problems', Information and Computation, 168, pp. 113 - 124, http://dx.doi.org/10.1006/inco.2000.3017

Journal articles | 2001

Boneh D; Shparlinski IE, 2001, 'On the unpredictability of bits of the elliptic curve Diffie-Hellman scheme', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2139 LNCS, pp. 201 - 212, http://dx.doi.org/10.1007/3-540-44647-8_12

Journal articles | 2001

Cohen SD; Niederreiter H; Shparlinski IE; Zieve M, 2001, 'Incomplete character sums and a special class of permutations', Journal de Theorie des Nombres de Bordeaux, 13, pp. 53 - 63, http://dx.doi.org/10.5802/jtnb.303

Journal articles | 2001

El Mahassni E; Shparlinski I, 2001, 'On Some Uniformity of Distribution Properties of ESIGN', Electronic Notes in Discrete Mathematics, 6, pp. 132 - 139, http://dx.doi.org/10.1016/S1571-0653(04)00164-7

Journal articles | 2001

El Mahassni E; Shparlinski I, 2001, 'Polynomial representations of the Diffie-Hellman mapping', Bulletin of the Australian Mathematical Society, 63, pp. 467 - 473, http://dx.doi.org/10.1017/s0004972700019547

Journal articles | 2001

Friedlander JB; Pomerance C; Shparlinski IE, 2001, 'Period of the power generator and small values of Carmichael's function', Mathematics of Computation, 70, pp. 1591 - 1605, http://dx.doi.org/10.1090/S0025-5718-00-01282-5

Journal articles | 2001

Friedlander JB; Shparlinsk IE, 2001, 'On the distribution of Diffie-Hellman triples with sparse exponents', SIAM Journal on Discrete Mathematics, 14, pp. 162 - 169, http://dx.doi.org/10.1137/S0895480199361740

Journal articles | 2001

Friedlander JB; Shparlinski IE, 2001, 'Double exponential sums over thin sets', Proceedings of the American Mathematical Society, 129, pp. 1617 - 1621, http://dx.doi.org/10.1090/s0002-9939-00-05921-9

Journal articles | 2001

Friedlander JB; Shparlinski IE, 2001, 'On the distribution of the power generator', Mathematics of Computation, 70, pp. 1575 - 1589, http://dx.doi.org/10.1090/S0025-5718-00-01283-7

Journal articles | 2001

Lieman D; Shparlinski I, 2001, 'On a new exponential sum', Canadian Mathematical Bulletin, 44, pp. 87 - 92, http://dx.doi.org/10.4153/CMB-2001-010-1

Journal articles | 2001

Niederreiter H; Shparlinski IE, 2001, 'On the distribution of inversive congruential pseudorandom numbers in parts of the period', Mathematics of Computation, 70, pp. 1569 - 1574, http://dx.doi.org/10.1090/S0025-5718-00-01273-4

Journal articles | 2001

Shparlinski I, 2001, 'On Some Properties of the Shrinking Generator', Designs, Codes, and Cryptography, 23, pp. 147 - 156, http://dx.doi.org/10.1023/A:1011256430812

Journal articles | 2001

Shparlinski I, 2001, 'On the Linear Complexity of the Power Generator', Designs, Codes, and Cryptography, 23, pp. 5 - 10, http://dx.doi.org/10.1023/A:1011264815860

Journal articles | 2001

Shparlinski I, 2001, 'On the Multiplicative Orders of γ and γ+γ^-1 over finite fields', Finite Fields and their Applications, 7, pp. 327 - 331, http://dx.doi.org/10.1006/ffta.2000.0292

Journal articles | 2001

Shparlinski IE; Silverman JH, 2001, 'On the Linear Complexity of the Naor-Reingold Pseudo-random Function from Elliptic Curves', Designs, Codes, and Cryptography, 24, pp. 279 - 289, http://dx.doi.org/10.1023/A:1011223204345

Journal articles | 2001

Shparlinski IE, 2001, 'On the Uniformity of Distribution of the Naor-Reingold Pseudo-Random Function', Finite Fields and their Applications, 7, pp. 318 - 326, http://dx.doi.org/10.1006/ffta.2000.0291

Journal articles | 2001

Shparlinski IE, 2001, 'On the uniformity of distribution of the RSA pairs', Mathematics of Computation, 70, pp. 801 - 808, http://dx.doi.org/10.1090/S0025-5718-00-01274-6

Journal articles | 2001

Shparlinski IE, 2001, 'Sparse polynomial approximation in finite fields', Conference Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 209 - 215, http://dx.doi.org/10.1145/380752.380803

Journal articles | 2000

Bernasconi A; Damm C; Shparlinski I, 2000, 'The average sensitivity of square-freeness', Computational Complexity, 9, pp. 39 - 51, http://dx.doi.org/10.1007/PL00001600

Journal articles | 2000

Canetti R; Friedlander J; Konyagin S; Larsen M; Lieman D; Shparlinski I, 2000, 'On the statistical properties of Diffie-Hellman distributions', Israel Journal of Mathematics, 120, pp. 23 - 46, http://dx.doi.org/10.1007/s11856-000-1270-1

Journal articles | 2000

Coppersmith D; Shparlinski I, 2000, 'On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping', JOURNAL OF CRYPTOLOGY, 13, pp. 339 - 360, http://dx.doi.org/10.1007/s001450010002

Journal articles | 2000

El Mahassni E; Shparlinski I, 2000, 'On some uniformity of distribution properties of ESIGN', Electronic Notes in Discrete Mathematics, 6, pp. 1 - 8

Journal articles | 2000

Friedlander JB; Hansen J; Shparlinski IE, 2000, 'Character sums with exponential functions', Mathematika, 47, pp. 75 - 85, http://dx.doi.org/10.1112/S0025579300015734

Journal articles | 2000

Griffin F; Shparlinski IE, 2000, 'On the linear complexity profile of the power generator', IEEE Transactions on Information Theory, 46, pp. 2159 - 2162, http://dx.doi.org/10.1109/18.868485

Journal articles | 2000

Gutierrez J; Niederreiter H; Shparlinski IE, 2000, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatshefte fur Mathematik, 129, pp. 31 - 36, http://dx.doi.org/10.1007/s006050050004

Journal articles | 2000

Karpinski M; Van Der Poorten A; Shparlinski I, 2000, 'Zero testing of p-adic and modular polynomials', Theoretical Computer Science, 233, pp. 309 - 317, http://dx.doi.org/10.1016/S0304-3975(99)00133-4

Journal articles | 2000

Niederreiter H; Shparlinski IE, 2000, 'Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus', Acta Arithmetica, 92, pp. 89 - 98, http://dx.doi.org/10.4064/aa-92-1-89-98

Journal articles | 2000

Niederreiter H; Shparlinski IE, 2000, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Applicable Algebra in Engineering, Communications and Computing, 10, pp. 189 - 202, http://dx.doi.org/10.1007/s002000050124

Journal articles | 2000

Shparlinski IE, 2000, 'Communication complexity and fourier coefficients of the Diffie-Hellman key', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1776 LNCS, pp. 259 - 268, http://dx.doi.org/10.1007/10719839_27

Journal articles | 2000

Shparlinski IE, 2000, 'Computing Jacobi Symbols modulo Sparse Integers and Polynomials and Some Applications', Journal of Algorithms, 36, pp. 241 - 252, http://dx.doi.org/10.1006/jagm.2000.1091

Journal articles | 2000

Shparlinski IE, 2000, 'Linear complexity of the Naor-Reingold pseudo-random function', Information Processing Letters, 76, pp. 95 - 99, http://dx.doi.org/10.1016/S0020-0190(00)00133-2

Journal articles | 2000

Shparlinski IE, 2000, 'On the Naor-Reingold pseudo-random function from elliptic curves', Applicable Algebra in Engineering, Communications and Computing, 11, pp. 27 - 34, http://dx.doi.org/10.1007/s002000000023

Journal articles | 2000

Von Zur Gathen J; Shparlinski IE, 2000, 'CREW PRAM complexity of modular inversion', SIAM Journal on Computing, 29, pp. 1839 - 1857, http://dx.doi.org/10.1137/S0097539797328070

Journal articles | 1999

Canetti R; Friedlander J; Shparlinski I, 1999, 'On certain exponential sums and the distribution of Diffie-Hellman triples', Journal of the London Mathematical Society, 59, pp. 799 - 812, http://dx.doi.org/10.1112/S002461079900736X

Journal articles | 1999

Everest GR; Shparlinski IE, 1999, 'Counting the values taken by algebraic exponential polynomials', Proceedings of the American Mathematical Society, 127, pp. 665 - 675, http://dx.doi.org/10.1090/s0002-9939-99-04728-0

Journal articles | 1999

Friedlander J; Larsen M; Lieman D; Shparlinski I, 1999, 'On the Correlation of Binary M-sequences', Designs, Codes, and Cryptography, 16, pp. 249 - 256, http://dx.doi.org/10.1023/A:1008383811226

Journal articles | 1999

Niederreiter H; Shparlinski IE, 1999, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and their Applications, 5, pp. 246 - 253, http://dx.doi.org/10.1006/ffta.1999.0257

Journal articles | 1999

Von Zur Gathen J; Shparlinski I, 1999, 'Computing components and projections of curves over finite fields', SIAM Journal on Computing, 28, pp. 822 - 840, http://dx.doi.org/10.1137/s009753979427741x

Journal articles | 1998

Von Zur Gathen J; Shparlinski I, 1998, 'Orders of Gauss periods in finite fields', Applicable Algebra in Engineering, Communications and Computing, 9, pp. 15 - 24, http://dx.doi.org/10.1007/s002000050093

Journal articles | 1996

Everest GR; Shparlinski IE, 1996, 'Divisor sums of generalised exponential polynomials', Canadian Mathematical Bulletin, 39, pp. 35 - 46, http://dx.doi.org/10.4153/CMB-1996-005-5

Journal articles | 1996

Karpinski M; Shparlinski I, 1996, 'On some approximation problems concerning sparse polynomials over finite fields', Theoretical Computer Science, 157, pp. 259 - 266, http://dx.doi.org/10.1016/0304-3975(95)00162-X

Journal articles | 1996

Shparlinski I, 1996, 'On exponential sums with sparse polynomials and rational functions', Journal of Number Theory, 60, pp. 233 - 244, http://dx.doi.org/10.1006/jnth.1996.0121

Journal articles | 1996

Shparlinski I, 1996, 'On finding primitive roots in finite fields', Theoretical Computer Science, 157, pp. 273 - 275, http://dx.doi.org/10.1016/0304-3975(95)00164-6

Journal articles | 1996

Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260

Journal articles | 1996

Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', Applicable Algebra in Engineering, Communications and Computing, 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260

Journal articles | 1996

Van Der Poorten AJ; Shparlinski IE, 1996, 'On linear recurrence sequences with polynomial coefficients', Glasgow Mathematical Journal, 38, pp. 147 - 155, http://dx.doi.org/10.1017/s0017089500031372

Journal articles | 1996

Von Zur Gathen J; Karpinski M; Shparlinski I, 1996, 'Counting curves and their projections', Computational Complexity, 6, pp. 64 - 99, http://dx.doi.org/10.1007/BF01202042

Journal articles | 1995

Pappalardi F; Shparlinski I, 1995, 'On artin′s conjecture over function fields', Finite Fields and Their Applications, 1, pp. 399 - 404, http://dx.doi.org/10.1006/ffta.1995.1030

Journal articles | 1993

MULLEN GL; SHPARLINSKI I, 1993, 'VALUES OF LINEAR RECURRING SEQUENCES OF VECTORS OVER FINITE-FIELDS', ACTA ARITHMETICA, 65, pp. 221 - 226, http://dx.doi.org/10.4064/aa-65-3-221-226

Journal articles | 1993

Shparlinski IE, 1993, 'Finding irreducible and primitive polynomials', Applicable Algebra in Engineering, Communication and Computing, 4, pp. 263 - 268, http://dx.doi.org/10.1007/BF01200150

Journal articles | 1993

Shparlinski IE, 1993, 'On bivariate polynomial factorization over finite fields', Mathematics of Computation, 60, pp. 787 - 791, http://dx.doi.org/10.1090/S0025-5718-1993-1176716-3

Journal articles | 1993

Shparlinski IE, 1993, 'On parameters of some graphs from finite fields', European Journal of Combinatorics, 14, pp. 589 - 591, http://dx.doi.org/10.1006/eujc.1993.1061

Journal articles | 1992

Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'Distances from differences of roots of polynomials to the nearest integers', Information Processing Letters, 43, pp. 143 - 146, http://dx.doi.org/10.1016/0020-0190(92)90006-H

Journal articles | 1992

Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity', Journal of Computational and Applied Mathematics, 39, pp. 151 - 163, http://dx.doi.org/10.1016/0377-0427(92)90126-I

Journal articles | 1992

SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1992, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', LECTURE NOTES IN MATHEMATICS, 1518, pp. 145 - 169, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KR02000014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 1992

SHPARLINSKI IE, 1992, 'ON GAUSSIAN SUMS FOR FINITE-FIELDS AND ELLIPTIC-CURVES', LECTURE NOTES IN COMPUTER SCIENCE, 573, pp. 5 - 15, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KQ18400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Journal articles | 1992

Shparlinski IE, 1992, 'A deterministic test for permutation polynomials', Computational Complexity, 2, pp. 129 - 132, http://dx.doi.org/10.1007/BF01202000

Journal articles | 1992

Shparlinskiĭ IE, 1992, 'On primitive elements in finite fields and on elliptic curves', Mathematics of the USSR - Sbornik, 71, pp. 41 - 50, http://dx.doi.org/10.1070/SM1992v071n01ABEH001389

Journal articles | 1992

Stepanov SA; Shparlinskii IE, 1992, 'An estimate of incomplete multiplicative character sum of polynomials', Discrete Mathematics and Applications, 2, pp. 169 - 174, http://dx.doi.org/10.1515/dma.1992.2.2.169

Journal articles | 1992

Van Der Poorten AJ; Shparlinski IE, 1992, 'On the number of zeros of exponential polynomials and related questions', Bulletin of the Australian Mathematical Society, 46, pp. 401 - 412, http://dx.doi.org/10.1017/S0004972700012065

Journal articles | 1991

Shparlinskii IE, 1991, 'Estimates of Gaussian sums', Mathematical Notes of the Academy of Sciences of the USSR, 50, pp. 740 - 746, http://dx.doi.org/10.1007/BF01156612

Journal articles | 1991

Shparlinskiy IE, 1991, 'On the Distribution of Values of Recurring Sequences and the Bell Numbers in Finite Fields', European Journal of Combinatorics, 12, pp. 81 - 87, http://dx.doi.org/10.1016/S0195-6698(13)80010-8

Journal articles | 1990

Perel'muter GI; Shparlinskii IE, 1990, 'The distribution of primitive roots in finite fields', Russian Mathematical Surveys, 45, pp. 223 - 224, http://dx.doi.org/10.1070/RM1990v045n01ABEH002330

Journal articles | 1990

Shparlinskii IE, 1990, 'Generalization of Chebyshev polynomials', Siberian Mathematical Journal, 31, pp. 183 - 185, http://dx.doi.org/10.1007/BF00971170

Journal articles | 1990

Shparlinskii IE, 1990, 'Some arithmetic properties of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 47, pp. 612 - 617, http://dx.doi.org/10.1007/BF01170895

Journal articles | 1990

Shparlinskiĭ IE; Skorobogatov AN, 1990, 'Exponential sums and rational points on complete intersections', Mathematika, 37, pp. 201 - 208, http://dx.doi.org/10.1112/S0025579300012912

Journal articles | 1990

Stepanov SA; Shparlinskii IE, 1990, 'On the construction of a primitive normal basis in a finite field', Mathematics of the USSR - Sbornik, 67, pp. 527 - 533, http://dx.doi.org/10.1070/SM1990v067n02ABEH001369

Journal articles | 1989

Shparlinskii IE, 1989, 'Dimension of BCH codes', Problems of information transmission, 25, pp. 77 - 80

Journal articles | 1989

Shparlinskii IE, 1989, 'On arithmetical properties of solutions of norm equations', Russian Mathematical Surveys, 44, pp. 216 - 217, http://dx.doi.org/10.1070/RM1989v044n03ABEH002131

Journal articles | 1989

Shparlinskii IE, 1989, 'On distribution of values of recurrence sequences', Problems of information transmission, 25, pp. 120 - 125

Journal articles | 1989

Shparlinskiĭ IE, 1989, 'On polynomials of prescribed height in finite fields', Mathematics of the USSR - Sbornik, 63, pp. 247 - 255, http://dx.doi.org/10.1070/SM1989v063n01ABEH003271

Journal articles | 1988

Shparlinskii IE, 1988, 'Residue classes modulo a prime number in a field of algebraic numbers', Mathematical Notes of the Academy of Sciences of the USSR, 43, pp. 249 - 252, http://dx.doi.org/10.1007/BF01139128

Journal articles | 1987

Shparlinskii IE, 1987, 'Number of different prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 42, pp. 773 - 780, http://dx.doi.org/10.1007/BF01138309

Journal articles | 1986

Shparlinskii IE, 1986, 'WEIGHT SPECTRA OF SOME CODES.', Problems of information transmission, 22, pp. 111 - 116

Journal articles | 1985

Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1985, 'On one sequence of iteration parameters', USSR Computational Mathematics and Mathematical Physics, 25, pp. 89 - 93, http://dx.doi.org/10.1016/0041-5553(85)90046-1

Journal articles | 1985

Shparlinskii IE, 1985, 'Coefficients of primitive polynomials', Mathematical Notes of the Academy of Sciences of the USSR, 38, pp. 951 - 954, http://dx.doi.org/10.1007/BF01157011

Journal articles | 1985

Shparlinskii IE, 1985, 'Number of prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, 38, pp. 529 - 532, http://dx.doi.org/10.1007/BF01137461

Journal articles | 1984

Kosachevskaya LL; Shparlinskii IE, 1984, 'The rate of convergence of some iterational processes', USSR Computational Mathematics and Mathematical Physics, 24, pp. 81 - 84, http://dx.doi.org/10.1016/0041-5553(84)90088-0

Journal articles | 1984

Shparlinskii IE, 1984, 'Communications of the moscow mathematical society: On the note of convergence of Newton's interpolation process and the power of certain codes', Russian Mathematical Surveys, 39, pp. 199 - 200, http://dx.doi.org/10.1070/RM1984v039n02ABEH003150

Journal articles | 1984

Shparlinskii IE, 1984, 'On a multiplicative generator of pseudorandom numbers', USSR Computational Mathematics and Mathematical Physics, 24, pp. 79 - 81, http://dx.doi.org/10.1016/0041-5553(84)90159-9

Journal articles | 1983

Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE, 1983, 'On the spline-based method for experimental data deconvolution', Computer Physics Communications, 29, pp. 227 - 230, http://dx.doi.org/10.1016/0010-4655(83)90002-4

Journal articles | 1983

Shparlinskii IE, 1983, 'On one property of a multiplicative transducer of pseudo-random numbers', USSR Computational Mathematics and Mathematical Physics, 23, pp. 158 - 159, http://dx.doi.org/10.1016/S0041-5553(83)80030-5

Journal articles | 1982

Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1982, 'On an iterative process for the numerical solution of systems of linear algebraic equations', USSR Computational Mathematics and Mathematical Physics, 22, pp. 232 - 237, http://dx.doi.org/10.1016/0041-5553(82)90114-8

Journal articles | 1982

Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE; Vystavkin AN, 1982, 'New improved algorithm for the iterative solution of a system of linear algebraic equations', Computer Physics Communications, 27, pp. 87 - 89, http://dx.doi.org/10.1016/0010-4655(82)90011-X

Journal articles | 1981

Shparlinskii IE, 1981, 'The distribution of the fractional parts of recurrent sequences', USSR Computational Mathematics and Mathematical Physics, 21, pp. 231 - 235, http://dx.doi.org/10.1016/0041-5553(81)90169-5

Journal articles | 1979

Levin MB; Shparlinskii IE, 1979, 'The uniform distribution of fractional parts of recurrent sequences', Russian Mathematical Surveys, 34, pp. 207 - 208, http://dx.doi.org/10.1070/RM1979v034n03ABEH003995

Journal articles | 1979

Shparlinskii IE, 1979, 'On a completely uniform distribution', USSR Computational Mathematics and Mathematical Physics, 19, pp. 249 - 253, http://dx.doi.org/10.1016/0041-5553(79)90117-4

Journal articles | 1978

Shparlinskii IE, 1978, 'Distribution of nonresidues and primitive roots in recurrent sequences', Mathematical Notes of the Academy of Sciences of the USSR, 24, pp. 823 - 828, http://dx.doi.org/10.1007/BF01141537
Working Papers | 2021

Chen C; Shparlinski IE, 2021, On a hybrid version of the Vinogradov mean value theorem, http://dx.doi.org10.1007/s10474-020-01111-9, http://arxiv.org/abs/1910.07329v1

Working Papers | 2021

Chen C; Shparlinski IE, 2021, Restricted Mean Value Theorems and the Metric Theory of Restricted Weyl Sums, Oxford University Press (OUP), http://dx.doi.org10.1093/qmath/haaa052, http://arxiv.org/abs/1912.01307v2

Working Papers | 2020

Banks WD; Shparlinski IE, 2020, Sums with the Möbius function twisted by characters with powerful moduli, American Mathematical Society (AMS), http://dx.doi.org10.1090/tran/7914, http://arxiv.org/abs/1801.10276v1

Working Papers | 2020

Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, Michigan Mathematical Journal, http://dx.doi.org10.1307/mmj/1573700737, http://arxiv.org/abs/1711.10582v1

Working Papers | 2020

Munsch M; Shparlinski IE, 2020, On smooth square-free numbers in arithmetic progressions, http://dx.doi.org10.1112/jlms.12297, http://arxiv.org/abs/1710.04705v3

Working Papers | 2019

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, http://dx.doi.org, http://arxiv.org/abs/1912.00345v4

Working Papers | 2017

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, http://dx.doi.org, http://arxiv.org/abs/1711.05335v2
Preprints | 2023

Brandes J; Chen C; Shparlinski IE, 2023, Local mean value estimates for Weyl sums, , http://arxiv.org/abs/2303.11913v1

Preprints | 2023

Browning T; Shparlinski I, 2023, Square-free values of random polynomials, , http://arxiv.org/abs/2305.15493v1

Preprints | 2023

Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, , http://arxiv.org/abs/2304.10980v1

Preprints | 2023

Bulinski K; Shparlinski IE, 2023, Counting elements of the congruence subgroup, , http://arxiv.org/abs/2308.10485v2

Preprints | 2023

Dubickas A; Sha M; Shparlinski IE, 2023, Euclidean minima of algebraic number fields, , http://arxiv.org/abs/2307.10880v1

Preprints | 2023

Garaev MZ; Shparlinski IE, 2023, On some congruences and exponential sums, , http://arxiv.org/abs/2304.08689v1

Preprints | 2023

Garaev MZ; Shparlinski IE, 2023, On the distribution of modular inverses from short intervals, , http://arxiv.org/abs/2304.07953v1

Preprints | 2023

Iyer S; Shparlinski I, 2023, Character sums over elements of extensions of finite fields with restricted coordinates, , http://arxiv.org/abs/2309.02948v1

Preprints | 2023

Kerr B; Mohammadi A; Shparlinski IE, 2023, Additive energy of polynomial images, , http://arxiv.org/abs/2306.10677v1

Preprints | 2023

Munsch M; Shparlinski IE, 2023, On bounds on Dedekind sums and moments of $L$-functions over subgroups, , http://arxiv.org/abs/2305.04304v2

Preprints | 2023

Mérai L; Shparlinski IE, 2023, Distribution of recursive matrix pseudorandom number generator modulo prime powers, , http://arxiv.org/abs/2302.03964v1

Preprints | 2023

Shparlinski IE; Wijaya LP, 2023, On Nonzero Coefficients of Binary Cyclotomic Polynomials, , http://arxiv.org/abs/2307.07229v1

Preprints | 2023

Shparlinski IE, 2023, On the number of Diophantine $m$-tuples in finite fields, , http://arxiv.org/abs/2301.04063v1

Preprints | 2022

Abdalaoui EHE; Shparlinski IE; Steiner RS, 2022, Chowla and Sarnak Conjectures for Kloosterman Sums, , http://arxiv.org/abs/2211.00379v1

Preprints | 2022

Banks W; Shparlinski IE, 2022, On the greatest common divisor of integer parts of polynomials, , http://arxiv.org/abs/2205.00253v2

Preprints | 2022

Fouvry É; Shparlinski IE, 2022, On character sums with determinants, , http://arxiv.org/abs/2210.15761v2

Preprints | 2022

Hauck M; Shparlinski IE, 2022, Smooth numbers with few non-zero binary digits, , http://arxiv.org/abs/2212.10209v2

Preprints | 2022

Kerr B; Shparlinski IE; Wu X; Xi P, 2022, Bounds on bilinear forms with Kloosterman sums, , http://arxiv.org/abs/2204.05038v5

Preprints | 2022

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials, , http://arxiv.org/abs/2208.01885v2

Preprints | 2022

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials, , http://dx.doi.org/10.48550/arxiv.2208.01885

Preprints | 2022

Mérai L; Shparlinski IE; Winterhof A, 2022, Character sums over sparse elements of finite fields, , http://arxiv.org/abs/2211.08452v1

Preprints | 2022

Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups, , http://arxiv.org/abs/2211.07739v1

Preprints | 2022

Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, , http://arxiv.org/abs/2203.03880v4

Preprints | 2022

Shparlinski IE, 2022, Multiplicative Properties of Hilbert Cubes, , http://arxiv.org/abs/2201.00585v2

Preprints | 2021

Bag N; Shparlinski IE, 2021, Bounds on bilinear sums of Kloosterman sums, , http://arxiv.org/abs/2111.07311v1

Preprints | 2021

Bagshaw C; Shparlinski IE, 2021, Energy bounds, bilinear sums and their applications in function fields, , http://arxiv.org/abs/2112.02257v1

Preprints | 2021

Baker RC; Chen C; Shparlinski IE, 2021, Bounds on the Norms of Maximal Operators on Weyl Sums, , http://dx.doi.org/10.48550/arxiv.2107.13674

Preprints | 2021

Baker RC; Chen C; Shparlinski IE, 2021, Large Weyl sums and Hausdorff dimension, , http://dx.doi.org/10.48550/arxiv.2108.10439

Preprints | 2021

Baker RC; Munsch M; Shparlinski IE, 2021, Additive energy and a large sieve inequality for sparse sequences, , http://dx.doi.org/10.48550/arxiv.2103.12659

Preprints | 2021

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions, , http://dx.doi.org/10.48550/arxiv.2102.01949

Preprints | 2021

Ghioca D; Shparlinski I, 2021, Order of torsion for reduction of linearly independent points for a family of Drinfeld modules, , http://dx.doi.org/10.48550/arxiv.2103.00641

Preprints | 2021

Kaminski M; Shparlinski IE; Waldschmidt M, 2021, On sets of linear forms of maximal complexity, , http://dx.doi.org/10.1007/s00037-022-00234-5

Conference Papers | 2021

Kaminski M; Shparlinski IE, 2021, 'Sets of Linear Forms Which Are Hard to Compute', in Leibniz International Proceedings in Informatics, LIPIcs, http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.66

Preprints | 2021

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, Energy bounds for modular roots and their applications, , http://dx.doi.org/10.48550/arxiv.2103.09405

Preprints | 2021

Ostafe A; Shparlinski IE; Voloch JF, 2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, , http://arxiv.org/abs/2110.10941v1

Preprints | 2021

Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions, , http://dx.doi.org/10.48550/arxiv.2108.13146

Preprints | 2021

Shparlinski IE; Thuswaldner JM, 2021, Weyl sums over integers with digital restrictions, , http://dx.doi.org/10.48550/arxiv.2105.04835

Preprints | 2021

Shparlinski IE, 2021, On the Glasner property for matrices with polynomial entries, , http://arxiv.org/abs/2111.05644v1

Preprints | 2020

Banks W; Shparlinski I, 2020, On a conjecture of Soundararajan, , http://dx.doi.org/10.48550/arxiv.2009.06800

Preprints | 2020

Brandes J; Shparlinski IE, 2020, Two-dimensional Weyl sums failing square-root cancellation along lines, , http://dx.doi.org/10.48550/arxiv.2012.08877

Preprints | 2020

Chen C; Shparlinski IE, 2020, Hybrid bounds on two-parametric family Weyl sums along smooth curves, , http://dx.doi.org/10.48550/arxiv.2003.02419

Preprints | 2020

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic, , http://dx.doi.org/10.48550/arxiv.2012.13711

Preprints | 2020

Karpinski M; Shparlinski I, 2020, Noisy polynomial interpolation modulo prime powers, , http://dx.doi.org/10.48550/arxiv.2006.05685

Preprints | 2020

Kerr B; Mello J; Shparlinski I, 2020, An effective local-global principle for algebraic varieties and the sum product problem in finite fields, , http://dx.doi.org/10.48550/arxiv.2005.02923

Preprints | 2020

Kerr B; Mello J; Shparlinski IE, 2020, On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields, , http://dx.doi.org/10.48550/arxiv.2008.00433

Preprints | 2020

Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers, , http://dx.doi.org/10.48550/arxiv.2001.03380

Preprints | 2020

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, Polynomial Equations in Subgroups and Applications, , http://dx.doi.org/10.48550/arxiv.2005.05315

Preprints | 2020

Li R; Shparlinski IE, 2020, Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers, , http://dx.doi.org/10.48550/arxiv.2001.09721

Preprints | 2020

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, Bounds of Trilinear and Trinomial Exponential Sums, , http://dx.doi.org/10.48550/arxiv.2003.03493

Preprints | 2020

Mérai L; Shparlinski IE, 2020, On the Dynamical System Generated by the Möbius transformation at Prime Times, , http://dx.doi.org/10.48550/arxiv.2009.01089

Preprints | 2020

Ostafe A; Shparlinski I, 2020, On the Skolem problem and some related questions for parametric families of linear recurrence sequences, , http://dx.doi.org/10.48550/arxiv.2005.06713

Preprints | 2020

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, On the distribution of modular square roots of primes, , http://dx.doi.org/10.48550/arxiv.2009.03460

Preprints | 2020

Shparlinski IE; Wang Q, 2020, Exponential sums with sparse polynomials over finite fields, , http://dx.doi.org/10.48550/arxiv.2007.14551

Preprints | 2020

di Benedetto D; Garaev MZ; García VC; González-Sánchez D; Shparlinski IE; Trujillo CA, 2020, New estimates for exponential sums over multiplicative subgroups and intervals in prime fields, , http://dx.doi.org/10.48550/arxiv.2003.06165

Preprints | 2019

Banks W; Shparlinski I, 2019, Congruences with intervals and arbitrary sets, , http://dx.doi.org/10.48550/arxiv.1907.03943

Preprints | 2019

Breuer F; Shparlinski IE, 2019, Lower bounds for periods of Ducci sequences, , http://dx.doi.org/10.48550/arxiv.1909.04462

Preprints | 2019

Chen C; Shparlinski IE, 2019, Hausdorff dimension of the large values of Weyl sums, , http://dx.doi.org/10.48550/arxiv.1904.04457

Preprints | 2019

Chen C; Shparlinski IE, 2019, New bounds of Weyl sums, , http://dx.doi.org/10.48550/arxiv.1903.07330

Preprints | 2019

Chen C; Shparlinski IE, 2019, On Large Values of Weyl Sums, , http://dx.doi.org/10.48550/arxiv.1901.01551

Preprints | 2019

Chen C; Shparlinski IE, 2019, On a Hybrid Version of the Vinogradov Mean Value Theorem, , http://dx.doi.org/10.48550/arxiv.1910.07329

Preprints | 2019

Chen C; Shparlinski IE, 2019, Restricted mean value theorems and metric theory of restricted Weyl sums, , http://dx.doi.org/10.48550/arxiv.1912.01307

Preprints | 2019

Chen C; Shparlinski IE, 2019, Small values of Weyl sums, , http://dx.doi.org/10.48550/arxiv.1907.03101

Preprints | 2019

Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height, , http://dx.doi.org/10.48550/arxiv.1909.00135

Preprints | 2019

Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2019, Bilinear forms in Weyl sums for modular square roots and applications, , http://dx.doi.org/10.48550/arxiv.1908.10143

Preprints | 2019

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, , http://dx.doi.org/10.48550/arxiv.1912.00345

Preprints | 2019

Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2019, On the distribution of multiplicatively dependent vectors, , http://dx.doi.org/10.48550/arxiv.1903.09796

Preprints | 2019

Macourt S; Shparlinski IE, 2019, Double Sums of Kloosterman Sums in Finite Fields, , http://dx.doi.org/10.48550/arxiv.1903.10070

Preprints | 2019

Mérai L; Ostafe A; Shparlinski IE, 2019, Dynamical irreducibility of polynomials modulo primes, , http://dx.doi.org/10.48550/arxiv.1905.11657

Preprints | 2019

Mérai L; Shparlinski IE, 2019, Unlikely intersections over finite fields: polynomial orbits in small subgroups, , http://dx.doi.org/10.48550/arxiv.1904.12621

Preprints | 2019

Ostafe A; Pottmeyer L; Shparlinski IE, 2019, Perfect powers in value sets and orbits of polynomials, , http://dx.doi.org/10.48550/arxiv.1907.12057

Preprints | 2019

Sha M; Shparlinski IE, 2019, Möbius Randomness Law for Frobenius Traces, , http://dx.doi.org/10.48550/arxiv.1909.00969

Preprints | 2019

Shparlinski IE; Technau M, 2019, Kloosterman sums with twice-differentiable functions, , http://dx.doi.org/10.48550/arxiv.1902.05989

Preprints | 2019

de la Bretèche R; Kurlberg P; Shparlinski IE, 2019, On the number of products which form perfect powers and discriminants of multiquadratic extensions, , http://dx.doi.org/10.48550/arxiv.1901.10694

Preprints | 2018

Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2018, Counting integers with a smooth totient, , http://dx.doi.org/10.48550/arxiv.1809.01214

Preprints | 2018

Banks WD; Shparlinski IE, 2018, Sums with the Mobius function twisted by characters with powerful moduli, , http://dx.doi.org/10.48550/arxiv.1801.10276

Preprints | 2018

Bordellès O; Dai L; Heyman R; Pan H; Shparlinski IE, 2018, On a sum involving the Euler function, , http://dx.doi.org/10.48550/arxiv.1808.00188

Preprints | 2018

Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2018, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups, , http://dx.doi.org/10.48550/arxiv.1811.04971

Preprints | 2018

Kerr B; Shparlinski IE, 2018, Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions, , http://dx.doi.org/10.48550/arxiv.1811.09329

Preprints | 2018

Korolev MA; Shparlinski IE, 2018, Sums of algebraic trace functions twisted by arithmetic functions, , http://dx.doi.org/10.48550/arxiv.1804.01337

Preprints | 2018

Munsch M; Shparlinski IE; Yau KH, 2018, Smooth squarefree and square-full integers in arithmetic progressions, , http://dx.doi.org/10.48550/arxiv.1810.02573

Preprints | 2018

Mérai L; Shparlinski IE, 2018, Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$, , http://dx.doi.org/10.48550/arxiv.1812.08837

Preprints | 2018

Mérai L; Shparlinski IE, 2018, Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields, , http://dx.doi.org/10.48550/arxiv.1803.02165

Preprints | 2018

Pakovich F; Shparlinski IE, 2018, Level curves of rational functions and unimodular points on rational curves, , http://dx.doi.org/10.48550/arxiv.1805.02913

Preprints | 2018

Ricotta G; Royer E; Shparlinski I, 2018, Kloosterman paths of prime powers moduli, II, , http://dx.doi.org/10.48550/arxiv.1810.01150

Preprints | 2018

Shkredov ID; Shparlinski IE, 2018, Double Character Sums with Intervals and Arbitrary Sets in Finite Fields, , http://dx.doi.org/10.48550/arxiv.1803.08699

Preprints | 2018

Shparlinski IE; Voloch JF, 2018, Binomial exponential sums, , http://dx.doi.org/10.48550/arxiv.1811.00765

Preprints | 2018

Shparlinski IE; Voloch JF, 2018, Value sets of sparse polynomials, , http://dx.doi.org/10.48550/arxiv.1809.02708

Preprints | 2018

Shparlinski IE; Winterhof A, 2018, Codes correcting restricted errors, , http://dx.doi.org/10.48550/arxiv.1811.03375

Preprints | 2017

Abdalaoui EHE; Shparlinski IE, 2017, Disjointness of the Möbius Transformation and Möbius Function, , http://dx.doi.org/10.48550/arxiv.1711.11062

Preprints | 2017

Bordellès O; Luca F; Moree P; Shparlinski IE, 2017, Denominators of Bernoulli polynomials, , http://dx.doi.org/10.48550/arxiv.1706.09804

Preprints | 2017

Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2017, Orbits of Polynomial Dynamical Systems Modulo Primes, , http://dx.doi.org/10.48550/arxiv.1702.01976

Preprints | 2017

Chang M-C; Kerr B; Shparlinski IE, 2017, On the exponential large sieve inequality for sparse sequences modulo primes, , http://dx.doi.org/10.48550/arxiv.1706.04776

Preprints | 2017

Dubickas A; Sha M; Shparlinski IE, 2017, On distances in lattices from algebraic number fields, , http://dx.doi.org/10.48550/arxiv.1703.02163

Preprints | 2017

Gómez-Pérez D; Mérai L; Shparlinski IE, 2017, On the Complexity of Exact Counting of Dynamically Irreducible Polynomials, , http://dx.doi.org/10.48550/arxiv.1706.04392

Preprints | 2017

Karpinski M; Mérai L; Shparlinski IE, 2017, Identity Testing and Interpolation from High Powers of Polynomials of Large Degree over Finite Fields, , http://dx.doi.org/10.48550/arxiv.1708.09095

Preprints | 2017

Kerr B; Shparlinski IE; Yau KH, 2017, A refinement of the Burgess bound for character sums, , http://dx.doi.org/10.48550/arxiv.1711.10582

Preprints | 2017

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, , http://dx.doi.org/10.48550/arxiv.1711.05335

Preprints | 2017

Luca F; Sha M; Shparlinski IE, 2017, On two functions arising in the study of the Euler and Carmichael quotients, , http://dx.doi.org/10.48550/arxiv.1705.00388

Preprints | 2017

Luca F; Shparlinski IE, 2017, On the error term of a lattice counting problem, , http://dx.doi.org/10.48550/arxiv.1705.08714

Preprints | 2017

Macourt S; Shkredov ID; Shparlinski IE, 2017, Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields, , http://dx.doi.org/10.48550/arxiv.1701.06192

Preprints | 2017

Munsch M; Shparlinski IE, 2017, On smooth square-free numbers in arithmetic progressions, , http://dx.doi.org/10.48550/arxiv.1710.04705

Preprints | 2017

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On abelian multiplicatively dependent points on a curve in a torus, , http://dx.doi.org/10.48550/arxiv.1704.04694

Preprints | 2017

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem, , http://dx.doi.org/10.48550/arxiv.1706.05874

Preprints | 2017

Pomerance C; Shparlinski IE, 2017, Connected components of the graph generated by power maps in prime finite fields, , http://dx.doi.org/10.48550/arxiv.1703.09292

Preprints | 2017

Roche-Newton O; Shparlinski I; Winterhof A, 2017, Analogues of the Balog--Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions, , http://dx.doi.org/10.48550/arxiv.1702.04590

Preprints | 2017

Shparlinski I, 2017, Trilinear forms with double Kloosterman sums, , http://dx.doi.org/10.48550/arxiv.1710.02777

Preprints | 2017

Shparlinski IE, 2017, Character sums with smooth numbers, , http://dx.doi.org/10.48550/arxiv.1705.10148

Preprints | 2017

Shparlinski IE, 2017, On short products of primes in arithmetic progressions, , http://dx.doi.org/10.48550/arxiv.1705.06087

Preprints | 2016

Banks W; Shparlinski I, 2016, Bounds on short character sums and L-functions for characters with a smooth modulus, , http://dx.doi.org/10.48550/arxiv.1605.07553

Preprints | 2016

Banks WD; Shparlinski IE, 2016, On the number of distinct quadratic fields generated by the Shanks sequence, , http://dx.doi.org/10.48550/arxiv.1602.06473

Preprints | 2016

Bell J; Shparlinski IE, 2016, Power Series Approximations to Fekete Polynomials, , http://dx.doi.org/10.48550/arxiv.1611.04356

Preprints | 2016

Dietmann R; Elsholtz C; Shparlinski IE, 2016, Prescribing the binary digits of squarefree numbers and quadratic residues, , http://dx.doi.org/10.48550/arxiv.1601.04754

Preprints | 2016

Gómez-Pérez D; Shparlinski IE, 2016, Arithmetic Properties of Integers in Chains and Reflections of $g$-ary Expansions, , http://dx.doi.org/10.48550/arxiv.1609.05950

Conference Papers | 2016

Kohel D; Shparlinski I, 2016, 'Preface', in Contemporary Mathematics, pp. vii - viii

Preprints | 2016

Liu K; Shparlinski IE; Zhang T, 2016, Bilinear Forms with Exponential Sums with Binomials, , http://dx.doi.org/10.48550/arxiv.1611.06635

Preprints | 2016

Liu K; Shparlinski IE; Zhang T, 2016, Cancellations between Kloosterman sums modulo a prime power with prime arguments, , http://dx.doi.org/10.48550/arxiv.1612.05905

Preprints | 2016

Liu K; Shparlinski IE; Zhang T, 2016, Divisor problem in arithmetic progressions modulo a prime power, , http://dx.doi.org/10.48550/arxiv.1602.03583

Preprints | 2016

Liu K; Shparlinski IE; Zhang T, 2016, Squares in Piatetski--Shapiro Sequences, , http://dx.doi.org/10.48550/arxiv.1610.07395

Preprints | 2016

Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2016, On multiplicatively dependent vectors of algebraic numbers, , http://dx.doi.org/10.48550/arxiv.1606.02874

Preprints | 2016

Petridis G; Shparlinski IE, 2016, Bounds on trilinear and quadrilinear exponential sums, , http://dx.doi.org/10.48550/arxiv.1604.08469

Preprints | 2016

Shkredov ID; Shparlinski IE, 2016, On Some Multiple Character Sums, , http://dx.doi.org/10.48550/arxiv.1610.01061

Conference Papers | 2016

Shparlinski I; Childs AM; van Dam W, 2016, 'Optimal Quantum Algorithm for Polynomial Interpolation', in Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi (ed.), Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming, DROPS, Rome, pp. 16:1 - 16:13, presented at 43rd International Colloquium on Automata, Languages, and Programming, Rome, 11 July 2016 - 15 July 2016, http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.16

Preprints | 2016

Shparlinski IE; Zhang TP, 2016, Cancellations Amongst Kloosterman Sums, , http://dx.doi.org/10.48550/arxiv.1601.05123

Preprints | 2016

Shparlinski IE; Zhao L, 2016, Elliptic curves in isogeny classes, , http://dx.doi.org/10.48550/arxiv.1611.05258

Preprints | 2016

Shparlinski IE; Zumalacárregui A, 2016, Sums of inverses in thin sets of finite fields, , http://dx.doi.org/10.48550/arxiv.1611.07647

Conference Papers | 2016

Shparlinski IE, 2016, 'Dynamical systems of non-algebraic origin: Fixed points and orbit lengths', in Kolyada S; Moller M; Moree P; Ward T (eds.), DYNAMICS AND NUMBERS, AMER MATHEMATICAL SOC, Max Planck Inst Math, Bonn, GERMANY, pp. 261 - 283, presented at International Conference on Dynamics and Numbers, Max Planck Inst Math, Bonn, GERMANY, 21 July 2014 - 25 July 2014, http://dx.doi.org/10.1090/conm/669/13432

Preprints | 2016

Shparlinski IE, 2016, Bilinear Forms with Kloosterman and Gauss Sums, , http://dx.doi.org/10.48550/arxiv.1608.06160

Preprints | 2016

Shparlinski IE, 2016, Constructing Dominating Sets in Circulant Graphs, , http://dx.doi.org/10.48550/arxiv.1602.01286

Preprints | 2015

Banks WD; Guo VZ; Shparlinski IE, 2015, Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$, , http://dx.doi.org/10.48550/arxiv.1508.03281

Preprints | 2015

Camburu O-M; Ciolan E-A; Luca F; Moree P; Shparlinski IE, 2015, Cyclotomic coefficients: gaps and jumps, , http://dx.doi.org/10.48550/arxiv.1507.07098

Preprints | 2015

Childs AM; van Dam W; Hung S-H; Shparlinski IE, 2015, Optimal quantum algorithm for polynomial interpolation, , http://dx.doi.org/10.48550/arxiv.1509.09271

Preprints | 2015

D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2015, Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems, , http://dx.doi.org/10.48550/arxiv.1505.05814

Preprints | 2015

Heyman R; Shparlinski IE, 2015, Counting irreducible binomials over finite fields, , http://dx.doi.org/10.48550/arxiv.1504.01172

Preprints | 2015

Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski I, 2015, Polynomial Interpolation and Identity Testing from High Powers over Finite Fields, , http://dx.doi.org/10.48550/arxiv.1502.06631

Preprints | 2015

Munsch M; Shparlinski IE, 2015, Upper and lower bounds for higher moments of theta functions, , http://dx.doi.org/10.48550/arxiv.1506.01999

Preprints | 2015

Nguyen PQ; Shparlinski IE, 2015, Counting Co-Cyclic Lattices, , http://dx.doi.org/10.48550/arxiv.1505.06429

Preprints | 2015

Sha M; Shparlinski IE, 2015, The Sato--Tate Distribution in Families of Elliptic Curves with a Rational Parameter of Bounded Height, , http://dx.doi.org/10.48550/arxiv.1512.07301

Preprints | 2015

Shparlinski IE; Weingartner AJ, 2015, An explicit polynomial analogue of Romanoff's theorem, , http://dx.doi.org/10.48550/arxiv.1510.08991

Preprints | 2015

Shparlinski IE, 2015, Linear Congruences with Ratios, , http://dx.doi.org/10.48550/arxiv.1503.03196

Preprints | 2015

Shparlinski IE, 2015, Linear Equations with Rational Fractions of Bounded Height and Stochastic Matrices, , http://dx.doi.org/10.48550/arxiv.1503.02370

Preprints | 2015

Shparlinski IE, 2015, On Bilinear Exponential and Character Sums with Reciprocals of Polynomials, , http://dx.doi.org/10.48550/arxiv.1504.03192

Preprints | 2015

de la Bretèche R; Sha M; Shparlinski IE; Voloch JF, 2015, The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1509.03009

Preprints | 2014

Banks WD; Shparlinski IE, 2014, Fractional parts of Dedekind sums, , http://dx.doi.org/10.48550/arxiv.1411.1820

Preprints | 2014

Blackburn SR; Konyagin SV; Shparlinski IE, 2014, Counting Additive Decompositions of Quadratic Residues in Finite Fields, , http://dx.doi.org/10.48550/arxiv.1403.2589

Preprints | 2014

Chang M-C; Shparlinski IE, 2014, Double Character Sums over Subgroups and Intervals, , http://dx.doi.org/10.48550/arxiv.1401.6611

Preprints | 2014

Chang M-C; Shparlinski IE, 2014, On the Density of Integer Points on Generalised Markoff-Hurwitz and Dwork Hypersurfaces, , http://dx.doi.org/10.48550/arxiv.1408.4514

Preprints | 2014

Dubickas A; Sha M; Shparlinski IE, 2014, Explicit form of Cassels' $p$-adic embedding theorem for number fields, , http://dx.doi.org/10.48550/arxiv.1401.6819

Preprints | 2014

Fite F; Shparlinski IE, 2014, On the singularity of the Demjanenko matrix of quotients of Fermat curves, , http://dx.doi.org/10.48550/arxiv.1404.5178

Preprints | 2014

Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values, , http://dx.doi.org/10.48550/arxiv.1401.1331

Preprints | 2014

Gathen JVZ; Shparlinski IE, 2014, Circulant graphs and GCD and LCM of Subsets, , http://dx.doi.org/10.48550/arxiv.1402.5449

Preprints | 2014

Harman G; Shparlinski IE, 2014, Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients, , http://dx.doi.org/10.48550/arxiv.1408.4515

Preprints | 2014

Heyman R; Shparlinski IE, 2014, On the Greatest Common Divisor of Shifted Sets, , http://dx.doi.org/10.48550/arxiv.1402.1208

Preprints | 2014

Kurlberg P; Luca F; Shparlinski I, 2014, On the Fixed Points of the Map x -> x^x Modulo a Prime, , http://dx.doi.org/10.48550/arxiv.1402.4464

Preprints | 2014

Munsch M; Shparlinski I, 2014, Congruences with intervals and subgroups modulo a prime, , http://dx.doi.org/10.48550/arxiv.1412.0440

Preprints | 2014

Roche-Newton O; Shparlinski I, 2014, Polynomial Values in Subfields and Affine Subspaces of Finite Fields, , http://dx.doi.org/10.48550/arxiv.1407.2273

Preprints | 2014

Sha M; Shparlinski IE, 2014, Effective results on linear dependence for elliptic curves, , http://dx.doi.org/10.48550/arxiv.1410.1596

Preprints | 2014

Sha M; Shparlinski IE, 2014, Lang-Trotter and Sato-Tate Distributions in Single and Double Parametric Families of Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1404.0182

Preprints | 2014

Shparlinski IE; Sutherland AV, 2014, Finding elliptic curves with a subgroup of prescribed size, , http://dx.doi.org/10.48550/arxiv.1403.7887

Preprints | 2014

Shparlinski IE; Sutherland AV, 2014, On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average, , http://dx.doi.org/10.48550/arxiv.1404.0399

Preprints | 2014

Shparlinski IE, 2014, Cayley graphs generated by small degree polynomials over finite fields, , http://dx.doi.org/10.48550/arxiv.1402.3492

Preprints | 2014

Shparlinski IE, 2014, On the Density of Integer Points on the Generalised Markoff-Hurwitz and Dwork Hypersurfaces, , http://dx.doi.org/10.48550/arxiv.1404.5866

Preprints | 2014

Shparlinski IE, 2014, Polynomial Values in Small Subgroups of Finite Fields, , http://dx.doi.org/10.48550/arxiv.1401.0964

Preprints | 2013

Ahmadi O; Shparlinski IE, 2013, Exponential Sums over Points of Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1302.4210

Preprints | 2013

Banks WD; Shparlinski IE, 2013, On Gauss sums and the evaluation of Stechkin's constant, , http://dx.doi.org/10.48550/arxiv.1310.5669

Preprints | 2013

Bourgain J; Konyagin S; Shparlinski I, 2013, Character Sums and Deterministic Polynomial Root Finding in Finite Fields, , http://dx.doi.org/10.48550/arxiv.1308.4803

Preprints | 2013

Chen Z; Shparlinski IE; Winterhof A, 2013, Covering sets for limited-magnitude errors, , http://dx.doi.org/10.48550/arxiv.1310.0120

Preprints | 2013

Gomez-Perez D; Shparlinski IE, 2013, Subgroups Generated by Rational Functions in Finite Fields, , http://dx.doi.org/10.48550/arxiv.1309.7378

Preprints | 2013

Heyman R; Shparlinski IE, 2013, On Shifted Eisenstein Polynomials, , http://dx.doi.org/10.48550/arxiv.1302.6097

Preprints | 2013

Heyman R; Shparlinski IE, 2013, On the Number of Eisenstein Polynomials of Bounded Height, , http://dx.doi.org/10.48550/arxiv.1302.6094

Preprints | 2013

Kaszian J; Moree P; Shparlinski IE, 2013, Periodic Structure of the Exponential Pseudorandom Number Generator, , http://dx.doi.org/10.48550/arxiv.1312.1311

Preprints | 2013

Koh D; Shen C-Y; Shparlinski I, 2013, Averaging operators over homogeneous varieties over finite fields, , http://dx.doi.org/10.48550/arxiv.1304.1990

Preprints | 2013

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2013, Functional Graphs of Polynomials over Finite Fields, , http://dx.doi.org/10.48550/arxiv.1307.2718

Preprints | 2013

Konyagin SV; Shparlinski IE, 2013, Quadratic Non-residues in Short Intervals, , http://dx.doi.org/10.48550/arxiv.1311.7016

Preprints | 2013

Luca F; Radziwill M; Shparlinski IE, 2013, On the Typical Size and Cancelations Among the Coefficients of Some Modular Forms, , http://dx.doi.org/10.48550/arxiv.1308.6606

Preprints | 2013

Shparlinski I, 2013, Additive Decompositions of Subgroups of Finite Fields, , http://dx.doi.org/10.48550/arxiv.1301.2872

Preprints | 2013

Shparlinski I, 2013, Evasive Properties of Sparse Graphs and Some Linear Equations in Primes, , http://dx.doi.org/10.48550/arxiv.1304.0188

Preprints | 2013

Shparlinski I, 2013, Multiple Exponential and Character Sums with Monomials, , http://dx.doi.org/10.48550/arxiv.1309.0324

Preprints | 2013

Shparlinski IE, 2013, On Solutions to Some Polynomial Congruences in Small Boxes, , http://dx.doi.org/10.48550/arxiv.1301.1758

Preprints | 2012

Baker RC; Banks WD; Brüdern J; Shparlinski IE; Weingartner AJ, 2012, Piatetski-Shapiro sequences, , http://dx.doi.org/10.48550/arxiv.1203.5884

Preprints | 2012

Bourgain J; Garaev M; Konyagin S; Shparlinski I, 2012, On Congruences with Products of Variables from Short Intervals and Applications, , http://dx.doi.org/10.48550/arxiv.1203.0017

Preprints | 2012

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, Multiplicative Congruences with Variables from Short Intervals, , http://dx.doi.org/10.48550/arxiv.1210.6429

Preprints | 2012

Dietmann R; Elsholtz C; Shparlinski IE, 2012, On Gaps Between Primitive Roots in the Hamming Metric, , http://dx.doi.org/10.48550/arxiv.1207.0842

Preprints | 2012

Harvey D; Shparlinski I, 2012, Statistics of Different Reduction Types of Fermat Curves, , http://dx.doi.org/10.48550/arxiv.1212.0915

Preprints | 2012

Kerr B; Shparlinski IE, 2012, On the Distribution of Values and Zeros of Polynomial Systems over Arbitrary Sets, , http://dx.doi.org/10.48550/arxiv.1210.6721

Preprints | 2012

Luca F; Shparlinski IE, 2012, On the Counting Function of Elliptic Carmichael Numbers, , http://dx.doi.org/10.48550/arxiv.1206.3476

Preprints | 2012

Shparlinski I, 2012, On the Product of Small Elkies Primes, , http://dx.doi.org/10.48550/arxiv.1301.0035

Preprints | 2012

Shparlinski IE; Steiner W, 2012, On digit patterns in expansions of rational numbers with prime denominator, , http://dx.doi.org/10.48550/arxiv.1205.5673

Preprints | 2012

Shparlinski IE, 2012, On the Lang-Trotter and Sato-Tate Conjectures on Average for Polynomial Families of Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1203.6500

Preprints | 2011

Bibak K; Shparlinski IE, 2011, On fully split lacunary polynomials in finite fields, , http://dx.doi.org/10.48550/arxiv.1111.4023

Preprints | 2011

Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1102.1053

Preprints | 2011

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2011, On the Hidden Shifted Power Problem, , http://dx.doi.org/10.48550/arxiv.1110.0812

Preprints | 2011

Bourgain J; Konyagin S; Shparlinski I, 2011, Distribution on elements of cosets of small subgroups and applications, , http://dx.doi.org/10.48550/arxiv.1103.0567

Preprints | 2011

Bourgain J; Konyagin SV; Shparlinski IE, 2011, Distribution of Elements of Cosets of Small Subgroups and Applications,

Preprints | 2011

Chang M-C; Cilleruelo J; Garaev MZ; Hernández J; Shparlinski IE; Zumalacárregui A, 2011, Points on curves in small boxes en applications, , http://dx.doi.org/10.48550/arxiv.1111.1543

Preprints | 2011

Ostafe A; Shparlinski I, 2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems, , http://dx.doi.org/10.48550/arxiv.1109.0575

Preprints | 2011

Shparlinski IE; Sutherland AV, 2011, On the Distribution of Atkin and Elkies Primes, , http://dx.doi.org/10.48550/arxiv.1112.3390

Preprints | 2011

Shparlinski IE, 2011, Fermat quotients: Exponential sums, value set and primitive roots, , http://dx.doi.org/10.48550/arxiv.1104.3909

Preprints | 2011

Shparlinski IE, 2011, Modular Hyperbolas, , http://dx.doi.org/10.48550/arxiv.1103.2879

Preprints | 2011

Shparlinski IE, 2011, On vanishing Fermat quotients and a bound of the Ihara sum, , http://dx.doi.org/10.48550/arxiv.1104.3910

Preprints | 2010

Balog A; Broughan KA; Shparlinski IE, 2010, On the Number of Solutions of Exponential Congruences, , http://dx.doi.org/10.48550/arxiv.1003.1997

Preprints | 2010

Banks WD; Pappalardi F; Shparlinski IE, 2010, On group structures realized by elliptic curves over arbitrary finite fields, , http://dx.doi.org/10.48550/arxiv.1003.3004

Preprints | 2010

Farashahi RR; Shparlinski IE, 2010, On Pseudopoints of Algebraic Curves, , http://dx.doi.org/10.48550/arxiv.1005.4775

Preprints | 2010

Farashahi RR; Shparlinski IE, 2010, On group structures realized by elliptic curves over a fixed finite field, , http://dx.doi.org/10.48550/arxiv.1003.3000

Preprints | 2010

Farashahi RR; Shparlinski IE, 2010, Pseudorandom Bits From Points on Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1005.4771

Preprints | 2010

Gonzalez JJA; Luca F; Pomerance C; Shparlinski I, 2010, On numbers $n$ dividing the $n$th term of a linear recurrence, , http://dx.doi.org/10.48550/arxiv.1010.4544

Preprints | 2010

Konyagin SV; Shparlinski IE, 2010, On the Convex Hull of the Points on Modular Hyperbolas, , http://dx.doi.org/10.48550/arxiv.1012.1444

Preprints | 2010

Ostafe A; Shparlinski IE, 2010, Pseudorandomness and Dynamics of Fermat Quotients, , http://dx.doi.org/10.48550/arxiv.1001.1504

Preprints | 2010

Shparlinski I, 2010, On Small Solutions to Quadratic Congruences, , http://dx.doi.org/10.48550/arxiv.1004.0715

Preprints | 2010

Shparlinski IE, 2010, On the Restricted Divisor Function in Arithmetic Progressions, , http://dx.doi.org/10.48550/arxiv.1003.5347

Preprints | 2009

Ahmadi O; Shparlinski IE, 2009, On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields, , http://dx.doi.org/10.48550/arxiv.0907.3664

Preprints | 2009

Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski I, 2009, Some Additive Combinatorics Problems in Matrix Rings, , http://dx.doi.org/10.48550/arxiv.0902.3482

Preprints | 2009

Glebsky L; Shparlinski IE, 2009, Short Cycles in Repeated Exponentiation Modulo a Prime, , http://dx.doi.org/10.48550/arxiv.0908.3920

Preprints | 2009

Ostafe A; Shparlinski I, 2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators, , http://dx.doi.org/10.48550/arxiv.0902.3884

Preprints | 2009

Ostafe A; Shparlinski IE, 2009, On the Length of Critical Orbits of Stable Quadratic Polynomials, , http://dx.doi.org/10.48550/arxiv.0909.3972

Preprints | 2009

Ostafe A; Shparlinski IE, 2009, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials, , http://dx.doi.org/10.48550/arxiv.0908.4519

Preprints | 2009

Pomerance C; Shparlinski IE, 2009, Rank statistics for a family of elliptic curves over a function field, , http://dx.doi.org/10.48550/arxiv.0903.2866

Preprints | 2009

Shparlinski IE; Stange KE, 2009, Character sums with division polynomials, , http://dx.doi.org/10.48550/arxiv.0912.5246

Preprints | 2009

Shparlinski IE, 2009, On Point Sets in Vector Spaces over Finite Fields That Determine Only Acute Angle Triangles, , http://dx.doi.org/10.48550/arxiv.0903.2520

Preprints | 2008

Ahmadi O; Shparlinski I, 2008, On the Sum-Product Problem on Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.0806.0640

Preprints | 2008

Loiperdinger SS; Shparlinski IE, 2008, On the Distribution of the Euler Function of Shifted Smooth Numbers, , http://dx.doi.org/10.48550/arxiv.0810.1093

Preprints | 2008

Naccache D; Shparlinski IE, 2008, Divisibility, Smoothness and Cryptographic Applications, , http://dx.doi.org/10.48550/arxiv.0810.2067

Preprints | 2008

Shparlinski I, 2008, On Some Weighted Average Values of L-functions, , http://dx.doi.org/10.48550/arxiv.0802.2378

Conference Papers | 2008

Shparlinski IE, 2008, 'OPEN PROBLEMS ON EXPONENTIAL AND CHARACTER SUMS', in Aoki T; Kanemitsu S; Liu JY (eds.), NUMBER THEORY: DREAMING IN DREAMS, WORLD SCIENTIFIC PUBL CO PTE LTD, JAPAN, Kinki Univ, Higashiosaka, pp. 222 - 242, presented at 5th China-Japan Seminar on Number Theory, JAPAN, Kinki Univ, Higashiosaka, 27 August 2008 - 31 August 2008, http://dx.doi.org/10.1142/9789814289924_0010

Conference Papers | 2008

Shparlinski IE, 2008, 'Pseudorandom Points on Elliptic Curves over Finite Fields', in Algebraic Geometry and Its Applications, WORLD SCIENTIFIC, presented at Proceedings of the First SAGA Conference, http://dx.doi.org/10.1142/9789812793430_0006

Preprints | 2008

Shparlinski IE, 2008, On Quadratic Fields Generated by Discriminants of Irreducible Trinomials, , http://dx.doi.org/10.48550/arxiv.0811.1300

Preprints | 2008

van Dam W; Shparlinski IE, 2008, Classical and Quantum Algorithms for Exponential Congruences, , http://dx.doi.org/10.48550/arxiv.0804.1109

Preprints | 2007

Ahmadi O; Shparlinski IE; Voloch JF, 2007, Multiplicative Order of Gauss Periods, , http://dx.doi.org/10.48550/arxiv.0707.4034

Preprints | 2007

Banks WD; Shparlinski IE, 2007, Prime numbers with Beatty sequences, , http://dx.doi.org/10.48550/arxiv.0708.1015

Preprints | 2007

Cojocaru AC; Shparlinski IE, 2007, Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average, , http://dx.doi.org/10.48550/arxiv.0705.3861

Conference Papers | 2007

EI-Mahassni E; Shparlinski IE, 2007, 'On the distribution of the elliptic curve power generator', in Mullen GL; Panario D; Shparlinski IE (eds.), FINITE FIELDS AND APPLICATIONS, AMER MATHEMATICAL SOC, AUSTRALIA, Melbourne, pp. 111 - 118, presented at 8th International Conference on Finite Fields and Applications, AUSTRALIA, Melbourne, 09 July 2007 - 13 July 2007, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000257880200009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Preprints | 2007

Ford K; Luca F; Shparlinski IE, 2007, On the largest prime factor of the Mersenne numbers, , http://dx.doi.org/10.48550/arxiv.0704.1327

Preprints | 2007

Friedlander JB; Kurlberg P; Shparlinski IE, 2007, Products in Residue Classes, , http://dx.doi.org/10.48550/arxiv.0708.1562

Preprints | 2007

Graham SW; Shparlinski IE, 2007, On RSA Moduli with Almost Half of the Bits Prescribed, , http://dx.doi.org/10.48550/arxiv.0709.2704

Preprints | 2007

Khan MR; Shparlinski IE; Yankov CL, 2007, On the Convex Closure of the Graph of Modular Inversions, , http://dx.doi.org/10.48550/arxiv.0711.4100

Preprints | 2007

Konyagin SV; Pomerance C; Shparlinski IE, 2007, On the Distribution of Pseudopowers, , http://dx.doi.org/10.48550/arxiv.0712.1080

Conference Papers | 2007

Luca F; Shparlinski IE, 2007, 'On Special Finite Fields', in Lachaud G; Ritzenthaler C; Tsfasman MA (eds.), ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, AMER MATHEMATICAL SOC, FRANCE, Ctr Int Rencontres Math, Marseilles, pp. 163 - 167, presented at 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, FRANCE, Ctr Int Rencontres Math, Marseilles, 05 November 2007 - 09 November 2007, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267679700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Preprints | 2007

Pomerance C; Shparlinski IE, 2007, On Pseudosquares and Pseudopowers, , http://dx.doi.org/10.48550/arxiv.0712.1081

Preprints | 2007

Saxena N; Severini S; Shparlinski I, 2007, Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics, , http://dx.doi.org/10.48550/arxiv.quant-ph/0703236

Conference Papers | 2007

Shparlinski IE; Steinfeld R, 2007, 'Collision in the DSA Function', in Li Y; Ling S; Niederreiter H; Wang H; Xing C; Zhang S (eds.), CODING AND CRYPTOLOGY, WORLD SCIENTIFIC PUBL CO PTE LTD, PEOPLES R CHINA, Fujian Normal Univ, Wuui Mt, pp. 226 - 232, presented at 1st International Workshop on Coding and Cryptology, PEOPLES R CHINA, Fujian Normal Univ, Wuui Mt, 11 June 2007 - 15 June 2007, http://dx.doi.org/10.1142/9789812832245_0017

Preprints | 2007

Shparlinski IE; Voloch JF, 2007, Visible Points on Curves over Finite Fields, , http://dx.doi.org/10.48550/arxiv.0704.2446

Preprints | 2007

Shparlinski IE, 2007, Approximation by Several Rationals, , http://dx.doi.org/10.48550/arxiv.0707.3371

Preprints | 2007

Shparlinski IE, 2007, Arithmetic and Geometric Progressions in Productsets over Finite Fields, , http://dx.doi.org/10.48550/arxiv.0711.1800

Preprints | 2007

Shparlinski IE, 2007, On The Solvability of Bilinear Equations in Finite Fields, , http://dx.doi.org/10.48550/arxiv.0708.2130

Preprints | 2007

Shparlinski IE, 2007, Tate-Shafarevich Groups and Frobenius Fields of Reductions of Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.0707.2976

Preprints | 2006

Banks WD; Garaev MZ; Heath-Brown DR; Shparlinski IE, 2006, Density of non-residues in Burgess-type intervals and applications, , http://dx.doi.org/10.48550/arxiv.math/0607692

Preprints | 2006

Banks WD; Shparlinski IE, 2006, Character sums with Beatty sequences on Burgess-type intervals, , http://dx.doi.org/10.48550/arxiv.math/0608042

Preprints | 2006

Banks WD; Shparlinski IE, 2006, Integers with a large smooth divisor, , http://dx.doi.org/10.48550/arxiv.math/0601460

Preprints | 2006

Banks WD; Shparlinski IE, 2006, Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height, , http://dx.doi.org/10.48550/arxiv.math/0609144

Preprints | 2006

Ford K; Shparlinski I, 2006, On curves over finite fields with Jacobians of small exponent, , http://dx.doi.org/10.48550/arxiv.math/0607474

Preprints | 2006

Luca F; Shparlinski IE, 2006, Arithmetic properties of the Ramanujan function, , http://dx.doi.org/10.48550/arxiv.math/0607591

Preprints | 2006

Shparlinski I, 2006, On a Generalisation of a Lehmer Problem, , http://dx.doi.org/10.48550/arxiv.math/0607414

Conference Papers | 2006

Shparlinski IE, 2006, 'DISTRIBUTION OF POINTS ON MODULAR HYPERBOLAS', in Kanemitsu S; Liu JY (ed.), NUMBER THEORY: SAILING ON THE SEA OF NUMBER THEORY, WORLD SCIENTIFIC PUBL CO PTE LTD, PEOPLES R CHINA, Weihai, pp. 155 - 189, presented at 4th China-Japan Seminar on Number Theory, PEOPLES R CHINA, Weihai, 30 August 2006 - 03 September 2006, http://dx.doi.org/10.1142/9789812770134_0007

Preprints | 2006

Shparlinski IE, 2006, Distribution of modular inverses and multiples of small integers and the Sato--Tate conjecture on average, , http://dx.doi.org/10.48550/arxiv.math/0608596

Preprints | 2006

Shparlinski IE, 2006, On Some Dynamical Systems in Finite Fields and Residue Rings, , http://dx.doi.org/10.48550/arxiv.math/0607779

Preprints | 2006

Shparlinski IE, 2006, On the distribution of Kloosterman sums, , http://dx.doi.org/10.48550/arxiv.math/0608595

Preprints | 2005

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, Uniform Distribution of Fractional Parts Related to Pseudoprimes, , http://dx.doi.org/10.48550/arxiv.math/0505098

Preprints | 2005

Klappenecker A; Roetteler M; Shparlinski I; Winterhof A, 2005, On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States, , http://dx.doi.org/10.48550/arxiv.quant-ph/0503239

Conference Papers | 2005

Shparlinski IE, 2005, 'Pseudorandom Number Generators from Elliptic Curves', in Luengo I (ed.), RECENT TRENDS IN CRYPTOGRAPHY, AMER MATHEMATICAL SOC, SPAIN, Real Soc Mat Espanola, Santander, pp. 121 - 141, presented at Summer School on Recent Trends in Cryptography, SPAIN, Real Soc Mat Espanola, Santander, 11 July 2005 - 15 July 2005, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000263678500005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Preprints | 2004

Contini S; Croot E; Shparlinski I, 2004, Complexity of Inverting the Euler Function, , http://dx.doi.org/10.48550/arxiv.math/0404116

Preprints | 2004

Everest G; Shparlinski IE, 2004, Prime divisors of sequences associated to elliptic curves, , http://dx.doi.org/10.48550/arxiv.math/0404129

Preprints | 2004

Garaev MZ; Luca F; Shparlinski IE, 2004, Character Sums and Congruences with n!, , http://dx.doi.org/10.48550/arxiv.math/0403422

Preprints | 2004

Garaev MZ; Luca F; Shparlinski IE, 2004, Exponential Sums and Congruences with Factorials, , http://dx.doi.org/10.48550/arxiv.math/0403424

Conference Papers | 2003

Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2003, 'Multiplicative structure of values of the Euler function', in VanDerPoorten A; Stein A (ed.), HIGH PRIMES AND MISDEMEANOURS: LECTURES IN HONOUR OF THE 60TH BIRTHDAY OF HUGH COWIE WILLIAMS, AMER MATHEMATICAL SOC, CANADA, Banff, pp. 29 - 47, presented at Conference in Number Theory in Honour of Hugh C Williams, CANADA, Banff, 24 May 2003 - 30 May 2003, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000223282500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2003

Banks WD; Shparlinski IE, 2003, 'Congruences and exponential sums with the Euler function', in VanDerPoorten A; Stein A (ed.), HIGH PRIMES AND MISDEMEANOURS: LECTURES IN HONOUR OF THE 60TH BIRTHDAY OF HUGH COWIE WILLIAMS, AMER MATHEMATICAL SOC, CANADA, Banff, pp. 49 - 59, presented at Conference in Number Theory in Honour of Hugh C Williams, CANADA, Banff, 24 May 2003 - 30 May 2003, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000223282500004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2003

Shparlinski IE, 2003, 'Orders of points on elliptic curves', in Gutierrez J; Shpilrain V; Yu JT (eds.), AFFINE ALGEBRAIC GEOMETRY, AMER MATHEMATICAL SOC, SPAIN, Seville, pp. 245 - 251, presented at 1st RSME-AMS Joint Meeting, SPAIN, Seville, 19 June 2003 - 21 June 2003, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000227464800015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2003

Shparlinski IE, 2003, 'Playing "hide-and-seek" with numbers: The hidden number problem, lattices and exponential sums', in Garret P; Lieman D (ed.), PUBLIC-KEY CRYPTOGRAPHY, AMER MATHEMATICAL SOC, MD, Baltimore, pp. 153 - 177, presented at Joint Annual Meeting of the American-Mathematical-Society/Mathematical-Association-of-America, MD, Baltimore, 17 January 2003, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000235211700007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2003

Von Zur Gathen J; Shokrollahi A; Shparlinski I, 2003, 'An authentication scheme based on roots of sparse polynomials', in Proceedings - 2003 IEEE Information Theory Workshop, ITW 2003, pp. 159 - 162, http://dx.doi.org/10.1109/ITW.2003.1216719

Conference Papers | 2002

Banks WD; Shparlinski IE, 2002, 'A variant of NTRU with non-invertible polynomials', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 62 - 70, http://dx.doi.org/10.1007/3-540-36231-2_6

Conference Papers | 2002

Lenstra AK; Shparlinski IE, 2002, 'Selective forgery of rsa signatures with fixed-pattern padding', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 228 - 236, http://dx.doi.org/10.1007/3-540-45664-3_16

Conference Papers | 2002

Li WCW; Näslund M; Shparlinski IE, 2002, 'Hidden number problem with the trace and bit security of XTR and LUC', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 433 - 448, http://dx.doi.org/10.1007/3-540-45708-9_28

Conference Papers | 2002

Pomerance C; Shparlinski IE, 2002, 'Smooth orders and cryptographic applications', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 338 - 348, http://dx.doi.org/10.1007/3-540-45455-1_27

Preprints | 2002

Russell A; Shparlinski I, 2002, Classical and Quantum Polynomial Reconstruction via Legendre Symbol Evaluation, , http://dx.doi.org/10.48550/arxiv.quant-ph/0212016

Conference Papers | 2002

Shparlinski IE; Steinfeld R, 2002, 'Chinese remaindering for algebraic numbers in a hidden field', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 349 - 356, http://dx.doi.org/10.1007/3-540-45455-1_28

Conference Papers | 2002

Vasco MIG; Näslund M; Shparlinski IE, 2002, 'The hidden number problem in extension fields and its applications', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 105 - 117

Conference Papers | 2001

Allender E; Saks M; Shparlinski I, 2001, 'A lower bound for primality', in Journal of Computer and System Sciences, pp. 356 - 366, http://dx.doi.org/10.1006/jcss.2000.1725

Conference Papers | 2001

Banks WD; Lieman D; Shparlinski IE; Van To T, 2001, 'Cryptographic applications of sparse Polynomials over Finite Rings', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 206 - 220, http://dx.doi.org/10.1007/3-540-45247-8_17

Conference Papers | 2001

El Mahassni E; Shparlinski I, 2001, 'On the uniformity of distribution of congruential generators over elliptic curves', in Helleseth T; Kumar PV; Yang K (eds.), SEQUENCES AND THEIR APPLICATIONS, PROCEEDINGS, SPRINGER-VERLAG LONDON LTD, NORWAY, BERGEN, pp. 257 - 264, presented at International Conference on Sequences and their Applications (SETA 01), NORWAY, BERGEN, 13 May 2001 - 17 May 2001, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000174706300019&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2001

Lenstra AK; Shparlinski IE, 2001, 'On the security of Lenstra’s variant of DSA without long inversions', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 64 - 72, http://dx.doi.org/10.1007/3-540-44586-2_5

Conference Papers | 2001

Mahassni EE; Nguyen PQ; Shparlinski IE, 2001, 'The insecurity of nyberg–rueppel and other DSA-like signature schemes with partially known nonces', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 97 - 109, http://dx.doi.org/10.1007/3-540-44670-2_9

Conference Papers | 2001

Nguyen PQ; Shparlinski IE, 2001, 'On the insecurity of a server-aided RSA protocol', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 21 - 35, http://dx.doi.org/10.1007/3-540-45682-1_2

Conference Papers | 2001

Plaku E; Shparlinski IE, 2001, 'On polynomial representations of boolean functions related to some number theoretic problems', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 305 - 316, http://dx.doi.org/10.1007/3-540-45294-x_26

Conference Papers | 2001

Shparlinski IE, 2001, 'Exponential sums and lattice reduction: Applications to cryptography', in Mullen GL; Stichtenoth H; TapiaRecillas H (eds.), FINITE FIELDS WITH APPLICATIONS TO CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS, SPRINGER-VERLAG BERLIN, MEXICO, OAXACA, pp. 286 - 298, presented at 6th International Conference on Finite Fields and Applications (Fq6), MEXICO, OAXACA, 21 May 2001 - 26 May 2001, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000179469500023&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2001

Shparlinski IE, 2001, 'On the generalised hidden number problem and bit security of XTR', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 268 - 277, http://dx.doi.org/10.1007/3-540-45624-4_28

Conference Papers | 2000

Banks WD; Griffin F; Lieman D; Shparlinski IE, 2000, 'Non-linear complexity of the naor-reingold pseudo-random function', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 53 - 59, http://dx.doi.org/10.1007/10719994_5

Conference Papers | 2000

Banks WD; Lieman D; Shparlinski IE, 2000, 'An Extremely Small and Efficient identification scheme', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 378 - 384, http://dx.doi.org/10.1007/10718964_31

Conference Papers | 2000

Banks WD; Lieman D; Shparlinski IE, 2000, 'An identification scheme based on sparse polynomials', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 68 - 74, http://dx.doi.org/10.1007/978-3-540-46588-1_6

Conference Papers | 2000

Friedlander JB; Hansen JSD; Shparlinski IE, 2000, 'On the distribution of the power generator modulo a prime power', in Nathanson MB (ed.), UNUSUAL APPLICATIONS OF NUMBER THEORY, AMER MATHEMATICAL SOC, NJ, Piscataway, pp. 71 - 79, presented at DIMACS Workshop on Unusual Applications of Number Theory, NJ, Piscataway, 10 January 2000 - 14 January 2000, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000224833300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 2000

Kohel DR; Shparlinski IE, 2000, 'On exponential sums and group generators for elliptic curves over finite fields', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 395 - 404, http://dx.doi.org/10.1007/10722028_24

Conference Papers | 2000

Niederreiter H; Shparlinski IE, 2000, 'Recent advances in the theory of nonlinear pseudorandom number generators', in Fang KT; Hickernell FJ; Niederreiter H (eds.), MONTE CARLO AND QUASI-MONTE CARLO METHODS 2000, SPRINGER-VERLAG BERLIN, PEOPLES R CHINA, HONG KONG BAPTIST UNIV, HONG KONG, pp. 86 - 102, presented at 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2000), PEOPLES R CHINA, HONG KONG BAPTIST UNIV, HONG KONG, 27 November 2000 - 01 December 2000, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000175526000006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Alexandris N; Burmester M; Chrissikopoulos V; Desmedt Y, 1999, 'Designated 2-verifier proofs and their application to electronic commerce', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 149 - 163, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Allender E; Saks M; Shparlinski I, 1999, 'Lower bound for primality', in Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 10 - 14

Conference Papers | 1999

Alonso C; Gutierrez J; Rubio R, 1999, 'On the dimension and the number of parameters of a unirational variety', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 3 - 9, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Bernasconi A; Damm C; Shparlinski IE, 1999, 'On the average sensitivity of testing square-free numbers', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 291 - 299, http://dx.doi.org/10.1007/3-540-48686-0_29

Conference Papers | 1999

Bernasconi A; Shparlinski I, 1999, 'Circuit complexity of testing square-free numbers', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 47 - 56, http://dx.doi.org/10.1007/3-540-49116-3_4

Conference Papers | 1999

Cai JY; Havas G; Mans B; Nerurkar A; Seifert JP; Shparlinski I, 1999, 'On routing in circulant graphs', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 360 - 369, http://dx.doi.org/10.1007/3-540-48686-0_36

Conference Papers | 1999

Conflitti A, 1999, 'On elements of high order in finite fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 11 - 14, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Dawson E; Simpson L; Golic J, 1999, 'A survey of divide and conquer attacks on certain irregularly clocked stream ciphers', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 165 - 185, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

De Bonis A; De Santis A, 1999, 'New results on the randomness of visual cryptography schemes', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 187 - 201, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800016&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Ding CS; Kohel DR; Ling S, 1999, 'Counting the number of points on affine diagonal curves', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 15 - 24, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Friedlander JB; Pomerance C; Shparlinski IE, 1999, 'Small values of the Carmichael function and cryptographic applications', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 25 - 32, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Gollmann D, 1999, 'Authentication - Myths and misconceptions', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 203 - 225, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800017&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Griffin F; Niederreiter H; Shparlinski IE, 1999, 'On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 87 - 93, http://dx.doi.org/10.1007/3-540-46796-3_9

Conference Papers | 1999

Griffin F; Shparlinski IE, 1999, 'On the linear complexity of the naor—reingold pseudo-random function', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 301 - 308, http://dx.doi.org/10.1007/978-3-540-47942-0_25

Conference Papers | 1999

Han WB, 1999, 'The distribution of the coefficients of primitive polynomials over finite fields', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 43 - 57, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Hoffstein J; Lieman D, 1999, 'The distribution of the quadratic symbol in function fields and a faster mathematical stream cipher', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 59 - 68, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Hoffstein J; Silverman JH, 1999, 'Polynomial rings and efficient public key authentication II', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 269 - 286, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Conference Papers | 1999

Karpinski M; Shparlinski I, 1999, 'On the computational hardness of testing square-freeness of sparse polynomials', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 492 - 497, http://dx.doi.org/10.1007/3-540-46796-3_47

Conference Papers | 1999

Kohel DR, 1999, 'Rational groups of elliptic curves suitable for cryptography', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 69 - 80, presented a

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