Professor Igor   Shparlinski
Professor

Professor Igor Shparlinski

Science
Sch of Mathematics & Statistic

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

Publications

  • Edited Books | 2020
    Professor Igor Shparlinski
    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
    Book Chapters | 2018
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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 | 2011
    Professor Igor Shparlinski
    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 | 2011
    Professor Igor Shparlinski
    Cillerueloa J; Lucab F; Shparlinskic IE, 2011, 'Power values of palindromes', in Frontiers of Combinatorics and Number Theory, pp. 103 - 110
    Book Chapters | 2007
    Professor Igor Shparlinski
    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
    Books | 2006
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Everest G; van der Poorten A; Shparlinski I; Ward T, 2003, Recurrence Sequences, American Mathematical Society, http://dx.doi.org/10.1090/surv/104
    Book Chapters | 2003
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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 | 2003
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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 | 2002
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Books | 2001
    Professor Igor Shparlinski
    Boztaş S; Shparlinski IE, 2001, Preface
    Book Chapters | 1999
    Professor Igor Shparlinski
    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
    Books | 1999
    Professor Igor Shparlinski
    Shparlinski IE, 1999, Finite Fields: Theory and Computation, Springer Netherlands, http://dx.doi.org/10.1007/978-94-015-9239-0
    Books | 1999
    Professor Igor Shparlinski
    Shparlinski I, 1999, Number Theoretic Methods in Cryptography, Birkhäuser Basel, http://dx.doi.org/10.1007/978-3-0348-8664-2
    Book Chapters | 1995
    Professor Igor Shparlinski
    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
    Books | 1992
    Professor Igor Shparlinski
    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 |
    Professor Igor Shparlinski
    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
    Book Chapters |
    Professor Igor Shparlinski
    Kaszián J; Moree P; Shparlinski IE, '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 |
    Professor Igor Shparlinski
    Shparlinski IE, 'Additive Combinatorics over Finite Fields: New Results and Applications', in Finite Fields and Their Applications, DE GRUYTER, http://dx.doi.org/10.1515/9783110283600.233
  • Journal articles | 2021
    Professor Igor Shparlinski
    Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv der Mathematik, http://dx.doi.org/10.1007/s00013-021-01623-y
    Journal articles | 2021
    Professor Igor Shparlinski
    Ghioca D; Shparlinski IE, 2021, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, http://dx.doi.org/10.1016/j.jnt.2021.06.006
    Journal articles | 2021
    Professor Igor Shparlinski
    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, vol. 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478
    Journal articles | 2021
    Professor Igor Shparlinski
    Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, vol. 27, pp. 903 - 917, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2021
    Professor Igor Shparlinski
    Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, vol. 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5
    Journal articles | 2021
    Professor Igor Shparlinski
    Shparlinski IE; Wang Q, 2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, vol. 35, pp. 976 - 987, http://dx.doi.org/10.1137/20M1357731
    Journal articles | 2021
    Professor Igor Shparlinski
    Banks W; Shparlinski I, 2021, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, http://dx.doi.org/10.1112/blms.12524
    Journal articles | 2021
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2021, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, pp. 1 - 20, http://dx.doi.org/10.4153/S0008414X21000080
    Journal articles | 2021
    Professor Igor Shparlinski
    Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, vol. 64, http://dx.doi.org/10.1016/j.jco.2020.101542
    Journal articles | 2021
    Professor Igor Shparlinski
    Sha M; Shparlinski IE, 2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, vol. 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363
    Journal articles | 2021
    Professor Igor Shparlinski
    Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, vol. 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743
    Journal articles | 2021
    Professor Igor Shparlinski
    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, http://dx.doi.org/10.1017/S0004972721000083
    Journal articles | 2021
    Professor Igor Shparlinski
    Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, vol. 219, pp. 228 - 236, http://dx.doi.org/10.1016/j.jnt.2020.09.020
    Journal articles | 2021
    Professor Igor Shparlinski
    Mérai L; Shparlinski IE, 2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, vol. 8, http://dx.doi.org/10.1007/s40687-021-00249-4
    Journal articles | 2021
    Professor Igor Shparlinski
    Shparlinski IE, 2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, vol. 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski IE; Voloch JF, 2020, 'Value Sets of Sparse Polynomials', Canadian Mathematical Bulletin, vol. 63, pp. 187 - 196, http://dx.doi.org/10.4153/S0008439519000316
    Journal articles | 2020
    Professor Igor Shparlinski
    Munsch M; Shparlinski IE, 2020, 'Smooth squarefree and square-full integers in arithmetic progressions', Journal of the London Mathematical Society, vol. 101, pp. 1941 - 1067, http://dx.doi.org/10.1112/jlms.12297
    Journal articles | 2020
    Professor Igor Shparlinski
    Liu K; Shparlinski IE; Zhang T, 2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, vol. 293, pp. 1505 - 1514, http://dx.doi.org/10.1002/mana.201900006
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski IE, 2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, vol. 148, pp. 2371 - 2377, http://dx.doi.org/10.1090/proc/14901
    Journal articles | 2020
    Professor Igor Shparlinski
    Banks W; Shparlinski I, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, vol. 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7
    Journal articles | 2020
    Professor Igor Shparlinski
    Mérai L; Shparlinski IE, 2020, 'Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$', Mathematics of Computation, vol. 322, pp. 911 - 922, http://dx.doi.org/10.1090/mcom/3467
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski IE; Technau M, 2020, 'Kloosterman sums with twice-differentiable functions', Functiones et Approximatio Commentarii Mathematici, vol. 63, pp. 113 - 124, http://dx.doi.org/10.7169/facm/1845
    Journal articles | 2020
    Professor Igor Shparlinski
    Korolev M; Shparlinski I, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions', Pacific Journal of Mathematics, vol. 304, pp. 505 - 522, http://dx.doi.org/10.2140/pjm.2020.304.505
    Journal articles | 2020
    Professor Igor Shparlinski
    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, vol. 215, pp. 261 - 274, http://dx.doi.org/10.1016/j.jnt.2020.02.004
    Journal articles | 2020
    Professor Igor Shparlinski
    Pakovich F; Shparlinski IE, 2020, 'Level curves of rational functions nd unimodular points on rational curves', Proceedings of the American Mathematical Society, vol. 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928
    Journal articles | 2020
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Shparlinski I; Chen C, 2020, 'On large values of Weyl sums', Advances in Mathematics, vol. 370, pp. 1 - 48, http://dx.doi.org/10.1016/j.aim.2020.107216
    Journal articles | 2020
    Professor Igor Shparlinski
    Chen C; Shparlinski IE, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, vol. 214, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023
    Journal articles | 2020
    Professor Igor Shparlinski
    Chen C; Shparlinski IE, 2020, 'On large values of Weyl sums', Advances in Mathematics, vol. 370, http://dx.doi.org/10.1016/j.aim.2020.107216
    Journal articles | 2020
    Professor Igor Shparlinski
    Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, vol. 375, http://dx.doi.org/10.1016/j.aim.2020.107369
    Journal articles | 2020
    Professor Igor Shparlinski
    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, vol. 6, http://dx.doi.org/10.1007/s40993-020-0191-9
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski IE, 2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, vol. 68, http://dx.doi.org/10.1016/j.ffa.2020.101747
    Journal articles | 2020
    Professor Igor Shparlinski
    Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, vol. 34, pp. 2124 - 2136, http://dx.doi.org/10.1137/20M1325502
    Journal articles | 2020
    Professor Igor Shparlinski
    Mérai L; Shparlinski IE, 2020, 'Unlikely intersections over finite fields: Polynomial orbits in small subgroups', Discrete and Continuous Dynamical Systems- Series A, vol. 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Voloch F, 2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, vol. 21, pp. 931 - 941, http://dx.doi.org/10.2422/2036-2145.201811_007
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, vol. 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, vol. 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369
    Journal articles | 2020
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, vol. 71, pp. 637 - 648, http://dx.doi.org/10.1093/qmathj/haz055
    Journal articles | 2020
    Professor Igor Shparlinski
    Ricotta G; Royer E; Shparlinski I, 2020, 'Kloosterman paths of prime powers moduli, II', Bulletin de la Societe Mathematique de France, vol. 148, pp. 173 - 188, http://dx.doi.org/10.24033/bsmf.2802
    Journal articles | 2020
    Professor Igor Shparlinski
    Gómez-Pérez D; Mérai L; Shparlinski IE, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, vol. 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I, 2020, 'Lower bounds for periods of Ducci sequences', Bulletin of the Australian Mathematical Society, vol. 102, pp. 31 - 38, http://dx.doi.org/10.1017/S0004972719001187
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Banks W, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, vol. 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Gomez-Perez D; Merai L, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, vol. 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Pakovich F, 2020, 'Level curves of rational functions and unimodular points on rational curves.', Proceedings of the American Mathematical Society, vol. 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Voloch F, 2020, 'Value sets of sparse polynomials', Canad. Math. Bull., vol. 63, pp. . 187 - 196, http://dx.doi.org/10.4153/S0008439519000316
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I, 2020, 'Unlikely intersections over finite fields: polynomial orbits in small subgroups', DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS., Ser.A, vol. 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070
    Journal articles | 2020
    Professor Igor Shparlinski
    Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., vol. 304, pp. 505 - 18, http://dx.doi.org/10.2140/pjm.2020.304.505
    Journal articles | 2020
    Professor Igor Shparlinski
    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 | 2019
    Professor Igor Shparlinski
    El Abdalaoui EH; Shparlinski IE, 2019, 'Disjointness of the Möbius Transformation and Möbius Function', Research in the Mathematical Sciences, vol. 6, http://dx.doi.org/10.1007/s40687-019-0180-6
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Shparlinski IE, 2019, 'ON SHORT PRODUCTS OF PRIMES IN ARITHMETIC PROGRESSIONS', Proceedings of the American Mathematical Society, vol. 147, pp. 977 - 986, http://dx.doi.org/10.1090/proc/14289
    Journal articles | 2019
    Professor Igor Shparlinski
    Liu K; Shparlinski IE; Zhang T, 2019, 'CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS', Mathematika, vol. 65, pp. 475 - 487, http://dx.doi.org/10.1112/s0025579318000554
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2019, 'Bounds on short character sums and L-functions with characters to a powerful modulus', Journal d'Analyse Mathematique, vol. 139, pp. 239 - 263, http://dx.doi.org/10.1007/s11854-019-0060-4
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Bordellès O; Dai L; Heyman R; Pan H; Shparlinski IE, 2019, 'On a sum involving the Euler function', Journal of Number Theory, vol. 202, pp. 278 - 297, http://dx.doi.org/10.1016/j.jnt.2019.01.006
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Macourt S; Shparlinski IE, 2019, 'Double sums of Kloosterman sums in finite fields', Finite Fields and their Applications, vol. 60, http://dx.doi.org/10.1016/j.ffa.2019.101575
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Shparlinski I; Zannier U, 2019, 'Arithmetic properties of quadratic exponential polynomials', New York Journal of Mathematics, vol. 25, pp. 207 - 218, https://www.emis.de/journals/NYJM/nyjm/j/2019/25-12p.pdf
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Mérai L; Shparlinski IE, 2019, 'Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields', Acta Arithmetica, vol. 188, pp. 401 - 411, http://dx.doi.org/10.4064/aa180307-20-8
    Journal articles | 2019
    Professor Igor Shparlinski
    Shparlinski IE, 2019, 'Bounds on average values of double incomplete Kloosterman sums', Journal of Number Theory, vol. 203, pp. 1 - 11, http://dx.doi.org/10.1016/j.jnt.2019.03.009
    Journal articles | 2019
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, vol. 15, pp. 469 - 477, http://dx.doi.org/10.1142/S1793042119500246
    Journal articles | 2018
    Professor Igor Shparlinski
    Shkredov ID; Shparlinski IE, 2018, 'Double Character Sums with Intervals and Arbitrary Sets', Proceedings of the Steklov Institute of Mathematics, vol. 303, pp. 239 - 258, http://dx.doi.org/10.1134/S0081543818080199
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'Multiplicative orders in orbits of polynomials over finite fields', Glasgow Mathematical Journal, vol. 60, pp. 487 - 493, http://dx.doi.org/10.1017/S0017089517000222
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'Linear equations with rational fractions of bounded height and stochastic matrices', Quarterly Journal of Mathematics, vol. 69, pp. 487 - 499, http://dx.doi.org/10.1093/qmath/hax049
    Journal articles | 2018
    Professor Igor Shparlinski
    Liu K; Shparlinski IE; Zhang T, 2018, 'Divisor problem in arithmetic progressions modulo a prime power', Advances in Mathematics, vol. 325, pp. 459 - 481, http://dx.doi.org/10.1016/j.aim.2017.12.006
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'Trilinear forms with double Kloosterman sums', International Journal of Number Theory, vol. 14, pp. 2195 - 2203, http://dx.doi.org/10.1142/S1793042118501312
    Journal articles | 2018
    Professor Igor Shparlinski
    Liu K; Shparlinski IE; Zhang T, 2018, 'Bilinear forms with exponential sums with binomials', Journal of Number Theory, vol. 188, pp. 172 - 185, http://dx.doi.org/10.1016/j.jnt.2017.12.011
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 166, pp. 173 - 189, http://dx.doi.org/10.1017/S0305004117000780
    Journal articles | 2018
    Professor Igor Shparlinski
    Bordellès O; Luca F; Moree P; Shparlinski IE, 2018, 'DENOMINATORS of BERNOULLI POLYNOMIALS', Mathematika, vol. 64, pp. 519 - 541, http://dx.doi.org/10.1112/S0025579318000153
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'Constructing Dominating Sets in Circulant Graphs', Annals of Combinatorics, vol. 22, pp. 201 - 211, http://dx.doi.org/10.1007/s00026-018-0377-1
    Journal articles | 2018
    Professor Igor Shparlinski
    Bordellès O; Luca F; Shparlinski IE, 2018, 'On the error term of a lattice counting problem', Journal of Number Theory, vol. 182, pp. 19 - 36, http://dx.doi.org/10.1016/j.jnt.2017.07.019
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 5, https://arxiv.org/abs/1706.05874
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 69, pp. 391 - 401, http://dx.doi.org/10.1093/qmath/hax045
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 146, pp. 2015 - 2025, http://dx.doi.org/10.1090/proc/13904
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2
    Journal articles | 2018
    Professor Igor Shparlinski
    Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski IE, 2018, 'Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields', Algorithmica, vol. 80, pp. 560 - 575, http://dx.doi.org/10.1007/s00453-016-0273-1
    Journal articles | 2018
    Professor Igor Shparlinski
    Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2018, 'On multiplicatively dependent vectors of algebraic numbers', Transactions of the American Mathematical Society, vol. 370, pp. 6221 - 6244, http://dx.doi.org/10.1090/tran/7115
    Journal articles | 2018
    Professor Igor Shparlinski
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2018, 'Multiplicative congruences with variables from short intervals', Journal d'Analyse Mathematique, vol. 124, pp. 117 - 147, http://dx.doi.org/10.1007/s11854-014-0029-2
    Journal articles | 2018
    Professor Igor Shparlinski
    Sha M; Shparlinski IE, 2018, 'The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height', Indagationes Mathematicae, vol. 28, pp. 306 - 320, http://dx.doi.org/10.1016/j.indag.2016.07.004
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437
    Journal articles | 2018
    Professor Igor Shparlinski
    Gómez-Pérez D; Shparlinski IE, 2018, 'Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions', Experimental Mathematics, vol. 27, pp. 184 - 192, http://dx.doi.org/10.1080/10586458.2016.1239146
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, vol. 191, pp. 194 - 212, http://dx.doi.org/10.1016/j.jnt.2018.04.017
    Journal articles | 2018
    Professor Igor Shparlinski
    Heyman R; Shparlinski IE, 2018, 'On shifted Eisenstein polynomials', Periodica Mathematica Hungarica, vol. 69, pp. 170 - 181, http://dx.doi.org/10.1007/s10998-014-0061-0
    Journal articles | 2018
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, vol. 49, pp. 74 - 84, http://dx.doi.org/10.1016/j.jco.2018.07.006
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'On Constructing Primitive Roots in Finite Fields With Advice', IEEE Transactions on Information Theory, vol. 64, pp. 7132 - 7136, http://dx.doi.org/10.1109/TIT.2018.2810938
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'Character sums with smooth numbers', Archiv der Mathematik, vol. 110, pp. 467 - 476, http://dx.doi.org/10.1007/s00013-018-1168-y
    Journal articles | 2018
    Professor Igor Shparlinski
    Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, vol. 459, pp. 53 - 81, http://dx.doi.org/10.1016/j.jmaa.2017.10.070
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE; Sutherland AV, 2018, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, vol. 14, pp. 285 - 297, http://dx.doi.org/10.1007/s10208-013-9181-9
    Journal articles | 2018
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Shparlinski IE, 2018, 'On the Győry-Sárközy-Stewart conjecture in function fields', Czechoslovak Mathematical Journal, vol. 68, pp. 1067 - 1077, http://dx.doi.org/10.21136/CMJ.2018.0085-17
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski IE; Zumalacárregui A, 2018, 'Sums of inverses in thin sets of finite fields', Proceedings of the American Mathematical Society, vol. 146, pp. 1377 - 1388, http://dx.doi.org/10.1090/proc/13915
    Journal articles | 2018
    Professor Igor Shparlinski
    Sha M; Shparlinski IE, 2018, 'Effective results on linear dependence for elliptic curves', Pacific Journal of Mathematics, vol. 295, pp. 123 - 144, http://dx.doi.org/10.2140/pjm.2018.295.123
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 18A, pp. 1 - 8, http://math.colgate.edu/~integers/vol18a.html
    Journal articles | 2018
    Professor Igor Shparlinski
    Shparlinski I; Voloch JF, 2018, 'Generators of Elliptic Curves over Finite Fields', Bulletin of the Institute of Mathematics Academia Sinica, vol. 9, pp. 657 - 670, https://web.ma.utexas.edu/users/voloch/Preprints/EC-Generators.pdf
    Journal articles | 2018
    Professor Igor Shparlinski
    Banks WD; Guo VZ; Shparlinski IE, 2018, 'Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$', Indagationes Mathematicae, vol. 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002
    Journal articles | 2018
    Professor Igor Shparlinski
    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, vol. 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437
    Journal articles | 2017
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Liu K; Shparlinski IE; Zhang T, 2017, 'Squares in Piatetski-Shapiro sequences', Acta Arithmetica, vol. 181, pp. 239 - 252, http://dx.doi.org/10.4064/aa8644-8-2017
    Journal articles | 2017
    Professor Igor Shparlinski
    Shkredov ID; Shparlinski IE, 2017, 'ON SOME MULTIPLE CHARACTER SUMS', Mathematika, vol. 63, pp. 553 - 560, http://dx.doi.org/10.1112/S0025579317000055
    Journal articles | 2017
    Professor Igor Shparlinski
    Dietmann R; Elsholtz C; Shparlinski IE, 2017, 'Prescribing the binary digits of squarefree numbers and quadratic residues', Transactions of the American Mathematical Society, vol. 369, pp. 8369 - 8388, http://dx.doi.org/10.1090/tran/6903
    Journal articles | 2017
    Professor Igor Shparlinski
    Bell J; Shparlinski IE, 2017, 'Power series approximations to Fekete polynomials', Journal of Approximation Theory, vol. 222, pp. 132 - 142, http://dx.doi.org/10.1016/j.jat.2017.07.002
    Journal articles | 2017
    Professor Igor Shparlinski
    Shparlinski IE; Yau KH, 2017, 'Double exponential sums with exponential functions', International Journal of Number Theory, vol. 13, pp. 2531 - 2543, http://dx.doi.org/10.1142/S179304211750141X
    Journal articles | 2017
    Professor Igor Shparlinski
    Luca F; Sha M; Shparlinski IE, 2017, 'On two functions arising in the study of the euler and carmichael quotients', Colloquium Mathematicum, vol. 149, pp. 179 - 192, http://dx.doi.org/10.4064/cm6910-3-2017
    Journal articles | 2017
    Professor Igor Shparlinski
    Shparlinski IE; Weingartner AJ, 2017, 'An explicit polynomial analogue of Romanoff's theorem', Finite Fields and their Applications, vol. 44, pp. 22 - 33, http://dx.doi.org/10.1016/j.ffa.2016.11.002
    Journal articles | 2017
    Professor Igor Shparlinski
    Shparlinski IE, 2017, 'On the convex hull of the points on multivariate modular hyperbolas', Journal of Number Theory, vol. 171, pp. 71 - 78, http://dx.doi.org/10.1016/j.jnt.2016.07.011
    Journal articles | 2017
    Professor Igor Shparlinski
    Dubickas A; Sha M; Shparlinski IE, 2017, 'On distances in lattices from algebraic number fields', Moscow Mathematical Journal, vol. 17, pp. 239 - 268, http://dx.doi.org/10.17323/1609-4514-2017-17-2-239-268
    Journal articles | 2017
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2017, 'On coincidences among quadratic fields generated by the shanks sequence', Quarterly Journal of Mathematics, vol. 68, pp. 465 - 484, http://dx.doi.org/10.1093/qmath/haw054
    Journal articles | 2017
    Professor Igor Shparlinski
    Shparlinski IE; Sutherland AV, 2017, 'Finding elliptic curves with a subgroup of prescribed size', International Journal of Number Theory, vol. 13, pp. 133 - 152, http://dx.doi.org/10.1142/S1793042117500099
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'Polynomial values in small subgroups of finite fields', Revista Matematica Iberoamericana, vol. 32, pp. 1127 - 1136, http://dx.doi.org/10.4171/RMI/909
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE; Zhang T, 2016, 'Cancellations amongst Kloosterman sums', Acta Arithmetica, vol. 176, pp. 201 - 210, http://dx.doi.org/10.4064/aa8365-6-2016
    Journal articles | 2016
    Professor Igor Shparlinski
    Nguyen PQ; Shparlinski IE, 2016, 'Counting Co-cyclic lattices', SIAM Journal on Discrete Mathematics, vol. 30, pp. 1358 - 1370, http://dx.doi.org/10.1137/15M103950X
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'On the additive energy of the distance set in finite fields', Finite Fields and their Applications, vol. 42, pp. 187 - 199, http://dx.doi.org/10.1016/j.ffa.2016.08.001
    Journal articles | 2016
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2016, 'Fractional parts of Dedekind sums', International Journal of Number Theory, vol. 12, pp. 1137 - 1147, http://dx.doi.org/10.1142/S179304211650069X
    Journal articles | 2016
    Professor Igor Shparlinski
    Harman G; Shparlinski IE, 2016, 'Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients', International Mathematics Research Notices, vol. 2016, pp. 1424 - 1446, http://dx.doi.org/10.1093/imrn/rnv182
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE; Yau KH, 2016, 'Bounds of double multiplicative character sums and gaps between residues of exponential functions', Journal of Number Theory, vol. 167, pp. 304 - 316, http://dx.doi.org/10.1016/j.jnt.2016.03.022
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'Linear congruences with ratios', Proceedings of the American Mathematical Society, vol. 144, pp. 2837 - 2846, http://dx.doi.org/10.1090/proc/12949
    Journal articles | 2016
    Professor Igor Shparlinski
    Heyman R; Shparlinski IE, 2016, 'Counting irreducible binomials over finite fields', Finite Fields and their Applications, vol. 38, pp. 1 - 12, http://dx.doi.org/10.1016/j.ffa.2015.12.001
    Journal articles | 2016
    Professor Igor Shparlinski
    Camburu OM; Ciolan EA; Luca F; Moree P; Shparlinski IE, 2016, 'Cyclotomic coefficients: Gaps and jumps', Journal of Number Theory, vol. 163, pp. 211 - 237, http://dx.doi.org/10.1016/j.jnt.2015.11.020
    Journal articles | 2016
    Professor Igor Shparlinski
    Banks WD; Guo VZ; Shparlinski IE, 2016, 'Almost primes of the form ⌊pc⌋', Indagationes Mathematicae, vol. 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002
    Journal articles | 2016
    Professor Igor Shparlinski
    Fité F; Shparlinski IE, 2016, 'On the singularity of the demjanenko matrix of quotients of fermat curves', Proceedings of the American Mathematical Society, vol. 144, pp. 55 - 63, http://dx.doi.org/10.1090/proc12717
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'Groups generated by iterations of polynomials over finite fields', Proceedings of the Edinburgh Mathematical Society, vol. 59, pp. 235 - 245, http://dx.doi.org/10.1017/S0013091515000097
    Journal articles | 2016
    Professor Igor Shparlinski
    Koh D; Shen CY; Shparlinski I, 2016, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, vol. 26, pp. 1415 - 1441, http://dx.doi.org/10.1007/s12220-015-9595-5
    Journal articles | 2016
    Professor Igor Shparlinski
    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, vol. 116, pp. 87 - 122, http://dx.doi.org/10.1016/j.jctb.2015.07.003
    Journal articles | 2016
    Professor Igor Shparlinski
    Rivat J; Shparlinski IE, 2016, 'Multiples of squares in short intervals', Functiones et Approximatio, Commentarii Mathematici, vol. 54, pp. 57 - 63, http://dx.doi.org/10.7169/facm/2016.54.1.5
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'Ratios of Small Integers in Multiplicative Subgroups of Residue Rings', Experimental Mathematics, vol. 25, pp. 273 - 280, http://dx.doi.org/10.1080/10586458.2015.1091754
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'On bilinear exponential and character sums with reciprocals of polynomials', Mathematika, vol. 62, pp. 842 - 859, http://dx.doi.org/10.1112/S0025579316000036
    Journal articles | 2016
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2016, 'On Gauss sums and the evaluation of Stechkin's constant', Mathematics of Computation, vol. 85, pp. 2569 - 2581, http://dx.doi.org/10.1090/mcom3056
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS', Bulletin of the Australian Mathematical Society, vol. 93, pp. 364 - 371, http://dx.doi.org/10.1017/S0004972715001240
    Journal articles | 2016
    Professor Igor Shparlinski
    Shparlinski IE, 2016, 'On small gaps between the elements of multiplicative subgroups of finite fields', Designs, Codes, and Cryptography, vol. 80, pp. 63 - 71, http://dx.doi.org/10.1007/s10623-015-0063-9
    Journal articles | 2016
    Professor Igor Shparlinski
    Chang MC; Shparlinski IE, 2016, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, vol. 282, pp. 935 - 954, http://dx.doi.org/10.1007/s00209-015-1571-z
    Journal articles | 2015
    Professor Igor Shparlinski
    Bourgain J; Konyagin SV; Shparlinski IE, 2015, 'Character sums and deterministic polynomial root finding in finite fields', Mathematics of Computation, vol. 84, pp. 2969 - 2977, http://dx.doi.org/10.1090/mcom/2946
    Journal articles | 2015
    Professor Igor Shparlinski
    Bretèche RDL; Sha M; Shparlinski IE; Voloch JF, 2015, 'The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves', Mathematische Zeitschrift, vol. 290, pp. 831 - 855, http://dx.doi.org/10.1007/s00209-018-2042-0
    Journal articles | 2015
    Professor Igor Shparlinski
    Munsch M; Shparlinski IE, 2015, 'Congruences with intervals and subgroups modulo a prime', Michigan Mathematical Journal, vol. 64, pp. 655 - 672, http://dx.doi.org/10.1307/mmj/1441116662
    Journal articles | 2015
    Professor Igor Shparlinski
    Shparlinski IE, 2015, 'Distribution of polynomial discriminants modulo a prime', Archiv der Mathematik, vol. 105, pp. 251 - 259, http://dx.doi.org/10.1007/s00013-015-0806-x
    Journal articles | 2015
    Professor Igor Shparlinski
    Konyagin SV; Shparlinski IE, 2015, 'Quadratic non-residues in short intervals', Proceedings of the American Mathematical Society, vol. 143, pp. 4261 - 4269, http://dx.doi.org/10.1090/S0002-9939-2015-12584-1
    Journal articles | 2015
    Professor Igor Shparlinski
    Blackburn SR; Konyagin SV; Shparlinski IE, 2015, 'Counting additive decompositions of quadratic residues in finite fields', Functiones et Approximatio, Commentarii Mathematici, vol. 52, pp. 223 - 227, http://dx.doi.org/10.7169/facm/2015.52.2.3
    Journal articles | 2015
    Professor Igor Shparlinski
    Kurlberg P; Luca F; Shparlinski IE, 2015, 'On the fixed points of the map x→xx modulo a prime', Mathematical Research Letters, vol. 22, pp. 141 - 168, http://dx.doi.org/10.4310/MRL.2015.v22.n1.a8
    Journal articles | 2015
    Professor Igor Shparlinski
    Gómez-Pérez D; Shparlinski IE, 2015, 'Subgroups generated by rational functions in finite fields', Monatshefte fur Mathematik, vol. 176, pp. 241 - 253, http://dx.doi.org/10.1007/s00605-014-0697-0
    Journal articles | 2015
    Professor Igor Shparlinski
    Sha M; Shparlinski IE, 2015, 'Lang-trotter and sato-tate distributions in single and double parametric families of elliptic curves', Acta Arithmetica, vol. 170, pp. 299 - 325, http://dx.doi.org/10.4064/aa170-4-1
    Journal articles | 2015
    Professor Igor Shparlinski
    Dubickas A; Sha M; Shparlinski I, 2015, 'Explicit form of Cassels' p-adic Embedding Theorem for Number Fields', Canadian Journal of Mathematics, vol. 67, pp. 1046 - 1064, http://dx.doi.org/10.4153/CJM-2015-021-2
    Journal articles | 2015
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, vol. 18, pp. 308 - 322, http://dx.doi.org/10.1112/S1461157015000017
    Journal articles | 2015
    Professor Igor Shparlinski
    Shparlinski IE, 2015, 'Cayley graphs generated by small degree polynomials over finite fields', SIAM Journal on Discrete Mathematics, vol. 29, pp. 376 - 381, http://dx.doi.org/10.1137/14095813X
    Journal articles | 2015
    Professor Igor Shparlinski
    Roche-Newton O; Shparlinski IE, 2015, 'Polynomial values in subfields and affine subspaces of finite fields', Quarterly Journal of Mathematics, vol. 66, pp. 693 - 706, http://dx.doi.org/10.1093/qmath/hau032
    Journal articles | 2015
    Professor Igor Shparlinski
    Shparlinski I, 2015, 'Points on Varieties over Finite Fields in Small Boxes', Contemporary Mathematics, vol. 655, pp. 209 - 233, http://dx.doi.org/10.1090/conm/655/13235
    Journal articles | 2015
    Professor Igor Shparlinski
    Shparlinski IE, 2015, 'Close values of shifted modular inversions and the decisional modular inversion hidden number problem', Advances in Mathematics of Communications, vol. 9, pp. 169 - 176, http://dx.doi.org/10.3934/amc.2015.9.169
    Journal articles | 2015
    Professor Igor Shparlinski
    Shparlinski IE, 2015, 'On the product of small Elkies primes', Proceedings of the American Mathematical Society, vol. 143, pp. 1441 - 1448, http://dx.doi.org/10.1090/S0002-9939-2014-12345-8
    Journal articles | 2015
    Professor Igor Shparlinski
    Heyman R; Shparlinski IE, 2015, 'On the greatest common divisor of shifted sets', Journal of Number Theory, vol. 154, pp. 63 - 73, http://dx.doi.org/10.1016/j.jnt.2015.02.012
    Journal articles | 2015
    Professor Igor Shparlinski
    Shparlinski IE, 2015, 'Small discriminants of complex multiplication fields of elliptic curves over finite fields', Czechoslovak Mathematical Journal, vol. 65, pp. 381 - 388, http://dx.doi.org/10.1007/s10587-015-0183-4
    Journal articles | 2015
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski IE, 2015, 'Circulant graphs and GCD and LCM of subsets', Information Processing Letters, vol. 115, pp. 134 - 138, http://dx.doi.org/10.1016/j.ipl.2014.07.014
    Journal articles | 2014
    Professor Igor Shparlinski
    Munsch M; Shparlinski IE, 2014, 'Upper and Lower Bounds for Higher Moments of Theta Functions', Quarterly Journal of Mathematics, vol. 67, pp. 53 - 73, http://dx.doi.org/10.1093/qmath/hav039
    Journal articles | 2014
    Professor Igor Shparlinski
    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, vol. 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880
    Journal articles | 2014
    Professor Igor Shparlinski
    Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, vol. 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809
    Journal articles | 2014
    Professor Igor Shparlinski
    Chang MC; Cilleruelo J; Garaev MZ; Hernández J; Shparlinski IE; Zumalacárregui A, 2014, 'Points on curves in small boxes and applications', Michigan Mathematical Journal, vol. 63, pp. 503 - 534, http://dx.doi.org/10.1307/mmj/1409932631
    Journal articles | 2014
    Professor Igor Shparlinski
    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, vol. 23, pp. 241 - 260, http://dx.doi.org/10.1080/10586458.2014.890918
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'On the distribution of points on the generalized markoff-hurwitz and dwork hypersurfaces', International Journal of Number Theory, vol. 10, pp. 151 - 160, http://dx.doi.org/10.1142/S1793042113500863
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields', Journal of Symbolic Computation, vol. 64, pp. 35 - 41, http://dx.doi.org/10.1016/j.jsc.2013.12.005
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE; Sutantyo D, 2014, 'Distribution of elliptic twin primes in isogeny and isomorphism classes', Journal of Number Theory, vol. 137, pp. 1 - 15, http://dx.doi.org/10.1016/j.jnt.2013.10.018
    Journal articles | 2014
    Professor Igor Shparlinski
    Chen Z; Shparlinski IE; Winterhof A, 2014, 'Covering sets for limited-magnitude errors', IEEE Transactions on Information Theory, vol. 60, pp. 5315 - 5321, http://dx.doi.org/10.1109/TIT.2014.2338078
    Journal articles | 2014
    Professor Igor Shparlinski
    Chang MC; Shparlinski IE, 2014, 'Double character sums over subgroups and intervals', Bulletin of the Australian Mathematical Society, vol. 90, pp. 376 - 390, http://dx.doi.org/10.1017/S0004972714000227
    Journal articles | 2014
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Friedlander JB; Shparlinski IE, 2014, 'Enumeration of certain varieties over a finite field', Proceedings of the American Mathematical Society, vol. 142, pp. 2615 - 2623, http://dx.doi.org/10.1090/S0002-9939-2014-11999-X
    Journal articles | 2014
    Professor Igor Shparlinski
    Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, vol. 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9
    Journal articles | 2014
    Professor Igor Shparlinski
    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, vol. 25, pp. 181 - 188, http://dx.doi.org/10.1007/s00200-014-0219-2
    Journal articles | 2014
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2014, 'On the counting function of elliptic carmichael numbers', Canadian Mathematical Bulletin, vol. 57, pp. 105 - 112, http://dx.doi.org/10.4153/CMB-2012-037-4
    Journal articles | 2014
    Professor Igor Shparlinski
    Ling S; Shparlinski I; Wang H, 2014, 'On the multidimensional distribution of the Naor-Reingold pseudo-random function', Mathematics of Computation, vol. 83, pp. 2429 - 2434, http://dx.doi.org/10.1090/S0025-5718-2014-02794-4
    Journal articles | 2014
    Professor Igor Shparlinski
    Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, vol. 70, pp. 301 - 325, http://dx.doi.org/10.1007/s00453-013-9810-3
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'Multiple exponential and character sums with monomials', Mathematika, vol. 60, pp. 363 - 373, http://dx.doi.org/10.1112/S0025579314000084
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv der Mathematik, vol. 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'Distribution of exponential functions modulo a prime power', Journal of Number Theory, vol. 143, pp. 224 - 231, http://dx.doi.org/10.1016/j.jnt.2014.04.010
    Journal articles | 2014
    Professor Igor Shparlinski
    Ahmadi O; Shparlinski IE, 2014, 'Exponential sums over points of elliptic curves', Journal of Number Theory, vol. 140, pp. 299 - 313, http://dx.doi.org/10.1016/j.jnt.2014.01.016
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, vol. 89, pp. 300 - 307, http://dx.doi.org/10.1017/S0004972713000671
    Journal articles | 2014
    Professor Igor Shparlinski
    Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, vol. 547, pp. 117 - 121, http://dx.doi.org/10.1016/j.tcs.2014.06.005
    Journal articles | 2013
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves', Michigan Mathematical Journal, vol. 62, pp. 491 - 505, http://dx.doi.org/10.1307/mmj/1378757885
    Journal articles | 2013
    Professor Igor Shparlinski
    Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, vol. 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012
    Journal articles | 2013
    Professor Igor Shparlinski
    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, vol. 280, pp. 61 - 90, http://dx.doi.org/10.1134/S0081543813010057
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, vol. 36, pp. 99 - 108, http://dx.doi.org/10.2996/kmj/1364562722
    Journal articles | 2013
    Professor Igor Shparlinski
    Baker RC; Banks WD; Brüdern J; Shparlinski IE; Weingartner AJ, 2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, vol. 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3
    Journal articles | 2013
    Professor Igor Shparlinski
    Farashahi RR; Fouque PA; Shparlinski IE; Tibouchi M; Voloch JF, 2013, 'Indifferentiable deterministic hashing to elliptic and hyperelliptic curves', Mathematics of Computation, vol. 82, pp. 491 - 512, http://dx.doi.org/10.1090/S0025-5718-2012-02606-8
    Journal articles | 2013
    Professor Igor Shparlinski
    Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, vol. 24, pp. 930 - 938, http://dx.doi.org/10.1016/j.indag.2013.02.005
    Journal articles | 2013
    Professor Igor Shparlinski
    Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte fur Mathematik, vol. 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, vol. 19, pp. 93 - 104, http://dx.doi.org/10.1016/j.ffa.2012.10.004
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, vol. 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470
    Journal articles | 2013
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, vol. 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, vol. 25, pp. 647 - 664, http://dx.doi.org/10.1515/FORM.2011.141
    Journal articles | 2013
    Professor Igor Shparlinski
    Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, vol. 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, vol. 67, pp. 55 - 61, http://dx.doi.org/10.1007/s10998-013-2736-3
    Journal articles | 2013
    Professor Igor Shparlinski
    Gutierrez J; Ibeas A; Gómez-Pérez D; Shparlinski IE, 2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs, Codes, and Cryptography, vol. 67, pp. 395 - 402, http://dx.doi.org/10.1007/s10623-012-9615-4
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, vol. 66, pp. 65 - 90, http://dx.doi.org/10.1007/978-1-4614-5389-5_4
    Journal articles | 2013
    Professor Igor Shparlinski
    Heyman R; Shparlinski IE, 2013, 'On the number of Eisenstein polynomials of bounded height', Applicable Algebra in Engineering, Communications and Computing, vol. 24, pp. 149 - 156, http://dx.doi.org/10.1007/s00200-013-0187-y
    Journal articles | 2013
    Professor Igor Shparlinski
    Cilleruelo J; Kumchev A; Luca F; Rué J; Shparlinski IE, 2013, 'On the fractional parts of an/n', Bulletin of the London Mathematical Society, vol. 45, pp. 249 - 256, http://dx.doi.org/10.1112/blms/bds084
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, vol. 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027
    Journal articles | 2013
    Professor Igor Shparlinski
    Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, vol. 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, vol. 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, vol. 43, pp. 361 - 371, http://dx.doi.org/10.1216/RMJ-2013-43-1-361
    Journal articles | 2013
    Professor Igor Shparlinski
    Shparlinski IE, 2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, vol. 113, pp. 414 - 417, http://dx.doi.org/10.1016/j.ipl.2013.03.016
    Journal articles | 2013
    Professor Igor Shparlinski
    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, vol. 87, pp. 527 - 528, http://dx.doi.org/10.1017/S0004972712001062
    Journal articles | 2013
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, vol. 43, http://dx.doi.org/10.1007/978-1-4614-6642-0
    Journal articles | 2012
    Professor Igor Shparlinski
    Banks WD; Pappalardi F; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, vol. 21, pp. 11 - 25, http://dx.doi.org/10.1080/10586458.2011.606075
    Journal articles | 2012
    Professor Igor Shparlinski
    Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, 'On the hidden shifted power problem', SIAM Journal on Computing, vol. 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414
    Journal articles | 2012
    Professor Igor Shparlinski
    Konyagin SV; Shparlinski IE, 2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, vol. 58, pp. 11 - 20, http://dx.doi.org/10.1112/S0025579311002117
    Journal articles | 2012
    Professor Igor Shparlinski
    Ling S; Shparlinski IE; Steinfeld R; Wang H, 2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, vol. 47, pp. 358 - 367, http://dx.doi.org/10.1016/j.jsc.2011.09.002
    Journal articles | 2012
    Professor Igor Shparlinski
    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, vol. 55, pp. 271 - 289, http://dx.doi.org/10.1017/S0013091510001355
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski I, 2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields', Bulletin of the Australian Mathematical Society, vol. 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887
    Journal articles | 2012
    Professor Igor Shparlinski
    Cilleruelo J; Shparlinski IE; Zumalacárregui A, 2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, vol. 19, pp. 335 - 343, http://dx.doi.org/10.4310/MRL.2012.v19.n2.a6
    Journal articles | 2012
    Professor Igor Shparlinski
    Bourgain J; Konyagin SV; Shparlinski IE, 2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, vol. 2012, pp. 1968 - 2009, http://dx.doi.org/10.1093/imrn/rnr097
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski IE, 2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, vol. 140, pp. 1199 - 1206, http://dx.doi.org/10.1090/S0002-9939-2011-11203-6
    Journal articles | 2012
    Professor Igor Shparlinski
    Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2012, 'Exponential and character sums with mersenne numbers', Journal of the Australian Mathematical Society, vol. 92, pp. 1 - 13, http://dx.doi.org/10.1017/S1446788712000109
    Journal articles | 2012
    Professor Igor Shparlinski
    Farashahi RR; Shparlinski IE, 2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, vol. 58, pp. 1242 - 1247, http://dx.doi.org/10.1109/TIT.2011.2170054
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski IE, 2012, 'Modular hyperbolas', Japanese Journal of Mathematics, vol. 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8
    Journal articles | 2012
    Professor Igor Shparlinski
    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, vol. 81, pp. 1093 - 1110, http://dx.doi.org/10.1090/S0025-5718-2011-02543-3
    Journal articles | 2012
    Professor Igor Shparlinski
    Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, vol. 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X
    Journal articles | 2012
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, vol. 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719
    Journal articles | 2012
    Professor Igor Shparlinski
    Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, vol. 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7
    Journal articles | 2012
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, vol. 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010
    Journal articles | 2012
    Professor Igor Shparlinski
    Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, vol. 12, http://dx.doi.org/10.1515/integers-2012-0012
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski IE, 2012, 'On the distribution of solutions to polynomial congruences', Archiv der Mathematik, vol. 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski IE, 2012, 'On the convex hull of solutions to polynomial congruences', Journal of Number Theory, vol. 132, pp. 254 - 257, http://dx.doi.org/10.1016/j.jnt.2011.06.016
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski IE, 2012, 'On the restricted divisor function in arithmetic progressions', Revista Matematica Iberoamericana, vol. 28, pp. 231 - 238, http://dx.doi.org/10.4171/rmi/675
    Journal articles | 2012
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, vol. 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2
    Journal articles | 2012
    Professor Igor Shparlinski
    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, vol. 152, pp. 571, http://dx.doi.org/10.1017/S0305004111000399
    Journal articles | 2012
    Professor Igor Shparlinski
    Farashahi RR; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, vol. 21, pp. 1 - 10, http://dx.doi.org/10.1080/10586458.2012.632754
    Journal articles | 2012
    Professor Igor Shparlinski
    Shparlinski IE; Stange KE, 2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, vol. 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x
    Journal articles | 2012
    Professor Igor Shparlinski
    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), vol. 7256 LNCS, pp. 542 - 555, http://dx.doi.org/10.1007/978-3-642-29344-3_46
    Journal articles | 2012
    Professor Igor Shparlinski
    Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, vol. 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426
    Journal articles | 2011
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2011, 'On the g-Ary expansions of middle binomial coefficients and catalan numbers', Rocky Mountain Journal of Mathematics, vol. 41, pp. 1291 - 1301, http://dx.doi.org/10.1216/RMJ-2011-41-4-1291
    Journal articles | 2011
    Professor Igor Shparlinski
    Fouvry E; Shparlinski IE, 2011, 'On a ternary quadratic form over primes', Acta Arithmetica, vol. 150, pp. 285 - 314, http://dx.doi.org/10.4064/aa150-3-5
    Journal articles | 2011
    Professor Igor Shparlinski
    Balog A; Broughan KA; Shparlinski IE, 2011, 'On the number of solutions of exponential congruences', Acta Arithmetica, vol. 148, pp. 93 - 103, http://dx.doi.org/10.4064/aa148-1-7
    Journal articles | 2011
    Professor Igor Shparlinski
    Fouvry E; Luca F; Pappalardi F; Shparlinski IE, 2011, 'Counting dihedral and quaternionic extensions', Transactions of the American Mathematical Society, vol. 363, pp. 3233 - 3253, http://dx.doi.org/10.1090/S0002-9947-2011-05233-5
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'On the average distribution of pseudorandom numbers generated by nonlinear permutations', Mathematics of Computation, vol. 80, pp. 1053 - 1061, http://dx.doi.org/10.1090/S0025-5718-2010-02408-1
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'Character sums with fermat quotients', Quarterly Journal of Mathematics, vol. 62, pp. 1031 - 1043, http://dx.doi.org/10.1093/qmath/haq028
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'Exponential sums with consecutive modular roots of an integer', Quarterly Journal of Mathematics, vol. 62, pp. 207 - 213, http://dx.doi.org/10.1093/qmath/hap023
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'On small solutions to quadratic congruences', Journal of Number Theory, vol. 131, pp. 1105 - 1111, http://dx.doi.org/10.1016/j.jnt.2010.12.002
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'Bounds of multiplicative character sums with Fermat quotients of primes', Bulletin of the Australian Mathematical Society, vol. 83, pp. 456 - 462, http://dx.doi.org/10.1017/S000497271000198X
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'Fermat quotients: Exponential sums, value set and primitive roots', Bulletin of the London Mathematical Society, vol. 43, pp. 1228 - 1238, http://dx.doi.org/10.1112/blms/bdr058
    Journal articles | 2011
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, vol. 139, pp. 3815 - 3820, http://dx.doi.org/10.1090/S0002-9939-2011-10843-8
    Journal articles | 2011
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, vol. 7, pp. 1557 - 1571, http://dx.doi.org/10.1142/S1793042111004484
    Journal articles | 2011
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, vol. 25, pp. 50 - 71, http://dx.doi.org/10.1137/100798466
    Journal articles | 2011
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, vol. 148, pp. 77 - 92, http://dx.doi.org/10.4064/aa148-1-6
    Journal articles | 2011
    Professor Igor Shparlinski
    Shparlinski IE, 2011, 'On the distribution of irreducible trinomials', Canadian Mathematical Bulletin, vol. 54, pp. 748 - 756, http://dx.doi.org/10.4153/CMB-2011-053-0
    Journal articles | 2011
    Professor Igor Shparlinski
    Fouvry E; Shparlinski IE, 2011, 'Smooth shifted monomial products', Publicationes Mathematicae, vol. 79, pp. 423 - 432, http://dx.doi.org/10.5486/PMD.2011.5089
    Journal articles | 2011
    Professor Igor Shparlinski
    Křížek M; Luca F; Shparlinski IE; Somer L, 2011, 'On the complexity of testing elite primes', Journal of Integer Sequences, vol. 14, pp. 1 - 5
    Journal articles | 2011
    Professor Igor Shparlinski
    Bibak K; Shparlinski IE, 2011, 'On Fully Split Lacunary Polynomials in Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, vol. 59, pp. 197 - 202, http://dx.doi.org/10.4064/ba59-3-1
    Journal articles | 2011
    Professor Igor Shparlinski
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, vol. abs/1102.1053
    Journal articles | 2010
    Professor Igor Shparlinski
    Ahmadi O; Shparlinski IE; Voloch JF, 2010, 'Multiplicative order of gauss periods', International Journal of Number Theory, vol. 6, pp. 877 - 882, http://dx.doi.org/10.1142/S1793042110003290
    Journal articles | 2010
    Professor Igor Shparlinski
    Bourgain J; Ford K; Konyagin SV; Shparlinski IE, 2010, 'On the divisibility of Fermat quotients', Michigan Mathematical Journal, vol. 59, pp. 313 - 328, http://dx.doi.org/10.1307/mmj/1281531459
    Journal articles | 2010
    Professor Igor Shparlinski
    Chan TH; Shparlinski IE, 2010, 'On the concentration of points on modular hyperbolas and exponential curves', Acta Arithmetica, vol. 142, pp. 59 - 66, http://dx.doi.org/10.4064/aa142-1-5
    Journal articles | 2010
    Professor Igor Shparlinski
    Ahmadi O; Shparlinski IE, 2010, 'On the distribution of the number of points on algebraic curves in extensions of finite fields', Mathematical Research Letters, vol. 17, pp. 689 - 699, http://dx.doi.org/10.4310/MRL.2010.v17.n4.a9
    Journal articles | 2010
    Professor Igor Shparlinski
    Ahmadi O; Shparlinski I, 2010, 'Bilinear character sums and sum-product problems on elliptic curves', Proceedings of the Edinburgh Mathematical Society, vol. 53, pp. 1 - 12, http://dx.doi.org/10.1017/S0013091508000771
    Journal articles | 2010
    Professor Igor Shparlinski
    Ford K; Khan MR; Shparlinski IE, 2010, 'Geometric properties of points on modular hyperbolas', Proceedings of the American Mathematical Society, vol. 138, pp. 4177 - 4185, http://dx.doi.org/10.1090/S0002-9939-2010-10561-0
    Journal articles | 2010
    Professor Igor Shparlinski
    Iosevich A; Shparlinski IE; Xiong M, 2010, 'Sets with integral distances in finite fields', Transactions of the American Mathematical Society, vol. 362, pp. 2189 - 2204, http://dx.doi.org/10.1090/S0002-9947-09-05004-1
    Journal articles | 2010
    Professor Igor Shparlinski
    Glebsky L; Shparlinski IE, 2010, 'Short cycles in repeated exponentiation modulo a prime', Designs, Codes, and Cryptography, vol. 56, pp. 35 - 42, http://dx.doi.org/10.1007/s10623-009-9339-2
    Journal articles | 2010
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2010, 'On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers', Annals of Combinatorics, vol. 14, pp. 507 - 524, http://dx.doi.org/10.1007/s00026-011-0074-9
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE, 2010, 'On point sets in vector spaces over finite fields that determine only acute angle triangles', Bulletin of the Australian Mathematical Society, vol. 81, pp. 114 - 120, http://dx.doi.org/10.1017/S0004972709000719
    Journal articles | 2010
    Professor Igor Shparlinski
    Gutierrez J; Shparlinski IE, 2010, 'Expansion of orbits of some dynamical systems over finite fields', Bulletin of the Australian Mathematical Society, vol. 82, pp. 232 - 239, http://dx.doi.org/10.1017/S0004972709001270
    Journal articles | 2010
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, vol. 138, pp. 2653 - 2656, http://dx.doi.org/10.1090/S0002-9939-10-10404-3
    Journal articles | 2010
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, vol. 79, pp. 501 - 511, http://dx.doi.org/10.1090/S0025-5718-09-02271-6
    Journal articles | 2010
    Professor Igor Shparlinski
    Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, vol. 23, pp. 501 - 513, http://dx.doi.org/10.1007/s13163-010-0029-4
    Journal articles | 2010
    Professor Igor Shparlinski
    Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, vol. 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0
    Journal articles | 2010
    Professor Igor Shparlinski
    Cilleruelo J; Luca F; Quirós A; Shparlinski IE, 2010, 'On squares in polynomial products', Monatshefte fur Mathematik, vol. 159, pp. 215 - 223, http://dx.doi.org/10.1007/s00605-008-0066-y
    Journal articles | 2010
    Professor Igor Shparlinski
    Rezaeian Farashahi R; Shparlinski IE, 2010, 'On the number of distinct elliptic curves in some families', Designs, Codes, and Cryptography, vol. 54, pp. 83 - 99, http://dx.doi.org/10.1007/s10623-009-9310-2
    Journal articles | 2010
    Professor Igor Shparlinski
    Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, vol. 16, pp. 320 - 328, http://dx.doi.org/10.1016/j.ffa.2010.05.002
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE, 2010, 'Some counting questions for matrices with restricted entries', Linear Algebra and Its Applications, vol. 432, pp. 155 - 160, http://dx.doi.org/10.1016/j.laa.2009.07.036
    Journal articles | 2010
    Professor Igor Shparlinski
    Chan TH; Shparlinski IE, 2010, 'Visible Points on Modular Exponential Curves', Bulletin of the Polish Academy of Sciences Mathematics, vol. 58, pp. 17 - 22, http://dx.doi.org/10.4064/ba58-1-2
    Journal articles | 2010
    Professor Igor Shparlinski
    Фридландер ДБ; Friedlander JB; Гонг K; Gong K; Шпарлинский ИЕ; Shparlinski IE, 2010, 'Суммы значений характеров на сдвинутых простых числах', Matematicheskie Zametki, vol. 88, pp. 605 - 619, http://dx.doi.org/10.4213/mzm8692
    Journal articles | 2010
    Professor Igor Shparlinski
    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, vol. 4, pp. 369 - 379, http://dx.doi.org/10.3934/amc.2010.4.369
    Journal articles | 2010
    Professor Igor Shparlinski
    von zur Gathen J; Mignotte M; Shparlinski IE, 2010, 'Approximate polynomial gcd: Small degree and small height perturbations', Journal of Symbolic Computation, vol. 45, pp. 879 - 886, http://dx.doi.org/10.1016/j.jsc.2010.04.001
    Journal articles | 2010
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2010, 'Sums with convolutions of Dirichlet characters', Manuscripta Mathematica, vol. 133, pp. 105 - 114, http://dx.doi.org/10.1007/s00229-010-0364-2
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE, 2010, 'On the size of the Gelfond exponent', Journal of Number Theory, vol. 130, pp. 1056 - 1060, http://dx.doi.org/10.1016/j.jnt.2009.09.005
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE, 2010, 'Tate-shafarevich groups and frobenius fields of reductions of elliptic curves', Quarterly Journal of Mathematics, vol. 61, pp. 255 - 263, http://dx.doi.org/10.1093/qmath/hap001
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE, 2010, 'On quadratic fields generated by discriminants of irreducible trinomials', Proceedings of the American Mathematical Society, vol. 138, pp. 125 - 132, http://dx.doi.org/10.1090/S0002-9939-09-10074-6
    Journal articles | 2010
    Professor Igor Shparlinski
    Karabina K; Menezes A; Pomerance C; Shparlinski IE, 2010, 'On the asymptotic effectiveness of Weil descent attacks', Journal of Mathematical Cryptology, vol. 4, pp. 175 - 191, http://dx.doi.org/10.1515/JMC.2010.007
    Journal articles | 2010
    Professor Igor Shparlinski
    Konyagin SV; Pomerance C; Shparlinski IE, 2010, 'On the distribution of pseudopowers', Canadian Journal of Mathematics, vol. 62, pp. 582 - 594, http://dx.doi.org/10.4153/CJM-2010-020-4
    Journal articles | 2010
    Professor Igor Shparlinski
    Friedlander JB; Gong K; Shparlinskii IE, 2010, 'Character sums over shifted primes', Mathematical Notes, vol. 88, pp. 585 - 598, http://dx.doi.org/10.1134/S0001434610090312
    Journal articles | 2010
    Professor Igor Shparlinski
    Loiperdinger SS; Shparlinski IE, 2010, 'ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS', COLLOQUIUM MATHEMATICUM, vol. 120, pp. 139 - 148, http://dx.doi.org/10.4064/cm120-1-10
    Journal articles | 2010
    Professor Igor Shparlinski
    Pomerance C; Shparlinski IE, 2010, 'Rank statistics for a family of elliptic curves over a function field', Pure and Applied Mathematics Quarterly, vol. 6, pp. 21 - 40, http://dx.doi.org/10.4310/PAMQ.2010.v6.n1.a2
    Journal articles | 2010
    Professor Igor Shparlinski
    Broughan KA; Luca F; Shparlinski IE, 2010, 'Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem', Integers, vol. 10, http://dx.doi.org/10.1515/integ.2010.041
    Journal articles | 2010
    Professor Igor Shparlinski
    Farashahi RR; Shparlinski IE, 2010, 'On pseudopoints of algebraic curves', Archiv der Mathematik, vol. 95, pp. 529 - 537, http://dx.doi.org/10.1007/s00013-010-0200-7
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2010, 'Partitions into two Lehmer numbers', Monatshefte fur Mathematik, vol. 160, pp. 429 - 441, http://dx.doi.org/10.1007/s00605-009-0130-2
    Journal articles | 2010
    Professor Igor Shparlinski
    Shparlinski IE, 2010, 'Numbers at work and play', Notices of the American Mathematical Society, vol. 57, pp. 334 - 342
    Journal articles | 2010
    Professor Igor Shparlinski
    Iosevich A; Shparlinski IE; Xiong M, 2010, 'SETS WITH INTEGRAL DISTANCES IN FINITE FIELDS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 362, pp. 2189 - 2204, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000275819200020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2009
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2009, 'Prime numbers with beatty sequences', Colloquium Mathematicum, vol. 115, pp. 147 - 157, http://dx.doi.org/10.4064/cm115-2-1
    Journal articles | 2009
    Professor Igor Shparlinski
    Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2009, 'Uniform Distribution of Fractional Parts Related to Pseudoprimes', Canadian Journal of Mathematics, vol. 61, pp. 481 - 502, http://dx.doi.org/10.4153/CJM-2009-025-2
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'On the distribution of arguments of gauss sums', Kodai Mathematical Journal, vol. 32, pp. 172 - 177, http://dx.doi.org/10.2996/kmj/1238594554
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'On the distribution of solutions to linear equations', Glasnik Matematicki, vol. 44, pp. 7 - 10, http://dx.doi.org/10.3336/gm.44.1.02
    Journal articles | 2009
    Professor Igor Shparlinski
    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, vol. 2009, pp. 3146 - 3147, http://dx.doi.org/10.1093/imrn/rnp041
    Journal articles | 2009
    Professor Igor Shparlinski
    Cojocaru AC; Luca F; Shparlinski IE, 2009, 'Pseudoprime reductions of elliptic curves', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 146, pp. 513 - 522, http://dx.doi.org/10.1017/S0305004108001758
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'On some weighted average values of l-functions', Bulletin of the Australian Mathematical Society, vol. 79, pp. 183 - 186, http://dx.doi.org/10.1017/S0004972708001020
    Journal articles | 2009
    Professor Igor Shparlinski
    Ford K; Luca F; Shparlinski IE, 2009, 'On the largest prime factor of the mersenne numbers', Bulletin of the Australian Mathematical Society, vol. 79, pp. 455 - 463, http://dx.doi.org/10.1017/S0004972709000033
    Journal articles | 2009
    Professor Igor Shparlinski
    Ahmadi O; Alon N; Blake IF; Shparlinski IE, 2009, 'Graphs with integral spectrum', Linear Algebra and Its Applications, vol. 430, pp. 547 - 552, http://dx.doi.org/10.1016/j.laa.2008.08.020
    Journal articles | 2009
    Professor Igor Shparlinski
    Bourgain J; Konyagin SV; Pomerance C; Shparlinski IE, 2009, 'On the smallest pseudopower', Acta Arithmetica, vol. 140, pp. 43 - 55, http://dx.doi.org/10.4064/aa140-1-3
    Journal articles | 2009
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2009, 'Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height', Israel Journal of Mathematics, vol. 173, pp. 253 - 277, http://dx.doi.org/10.1007/s11856-009-0091-0
    Journal articles | 2009
    Professor Igor Shparlinski
    Farashahi RR; Shparlinski IE; Voloch JF, 2009, 'On hashing into elliptic curves', Journal of Mathematical Cryptology, vol. 3, pp. 353 - 360, http://dx.doi.org/10.1515/JMC.2009.022
    Journal articles | 2009
    Professor Igor Shparlinski
    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), vol. 5557 LNCS, pp. 77 - 81, http://dx.doi.org/10.1007/978-3-642-01877-0_8
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'On a generalisation of a Lehmer problem', Mathematische Zeitschrift, vol. 263, pp. 619 - 631, http://dx.doi.org/10.1007/s00209-008-0434-2
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'EXPONENTS OF MODULAR REDUCTIONS OF FAMILIES OF ELLIPTIC CURVES', REVISTA DE LA UNION MATEMATICA ARGENTINA, vol. 50, pp. 69 - 74, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000268682800008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture', SIAM Journal on Discrete Mathematics, vol. 23, pp. 2093 - 2099, http://dx.doi.org/10.1137/090770746
    Journal articles | 2009
    Professor Igor Shparlinski
    Cojocaru AC; Shparlinski IE, 2009, 'On the embedding degree of reductions of an elliptic curve', Information Processing Letters, vol. 109, pp. 652 - 654, http://dx.doi.org/10.1016/j.ipl.2009.02.018
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'Exponential Sums with Farey Fractions', Bulletin of the Polish Academy of Sciences Mathematics, vol. 57, pp. 101 - 107, http://dx.doi.org/10.4064/ba57-2-2
    Journal articles | 2009
    Professor Igor Shparlinski
    Abercrombie AG; Banks WD; Shparlinski IE, 2009, 'Arithmetic functions on Beatty sequences', Acta Arithmetica, vol. 136, pp. 81 - 89, http://dx.doi.org/10.4064/aa136-1-6
    Journal articles | 2009
    Professor Igor Shparlinski
    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, vol. 15, pp. 738 - 747, http://dx.doi.org/10.1016/j.ffa.2009.08.002
    Journal articles | 2009
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2009, 'Multiplicative character sums with twice-differentiable functions', Quarterly Journal of Mathematics, vol. 60, pp. 401 - 411, http://dx.doi.org/10.1093/qmath/han023
    Journal articles | 2009
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2009, 'On quadratic fields generated by the Shanks sequence', Proceedings of the Edinburgh Mathematical Society, vol. 52, pp. 719 - 729, http://dx.doi.org/10.1017/S001309150700123X
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'On the values of Kloosterman sums', IEEE Transactions on Information Theory, vol. 55, pp. 2599 - 2601, http://dx.doi.org/10.1109/TIT.2009.2018320
    Journal articles | 2009
    Professor Igor Shparlinski
    Igor S, 2009, 'Some special character sums over elliptic curves', Boletin de la Sociedad Matematica Mexicana, vol. 15, pp. 37 - 40
    Journal articles | 2009
    Professor Igor Shparlinski
    Shparlinski IE, 2009, 'Bilinear sums with exponential functions', Proceedings of the American Mathematical Society, vol. 137, pp. 2217 - 2224, http://dx.doi.org/10.1090/S0002-9939-09-09882-7
    Journal articles | 2009
    Professor Igor Shparlinski
    Balasuriya S; Winterhof A; Shparlinski IE, 2009, 'An average bound for character sums with some counter-dependent recurrence sequences', Rocky Mountain Journal of Mathematics, vol. 39, pp. 1403 - 1409, http://dx.doi.org/10.1216/RMJ-2009-39-5-1403
    Journal articles | 2009
    Professor Igor Shparlinski
    Journal articles | 2009
    Professor Igor Shparlinski
    Balasuriya S; Shparlinski IE; Sutantyo D, 2009, 'Multiplicative character sums with the Euler function', Studia Scientiarum Mathematicarum Hungarica, vol. 46, pp. 223 - 229, http://dx.doi.org/10.1556/SScMath.46.2009.2.1087
    Journal articles | 2009
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski IE, 2009, 'Subset sum pseudorandom numbers: Fast generation and distribution', Journal of Mathematical Cryptology, vol. 3, pp. 149 - 163, http://dx.doi.org/10.1515/JMC.2009.007
    Journal articles | 2009
    Professor Igor Shparlinski
    Friedlander JB; Shparlinski IE, 2009, 'On the density of some special primes', Journal of Mathematical Cryptology, vol. 3, pp. 265 - 271, http://dx.doi.org/10.1515/JMC.2009.016
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average', Michigan Mathematical Journal, vol. 56, pp. 99 - 111, http://dx.doi.org/10.1307/mmj/1213972400
    Journal articles | 2008
    Professor Igor Shparlinski
    Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'Products in residue classes', Mathematical Research Letters, vol. 15, pp. 1133 - 1147, http://dx.doi.org/10.4310/mrl.2008.v15.n6.a6
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'Exponential sums and prime divisors of sparse integers', Periodica Mathematica Hungarica, vol. 57, pp. 93 - 99, http://dx.doi.org/10.1007/s10998-008-7093-3
    Journal articles | 2008
    Professor Igor Shparlinski
    Kohnen W; Lau YK; Shparlinski IE, 2008, 'On the number of sign changes of hecke eigenvalues of newforms', Journal of the Australian Mathematical Society, vol. 85, pp. 87 - 94, http://dx.doi.org/10.1017/S1446788708000323
    Journal articles | 2008
    Professor Igor Shparlinski
    Cojocaru AC; Shparlinski IE, 2008, 'Distribution of farey fractions in residue classes and lang-trotter conjectures on average', Proceedings of the American Mathematical Society, vol. 136, pp. 1977 - 1986, http://dx.doi.org/10.1090/S0002-9939-08-09324-6
    Journal articles | 2008
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2008, 'On quadratic fields generated by polynomials', Archiv der Mathematik, vol. 91, pp. 399 - 408, http://dx.doi.org/10.1007/s00013-008-2656-2
    Journal articles | 2008
    Professor Igor Shparlinski
    Khan MR; Shparlinski IE; Yankov CL, 2008, 'On the convex closure of the graph of modular inversions', Experimental Mathematics, vol. 17, pp. 91 - 104, http://dx.doi.org/10.1080/10586458.2008.10129021
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski I, 2008, 'Bilinear character sums over elliptic curves', Finite Fields and their Applications, vol. 14, pp. 132 - 141, http://dx.doi.org/10.1016/j.ffa.2006.12.005
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2008, 'On the number of distances between the coordinates of points on modular hyperbolas', Journal of Number Theory, vol. 128, pp. 1224 - 1230, http://dx.doi.org/10.1016/j.jnt.2007.04.016
    Journal articles | 2008
    Professor Igor Shparlinski
    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, vol. 40, pp. 88 - 96, http://dx.doi.org/10.1112/blms/bdm111
    Journal articles | 2008
    Professor Igor Shparlinski
    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, vol. 2008, http://dx.doi.org/10.1093/imrn/rnn090
    Journal articles | 2008
    Professor Igor Shparlinski
    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), vol. 5106 LNCS, pp. 1 - 10, http://dx.doi.org/10.1007/978-3-540-89304-2_1
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski I, 2008, 'On the elliptic curve analogue of the sum-product problem', Finite Fields and their Applications, vol. 14, pp. 721 - 726, http://dx.doi.org/10.1016/j.ffa.2007.12.002
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2008, 'Visible points on multidimensional modular hyperbolas', Journal of Number Theory, vol. 128, pp. 2695 - 2703, http://dx.doi.org/10.1016/j.jnt.2008.02.011
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'On the solvability of bilinear equations in finite fields', Glasgow Mathematical Journal, vol. 50, pp. 523 - 529, http://dx.doi.org/10.1017/S0017089508004382
    Journal articles | 2008
    Professor Igor Shparlinski
    Journal articles | 2008
    Professor Igor Shparlinski
    Bourgain J; Shparlinski IE, 2008, 'Distribution of consecutive modular roots of an integer', Acta Arithmetica, vol. 134, pp. 83 - 91, http://dx.doi.org/10.4064/aa134-1-6
    Journal articles | 2008
    Professor Igor Shparlinski
    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), vol. 4957 LNCS, pp. 284 - 292, http://dx.doi.org/10.1007/978-3-540-78773-0_25
    Journal articles | 2008
    Professor Igor Shparlinski
    Graham SW; Shparlinski IE, 2008, 'On RSA moduli with almost half of the bits prescribed', Discrete Applied Mathematics, vol. 156, pp. 3150 - 3154, http://dx.doi.org/10.1016/j.dam.2007.12.012
    Journal articles | 2008
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2008, 'On the values of the divisor function', Monatshefte fur Mathematik, vol. 154, pp. 59 - 69, http://dx.doi.org/10.1007/s00605-007-0511-3
    Journal articles | 2008
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2008, 'Arithmetic properties of Apéry numbers', Journal of the London Mathematical Society, vol. 78, pp. 545 - 562, http://dx.doi.org/10.1112/jlms/jdn031
    Journal articles | 2008
    Professor Igor Shparlinski
    Balasuriya S; Banks WD; Shparlinski IE, 2008, 'Congruences and exponential sums with the sum of aliquot divisors function', International Journal of Number Theory, vol. 4, pp. 903 - 909, http://dx.doi.org/10.1142/S179304210800178X
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski I, 2008, 'On the size of the Jacobians of curves over finite fields', Bulletin of the Brazilian Mathematical Society, vol. 39, pp. 587 - 595, http://dx.doi.org/10.1007/s00574-008-0006-4
    Journal articles | 2008
    Professor Igor Shparlinski
    Journal articles | 2008
    Professor Igor Shparlinski
    Ford K; Shparlinski I, 2008, 'On curves over finite fields with Jacobians of small exponent', International Journal of Number Theory, vol. 4, pp. 819 - 826, http://dx.doi.org/10.1142/S1793042108001687
    Journal articles | 2008
    Professor Igor Shparlinski
    Luca F; Shparlinski IE; Thangadurai R, 2008, 'Quadratic non-residues versus primitive roots modulo p', Journal of the Ramanujan Mathematical Society, vol. 23, pp. 97 - 104
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'Arithmetic and geometric progressions in product sets over finite fields', Bulletin of the Australian Mathematical Society, vol. 78, pp. 357 - 364, http://dx.doi.org/10.1017/S0004972708000695
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'On the distribution of kloosterman sums', Proceedings of the American Mathematical Society, vol. 136, pp. 419 - 425, http://dx.doi.org/10.1090/S0002-9939-07-08943-5
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski I, 2008, 'On the exponential sum-product problem', Indagationes Mathematicae, vol. 19, pp. 325 - 331, http://dx.doi.org/10.1016/S0019-3577(08)80006-7
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'Approximation by several rationals', Bulletin of the Australian Mathematical Society, vol. 77, pp. 325 - 329, http://dx.doi.org/10.1017/S0004972708000373
    Journal articles | 2008
    Professor Igor Shparlinski
    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), vol. 4957 LNCS, pp. 276 - 283, http://dx.doi.org/10.1007/978-3-540-78773-0_24
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE, 2008, 'Infinite hilbert class field towers over cyclotomic fields', Glasgow Mathematical Journal, vol. 50, pp. 27 - 32, http://dx.doi.org/10.1017/S0017089507003977
    Journal articles | 2008
    Professor Igor Shparlinski
    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, vol. 56, pp. 1 - 7, http://dx.doi.org/10.4064/ba56-1-1
    Journal articles | 2008
    Professor Igor Shparlinski
    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, vol. 40, pp. 532, http://dx.doi.org/10.1112/blms/bdn037
    Journal articles | 2008
    Professor Igor Shparlinski
    Shparlinski IE; Voloch JF, 2008, 'Average distribution of prime ideals in families of number fields', Bulletin of the Brazilian Mathematical Society, vol. 39, pp. 417 - 425, http://dx.doi.org/10.1007/s00574-008-0014-4
    Journal articles | 2008
    Professor Igor Shparlinski
    Blackburn SR; Shparlinski IE, 2008, 'On the average energy of circulant graphs', Linear Algebra and Its Applications, vol. 428, pp. 1956 - 1963, http://dx.doi.org/10.1016/j.laa.2007.11.003
    Journal articles | 2007
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2007, 'Pseudoprime Cullen and Woodall numbers', Colloquium Mathematicum, vol. 107, pp. 35 - 43, http://dx.doi.org/10.4064/cm107-1-5
    Journal articles | 2007
    Professor Igor Shparlinski
    Lange T; Shparlinski IE, 2007, 'Distribution of some sequences of points on elliptic curves', Journal of Mathematical Cryptology, vol. 1, pp. 1 - 11, http://dx.doi.org/10.1515/JMC.2007.001
    Journal articles | 2007
    Professor Igor Shparlinski
    Saxena N; Severini S; Shparlinski I, 2007, 'Parameters of integral circulant graphs and periodic quantum dynamics', International Journal of Quantum Information, vol. 5, pp. 417 - 430, http://dx.doi.org/10.1142/S0219749907002918
    Journal articles | 2007
    Professor Igor Shparlinski
    Friedlander JB; Shparlinski IE, 2007, 'Least totient in a residue class', Bulletin of the London Mathematical Society, vol. 39, pp. 425 - 432, http://dx.doi.org/10.1112/blms/bdm027
    Journal articles | 2007
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2007, 'Prime divisors in Beatty sequences', Journal of Number Theory, vol. 123, pp. 413 - 425, http://dx.doi.org/10.1016/j.jnt.2006.07.011
    Journal articles | 2007
    Professor Igor Shparlinski
    Balasuriya S; Shparlinski IE, 2007, 'Character sums with subsequence sums', Periodica Mathematica Hungarica, vol. 55, pp. 215 - 221, http://dx.doi.org/10.1007/s10998-007-4215-4
    Journal articles | 2007
    Professor Igor Shparlinski
    Ahmadi O; Shparlinski IE, 2007, 'Distribution of matrices with restricted entries over finite fields', Indagationes Mathematicae, vol. 18, pp. 327 - 337, http://dx.doi.org/10.1016/S0019-3577(07)00013-4
    Journal articles | 2007
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2007, 'Arithmetic functions with linear recurrence sequences', Journal of Number Theory, vol. 125, pp. 459 - 472, http://dx.doi.org/10.1016/j.jnt.2006.12.006
    Journal articles | 2007
    Professor Igor Shparlinski
    Garaev MZ; Luca F; Shparlinski IE, 2007, 'Exponential sums with Catalan numbers and middle binomial coefficients', Indagationes Mathematicae, vol. 18, pp. 23 - 37, http://dx.doi.org/10.1016/S0019-3577(07)80004-8
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'Character sums over shifted smooth numbers', Proceedings of the American Mathematical Society, vol. 135, pp. 2699 - 2705, http://dx.doi.org/10.1090/S0002-9939-07-08785-0
    Journal articles | 2007
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2007, 'On values taken by the largest prime factor of shifted primes', Journal of the Australian Mathematical Society, vol. 82, pp. 133 - 147, http://dx.doi.org/10.1017/s1446788700017511
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'On the distribution of points on multidimensional modular hyperbolas', Proceedings of the Japan Academy Series A: Mathematical Sciences, vol. 83, pp. 5 - 9, http://dx.doi.org/10.3792/pjaa.83.5
    Journal articles | 2007
    Professor Igor Shparlinski
    Ahmadi O; Shparlinski IE, 2007, 'Geometric progressions in sumsets over finite fields', Monatshefte fur Mathematik, vol. 152, pp. 177 - 185, http://dx.doi.org/10.1007/s00605-007-0471-7
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'On some dynamical systems in finite fields and residue rings', Discrete and Continuous Dynamical Systems, vol. 17, pp. 901 - 917, http://dx.doi.org/10.3934/dcds.2007.17.901
    Journal articles | 2007
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2007, 'Discriminants of complex multiplication fields of elliptic curves over finite fields', Canadian Mathematical Bulletin, vol. 50, pp. 409 - 417, http://dx.doi.org/10.4153/CMB-2007-039-2
    Journal articles | 2007
    Professor Igor Shparlinski
    Banks WD; Luca F; Shparlinski IE, 2007, 'Estimates for Wieferich numbers', Ramanujan Journal, vol. 14, pp. 361 - 378, http://dx.doi.org/10.1007/s11139-007-9030-z
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', Journal of Number Theory, vol. 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', JOURNAL OF NUMBER THEORY, vol. 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'Bounds on the Fourier coefficients of the weighted sum function', Information Processing Letters, vol. 103, pp. 83 - 87, http://dx.doi.org/10.1016/j.ipl.2007.02.011
    Journal articles | 2007
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2007, 'On finite fields for pairing based cryptography', ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 1, pp. 281 - 286, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254707500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'Communication complexity of some number theoretic functions', Applied Mathematics Letters, vol. 20, pp. 872 - 875, http://dx.doi.org/10.1016/j.aml.2006.05.024
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE; Steinfeld R, 2007, 'Chinese remaindering with multiplicative noise', Theory of Computing Systems, vol. 40, pp. 33 - 41, http://dx.doi.org/10.1007/s00224-005-1272-9
    Journal articles | 2007
    Professor Igor Shparlinski
    Becheanu M; Luca F; Shparlinski IE, 2007, 'On the sums of complementary divisors', INTERNATIONAL JOURNAL OF NUMBER THEORY, vol. 3, pp. 635 - 648, http://dx.doi.org/10.1142/S1793042107001152
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE; Voloch JF, 2007, 'Visible Points on Curves over Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, vol. 55, pp. 193 - 199, http://dx.doi.org/10.4064/ba55-3-1
    Journal articles | 2007
    Professor Igor Shparlinski
    Journal articles | 2007
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2007, 'On the square-free parts of ⌊en!⌋', Glasgow Mathematical Journal, vol. 49, pp. 391 - 403, http://dx.doi.org/10.1017/S0017089507003734
    Journal articles | 2007
    Professor Igor Shparlinski
    Blake IF; Shparlinski IE, 2007, 'Statistical distribution and collisions of VSH', JOURNAL OF MATHEMATICAL CRYPTOLOGY, vol. 1, pp. 329 - 349, http://dx.doi.org/10.1515/JMC.2007.016
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski I, 2007, 'A computational introduction to number theory and algebra', MATHEMATICS OF COMPUTATION, vol. 76, pp. 1697 - 1698, http://dx.doi.org/10.1090/S0025-5718-07-01995-3
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'Distribution of roots of polynomial congruences', International Journal of Mathematics and Mathematical Sciences, vol. 2007, http://dx.doi.org/10.1155/2007/37853
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE, 2007, 'On the distribution of angles of the salié sums', Bulletin of the Australian Mathematical Society, vol. 75, pp. 221 - 227, http://dx.doi.org/10.1017/s0004972700039150
    Journal articles | 2007
    Professor Igor Shparlinski
    Balasuriya S; Luca F; Shparlinski IE, 2007, 'Prime Divisors Of Some Recurrence Sequence', Periodica Mathematica Hungarica, vol. 54, pp. 215 - 227, http://dx.doi.org/10.1007/s-10998-007-2215-z
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2007, 'Quantum period reconstruction of approximate sequences', Information Processing Letters, vol. 103, pp. 211 - 215, http://dx.doi.org/10.1016/j.ipl.2007.02.019
    Journal articles | 2007
    Professor Igor Shparlinski
    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, vol. 307, pp. 1218 - 1219, http://dx.doi.org/10.1016/j.disc.2006.10.009
    Journal articles | 2007
    Professor Igor Shparlinski
    Shparlinski IE; Sutantyo D, 2007, 'On the set of the largest prime divisors', Publicationes Mathematicae, vol. 71, pp. 95 - 100
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Friedlander JB; Luca F; Pappalardi F; Shparlinski IE, 2006, 'Coincidences in the values of the Euler and Carmichael functions', Acta Arithmetica, vol. 122, pp. 207 - 234, http://dx.doi.org/10.4064/aa122-3-1
    Journal articles | 2006
    Professor Igor Shparlinski
    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, vol. 52, pp. 3299 - 3304, http://dx.doi.org/10.1109/TIT.2006.876352
    Journal articles | 2006
    Professor Igor Shparlinski
    Contini S; Croot E; Shparlinski IE, 2006, 'Complexity of inverting the Euler function', Mathematics of Computation, vol. 75, pp. 983 - 996, http://dx.doi.org/10.1090/S0025-5718-06-01826-6
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski IE, 2006, 'On some generalisations of the Erdos distance problem over finite fields', Bulletin of the Australian Mathematical Society, vol. 73, pp. 285 - 292, http://dx.doi.org/10.1017/S0004972700038867
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2006, 'Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function', Indagationes Mathematicae, vol. 17, pp. 611 - 625, http://dx.doi.org/10.1016/S0019-3577(06)81037-2
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski IE, 2006, 'On RSA moduli with prescribed bit patterns', Designs, Codes, and Cryptography, vol. 39, pp. 113 - 122, http://dx.doi.org/10.1007/s10623-005-3137-2
    Journal articles | 2006
    Professor Igor Shparlinski
    Garaev MZ; Luca F; Shparlinski IE, 2006, 'Catalan and Apéry numbers in residue classes', Journal of Combinatorial Theory. Series A, vol. 113, pp. 851 - 865, http://dx.doi.org/10.1016/j.jcta.2005.08.003
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2006, 'Non-residues and primitive roots in beatty sequences', Bulletin of the Australian Mathematical Society, vol. 73, pp. 433 - 443, http://dx.doi.org/10.1017/s0004972700035449
    Journal articles | 2006
    Professor Igor Shparlinski
    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), vol. 3887 LNCS, pp. 793 - 799, http://dx.doi.org/10.1007/11682462_72
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2006, 'Short character sums with beatty sequences', Mathematical Research Letters, vol. 13, pp. 539 - 547, http://dx.doi.org/10.4310/MRL.2006.v13.n4.a4
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Friedlander JB; Konyagin SV; Shparlinski IE, 2006, 'Incomplete exponential sums and Diffie-Hellman triples', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 140, pp. 193 - 206, http://dx.doi.org/10.1017/S0305004105008947
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2006, 'Elliptic curves with low embedding degree', Journal of Cryptology, vol. 19, pp. 553 - 562, http://dx.doi.org/10.1007/s00145-006-0544-0
    Journal articles | 2006
    Professor Igor Shparlinski
    Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Exponential sums with Dickson polynomials', Finite Fields and their Applications, vol. 12, pp. 16 - 25, http://dx.doi.org/10.1016/j.ffa.2004.08.001
    Journal articles | 2006
    Professor Igor Shparlinski
    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), vol. 4086 LNCS, pp. 295 - 303, http://dx.doi.org/10.1007/11863854_25
    Journal articles | 2006
    Professor Igor Shparlinski
    El-Mahassni ED; Shparlinski IE; Winterhof A, 2006, 'Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers', Monatshefte fur Mathematik, vol. 148, pp. 297 - 307, http://dx.doi.org/10.1007/s00605-005-0355-7
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2006, 'Arithmetic properties of the Ramanujan function', Proceedings of the Indian Academy of Sciences: Mathematical Sciences, vol. 116, pp. 1 - 8, http://dx.doi.org/10.1007/BF02829735
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2006, 'Congruences and rational exponential sums with the euler function', Rocky Mountain Journal of Mathematics, vol. 36, pp. 1415 - 1426, http://dx.doi.org/10.1216/rmjm/1181069373
    Journal articles | 2006
    Professor Igor Shparlinski
    Blake IF; Garefalakis T; Shparlinski IE, 2006, 'On the bit security of the Diffie-Hellman key', Applicable Algebra in Engineering, Communications and Computing, vol. 16, pp. 397 - 404, http://dx.doi.org/10.1007/s00200-005-0184-x
    Journal articles | 2006
    Professor Igor Shparlinski
    Blackburn SR; Shparlinski IE, 2006, 'Character sums and nonlinear recurrence sequences', Discrete Mathematics, vol. 306, pp. 1126 - 1131, http://dx.doi.org/10.1016/j.disc.2006.02.012
    Journal articles | 2006
    Professor Igor Shparlinski
    Garaev MZ; Luca F; Shparlinski IE, 2006, 'Distribution of harmonic sums and Bernoulli polynomials modulo a prime', Mathematische Zeitschrift, vol. 253, pp. 855 - 865, http://dx.doi.org/10.1007/s00209-006-0939-5
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Double character sums over elliptic curves and finite fields', PURE AND APPLIED MATHEMATICS QUARTERLY, vol. 2, pp. 179 - 197, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000241377300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2006, 'Average Value of the Euler Function on Binary Palindromes', Bulletin of the Polish Academy of Sciences Mathematics, vol. 54, pp. 95 - 101, http://dx.doi.org/10.4064/ba54-2-1
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski IE, 2006, 'Primitive Points on a Modular Hyperbola', Bulletin of the Polish Academy of Sciences Mathematics, vol. 54, pp. 193 - 200, http://dx.doi.org/10.4064/ba54-3-1
    Journal articles | 2006
    Professor Igor Shparlinski
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', Journal of Algorithms, vol. 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski I, 2006, 'On the energy of some circulant graphs', Linear Algebra and Its Applications, vol. 414, pp. 378 - 382, http://dx.doi.org/10.1016/j.laa.2005.10.020
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2006, 'Uniformity of distribution modulo 1 of the geometric mean prime divisor', Boletin de la Sociedad Matematica Mexicana, vol. 12, pp. 155 - 163
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2006, 'Some divisibilities amongst the terms of linear recurrences', Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, vol. 76, pp. 143 - 156, http://dx.doi.org/10.1007/BF02960862
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2006, 'On the nonlinearity of linear recurrence sequences', Applied Mathematics Letters, vol. 19, pp. 340 - 344, http://dx.doi.org/10.1016/j.aml.2005.04.015
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski IE, 2006, 'Truncations of L-functions in residue classes', Glasgow Mathematical Journal, vol. 48, pp. 347 - 350, http://dx.doi.org/10.1017/S0017089506003120
    Journal articles | 2006
    Professor Igor Shparlinski
    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, vol. 81, pp. 1 - 22, http://dx.doi.org/10.4171/CMH/40
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski I, 2006, 'On the set of distances between two sets over finite fields', International Journal of Mathematics and Mathematical Sciences, vol. 2006, http://dx.doi.org/10.1155/IJMMS/2006/59482
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; McKee J; Shparlinsk IE, 2006, 'Small exponent point groups on elliptic curves', Journal de Theorie des Nombres de Bordeaux, vol. 18, pp. 471 - 476, http://dx.doi.org/10.5802/jtnb.554
    Journal articles | 2006
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski IE, 2006, 'GCD of random linear combinations', Algorithmica (New York), vol. 46, pp. 137 - 148, http://dx.doi.org/10.1007/s00453-006-0072-1
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Character sums with exponential functions over smooth numbers', Indagationes Mathematicae, vol. 17, pp. 157 - 168, http://dx.doi.org/10.1061/(ASCE)0733-9372(2006)132:2(157)
    Journal articles | 2006
    Professor Igor Shparlinski
    Coppersmith D; Howgrave-Graham N; Nguyễn PQ; Shparlinski IE, 2006, 'Testing set proportionality and the Ádám isomorphism of circulant graphs', Journal of Discrete Algorithms, vol. 4, pp. 324 - 335, http://dx.doi.org/10.1016/j.jda.2005.06.003
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2006, 'Multiplicative character sums with the sum of g-ary digits function', Ramanujan Journal, vol. 11, pp. 215 - 219, http://dx.doi.org/10.1007/s11139-006-6508-z
    Journal articles | 2006
    Professor Igor Shparlinski
    Shparlinski IE, 2006, 'On the sum of iterations of the Euler function', Journal of Integer Sequences, vol. 9, pp. 1 - 5
    Journal articles | 2006
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2006, 'On the number of polynomial maps into $\mathbb{Z}_{n}$', Tsukuba Journal of Mathematics, vol. 30, http://dx.doi.org/10.21099/tkbjm/1496165073
    Journal articles | 2006
    Professor Igor Shparlinski
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', JOURNAL OF ALGORITHMS-COGNITION INFORMATICS AND LOGIC, vol. 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks MK, 2006, 'Editor’s Note', Journal of Environmental Engineering, vol. 132, pp. 157 - 157, http://dx.doi.org/10.1061/(asce)0733-9372(2006)132:2(157)
    Journal articles | 2006
    Professor Igor Shparlinski
    Banks WD; Luca F; Shparlinski IE, 2006, 'Common divisors of the Euler function at related arguments', ACTA SCIENTIARUM MATHEMATICARUM, vol. 72, pp. 525 - 536, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000216758800005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2006
    Professor Igor Shparlinski
    Journal articles | 2005
    Professor Igor Shparlinski
    Banks WD; Harman G; Shparlinski IE, 2005, 'Distributional properties of the largest prime factor', Michigan Mathematical Journal, vol. 53, pp. 665 - 681, http://dx.doi.org/10.1307/mmj/1133894172
    Journal articles | 2005
    Professor Igor Shparlinski
    Shparlinski I; Winterhof A, 2005, 'A hidden number problem in small subgroups', Mathematics of Computation, vol. 74, pp. 2073 - 2080, http://dx.doi.org/10.1090/S0025-5718-05-01797-7
    Journal articles | 2005
    Professor Igor Shparlinski
    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, vol. 133, pp. 3463 - 3468, http://dx.doi.org/10.1090/S0002-9939-05-07962-1
    Journal articles | 2005
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Banks WD; Ford K; Luca F; Pappalardi F; Shparlinski IE, 2005, 'Values of the Euler function in various sequences', Monatshefte fur Mathematik, vol. 146, pp. 1 - 19, http://dx.doi.org/10.1007/s00605-005-0302-7
    Journal articles | 2005
    Professor Igor Shparlinski
    Shparlinski IE, 2005, 'On the singularity of generalised Vandermonde matrices over finite fields', Finite Fields and their Applications, vol. 11, pp. 193 - 199, http://dx.doi.org/10.1016/j.ffa.2004.11.001
    Journal articles | 2005
    Professor Igor Shparlinski
    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, vol. 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002
    Journal articles | 2005
    Professor Igor Shparlinski
    Banks WD; Luca F; Shparlinski IE, 2005, 'Irrationality of power series for various number theoretic functions', Manuscripta Mathematica, vol. 117, pp. 183 - 197, http://dx.doi.org/10.1007/s00229-005-0564-3
    Journal articles | 2005
    Professor Igor Shparlinski
    Banks WD; Luca F; Shparlinski IE, 2005, 'Some divisibility properties of the Euler function', Glasgow Mathematical Journal, vol. 47, pp. 517 - 528, http://dx.doi.org/10.1017/S0017089505002752
    Journal articles | 2005
    Professor Igor Shparlinski
    Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2005, 'Predicting nonlinear pseudorandom number generators', Mathematics of Computation, vol. 74, pp. 1471 - 1494, http://dx.doi.org/10.1090/S0025-5718-04-01698-9
    Journal articles | 2005
    Professor Igor Shparlinski
    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, vol. 15, pp. 329 - 337, http://dx.doi.org/10.1007/s00200-004-0161-9
    Journal articles | 2005
    Professor Igor Shparlinski
    Everest G; Shparlinski IE, 2005, 'Prime divisors of sequences associated to elliptic curves', Glasgow Mathematical Journal, vol. 47, pp. 115 - 122, http://dx.doi.org/10.1017/S0017089504002113
    Journal articles | 2005
    Professor Igor Shparlinski
    Shparlinski I; Winterhof A, 2005, 'Noisy interpolation of sparse polynomials in finite fields', Applicable Algebra in Engineering, Communications and Computing, vol. 16, pp. 307 - 317, http://dx.doi.org/10.1007/s00200-005-0180-1
    Journal articles | 2005
    Professor Igor Shparlinski
    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, vol. 46, http://dx.doi.org/10.1063/1.1998831
    Journal articles | 2005
    Professor Igor Shparlinski
    Contini S; Shparlinski IE, 2005, 'On Stern's attack against secret truncated linear congruential generators', Lecture Notes in Computer Science, vol. 3574, pp. 52 - 60, http://dx.doi.org/10.1007/11506157_5
    Journal articles | 2005
    Professor Igor Shparlinski
    Lange T; Shparlinski IE, 2005, 'Certain exponential sums and random walks on elliptic curves', Canadian Journal of Mathematics, vol. 57, pp. 338 - 350, http://dx.doi.org/10.4153/CJM-2005-015-8
    Journal articles | 2005
    Professor Igor Shparlinski
    Hess F; Shparlinski IE, 2005, 'On the linear complexity and multidimensional distribution of congruential generators over elliptic curves', Designs, Codes, and Cryptography, vol. 35, pp. 111 - 117, http://dx.doi.org/10.1007/s10623-003-6153-0
    Journal articles | 2005
    Professor Igor Shparlinski
    Banks WD; Luca F; Saidak F; Shparlinski IE, 2005, 'Values of arithmetical functions equal to a sum of two squares', Quarterly Journal of Mathematics, vol. 56, pp. 123 - 139, http://dx.doi.org/10.1093/qmath/hah039
    Journal articles | 2005
    Professor Igor Shparlinski
    Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, 'Uniform Distribution of the Fractional Part of the Average Prime Divisor', Forum Mathematicum, vol. 17, pp. 885 - 901, http://dx.doi.org/10.1515/form.2005.17.6.885
    Journal articles | 2005
    Professor Igor Shparlinski
    Shparlinski IE, 2005, 'On the value set of the Ramanujan function', Archiv der Mathematik, vol. 85, pp. 508 - 513, http://dx.doi.org/10.1007/s00013-005-1322-1
    Journal articles | 2005
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Shparlinski IE; Winterhof A, 2005, 'On the linear complexity of bounded integer sequences over different moduli', Information Processing Letters, vol. 96, pp. 175 - 177, http://dx.doi.org/10.1016/j.ipl.2005.08.004
    Journal articles | 2005
    Professor Igor Shparlinski
    Garaev MZ; Luca F; Shparlinski IE, 2005, 'Waring problem with factorials', Bulletin of the Australian Mathematical Society, vol. 71, pp. 259 - 264, http://dx.doi.org/10.1017/s0004972700038223
    Journal articles | 2005
    Professor Igor Shparlinski
    Levieil E; Luca F; Shparlinski IE, 2005, 'Bounding the number of solutions of some congruences', Boletin de la Sociedad Matematica Mexicana, vol. 11, pp. 175 - 180
    Journal articles | 2005
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2005, 'On the largest prime factor of n! + 2n − 1', Journal de Theorie des Nombres de Bordeaux, vol. 17, pp. 859 - 870, http://dx.doi.org/10.5802/jtnb.524
    Journal articles | 2005
    Professor Igor Shparlinski
    De Koninck JM; Luca F; Shparlinski IE, 2005, 'Powerful numbers in short intervals', Bulletin of the Australian Mathematical Society, vol. 71, pp. 11 - 16, http://dx.doi.org/10.1017/s0004972700037953
    Journal articles | 2005
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2005, 'Prime divisors of palindromes', Periodica Mathematica Hungarica, vol. 51, pp. 1 - 10, http://dx.doi.org/10.1007/s10998-005-0016-6
    Journal articles | 2005
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2005, 'Prime divisors of shifted factorials', Bulletin of the London Mathematical Society, vol. 37, pp. 809 - 817, http://dx.doi.org/10.1112/S0024609305004923
    Journal articles | 2005
    Professor Igor Shparlinski
    Friedlander JB; Pomerance C; Shparlinski IE, 2005, 'Finding the group structure of elliptic curves over finite fields', Bulletin of the Australian Mathematical Society, vol. 72, pp. 251 - 263, http://dx.doi.org/10.1017/s0004972700035048
    Journal articles | 2005
    Professor Igor Shparlinski
    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, vol. 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002
    Journal articles | 2005
    Professor Igor Shparlinski
    Hallgren S; Russell A; Shparlinski IE, 2005, 'Quantum noisy rational function reconstruction', Lecture Notes in Computer Science, vol. 3595, pp. 420 - 429, http://dx.doi.org/10.1007/11533719_43
    Journal articles | 2005
    Professor Igor Shparlinski
    Levieil E; Luca F; Shparlinski IE, 2005, 'Prime divisors of some shifted products', International Journal of Mathematics and Mathematical Sciences, vol. 2005, pp. 3057 - 3073, http://dx.doi.org/10.1155/IJMMS.2005.3057
    Journal articles | 2005
    Professor Igor Shparlinski
    Cohen SD; Dewar M; Friedlander JB; Panario D; Shparlinski IE, 2005, 'Polynomial gauss sums', Proceedings of the American Mathematical Society, vol. 133, pp. 2225 - 2231, http://dx.doi.org/10.1090/S0002-9939-05-08004-4
    Journal articles | 2005
    Professor Igor Shparlinski
    Shparlinski IE, 2005, 'On the nonlinearity of the sequence of signs of Kloosterman sums', Bulletin of the Australian Mathematical Society, vol. 71, pp. 405 - 409, http://dx.doi.org/10.1017/s0004972700038405
    Journal articles | 2005
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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 | 2004
    Professor Igor Shparlinski
    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, vol. 16, pp. 107 - 123, http://dx.doi.org/10.5802/jtnb.436
    Journal articles | 2004
    Professor Igor Shparlinski
    Goresky M; Klapper A; Murty R; Shparlinski I, 2004, 'On decimations of ℓ-sequences', SIAM Journal on Discrete Mathematics, vol. 18, pp. 130 - 140, http://dx.doi.org/10.1137/S0895480102403428
    Journal articles | 2004
    Professor Igor Shparlinski
    Chou WS; Shparlinski IE, 2004, 'On the cycle structure of repeated exponentiation modulo a prime', Journal of Number Theory, vol. 107, pp. 345 - 356, http://dx.doi.org/10.1016/j.jnt.2004.04.005
    Journal articles | 2004
    Professor Igor Shparlinski
    Russell A; Shparlinski IE, 2004, 'Classical and quantum function reconstruction via character evaluation', Journal of Complexity, vol. 20, pp. 404 - 422, http://dx.doi.org/10.1016/j.jco.2003.08.019
    Journal articles | 2004
    Professor Igor Shparlinski
    Shparlinski IE; Steinfield R, 2004, 'Noisy Chinese remaindering in the Lee norm', Journal of Complexity, vol. 20, pp. 423 - 437, http://dx.doi.org/10.1016/j.jco.2003.08.020
    Journal articles | 2004
    Professor Igor Shparlinski
    Shparlinski IE, 2004, 'Distribution of exponential functions with squarefull exponent in residue rings', Indagationes Mathematicae, vol. 15, pp. 283 - 289, http://dx.doi.org/10.1016/S0019-3577(04)90020-1
    Journal articles | 2004
    Professor Igor Shparlinski
    Shparlinski IE, 2004, 'Security of polynomial transformations of the Diffie-Hellman key', Finite Fields and their Applications, vol. 10, pp. 123 - 131, http://dx.doi.org/10.1016/S1071-5797(03)00048-0
    Journal articles | 2004
    Professor Igor Shparlinski
    Shparlinski IE, 2004, 'Bounds of Gauss sums in finite fields', Proceedings of the American Mathematical Society, vol. 132, pp. 2817 - 2824, http://dx.doi.org/10.1090/S0002-9939-04-07133-3
    Journal articles | 2004
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2004, 'Arithmetic properties of numbers with restricted digits', Acta Arithmetica, vol. 112, pp. 313 - 332, http://dx.doi.org/10.4064/aa112-4-1
    Journal articles | 2004
    Professor Igor Shparlinski
    Banks WD; Conflitti A; Friedlander JB; Shparlinski IE, 2004, 'Exponential sums over Mersenne numbers', Compositio Mathematica, vol. 140, pp. 15 - 30, http://dx.doi.org/10.1112/S0010437X03000022
    Journal articles | 2004
    Professor Igor Shparlinski
    Garaev MZ; Luca F; Shparlinski IE, 2004, 'Character sums and congruences with n!', Transactions of the American Mathematical Society, vol. 356, pp. 5089 - 5102, http://dx.doi.org/10.1090/S0002-9947-04-03612-8
    Journal articles | 2004
    Professor Igor Shparlinski
    Banks WD; Conflitti A; Shparlinski IE, 2004, 'Number theoretic designs for directed regular graphs of small diameter', SIAM Journal on Discrete Mathematics, vol. 17, pp. 377 - 383, http://dx.doi.org/10.1137/S0895480101396676
    Journal articles | 2004
    Professor Igor Shparlinski
    Conflitti A; Shparlinski IE, 2004, 'On the multidimensional distribution of the subset sum generator of pseudorandom numbers', Mathematics of Computation, vol. 73, pp. 1005 - 1011, http://dx.doi.org/10.1090/S0025-5718-03-01563-1
    Journal articles | 2004
    Professor Igor Shparlinski
    Luca F; Mireles DJ; Shparlinski IE, 2004, 'Florianptic curves', Illinois Journal of Mathematics, vol. 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069
    Journal articles | 2004
    Professor Igor Shparlinski
    Luca F; Mireles DJ; Shparlinski IE, 2004, 'Mov attack in various subgroups on elliptic curves', ILLINOIS JOURNAL OF MATHEMATICS, vol. 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069
    Journal articles | 2004
    Professor Igor Shparlinski
    Shparlinski IE, 2004, 'Exponential function analogue of kloosterman sums', Rocky Mountain Journal of Mathematics, vol. 34, pp. 1497 - 1502, http://dx.doi.org/10.1216/rmjm/1181069811
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 2947, pp. 159 - 172
    Journal articles | 2004
    Professor Igor Shparlinski
    Banks WD; Harcharras A; Shparlinski IE, 2004, 'Smooth values of shifted primes in arithmetic progressions', Michigan Mathematical Journal, vol. 52, pp. 603 - 618, http://dx.doi.org/10.1307/mmj/1100623415
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 2976, pp. 589 - 598, http://dx.doi.org/10.1007/978-3-540-24698-5_61
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 3108, pp. 370 - 378, http://dx.doi.org/10.1007/978-3-540-27800-9_32
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 3357, pp. 241 - 251
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 2947, pp. 416 - 424, http://dx.doi.org/10.1007/978-3-540-24632-9_30
    Journal articles | 2004
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski IE, 2004, 'Polynomial Interpolation from Multiples', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 15, pp. 1125 - 1130
    Journal articles | 2004
    Professor Igor Shparlinski
    Dewar M; Panario D; Shparlinski IE, 2004, 'Distribution of exponential functions with k-full exponent modulo a prime', Indagationes Mathematicae, vol. 15, pp. 497 - 503, http://dx.doi.org/10.1016/S0019-3577(04)80014-4
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 3341, pp. 464 - 469
    Journal articles | 2004
    Professor Igor Shparlinski
    Frandsen GS; Shparlinski IE, 2004, 'On Reducing a System of Equations to a Single Equation', BRICS Report Series, vol. 11, http://dx.doi.org/10.7146/brics.v11i6.21831
    Journal articles | 2004
    Professor Igor Shparlinski
    Shparlinski IE, 2004, 'On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA', Information Processing Letters, vol. 92, pp. 143 - 147, http://dx.doi.org/10.1016/j.ipl.2004.07.004
    Journal articles | 2004
    Professor Igor Shparlinski
    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), vol. 3357, pp. 241 - 251
    Journal articles | 2003
    Professor Igor Shparlinski
    Luca F; Shparlinski IE, 2003, 'Average multiplicative orders of elements modulo n', Acta Arithmetica, vol. 109, pp. 387 - 411, http://dx.doi.org/10.4064/aa109-4-7
    Journal articles | 2003
    Professor Igor Shparlinski
    Howgrave-Graham NA; Nguyen PQ; Shparlinski IE, 2003, 'Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation', Mathematics of Computation, vol. 72, pp. 1473 - 1485, http://dx.doi.org/10.1090/S0025-5718-03-01495-9
    Journal articles | 2003
    Professor Igor Shparlinski
    Khan MR; Shparlinski IE, 2003, 'On the maximal difference between an element and its inverse modulo n', Periodica Mathematica Hungarica, vol. 47, pp. 111 - 117, http://dx.doi.org/10.1023/b:mahu.0000010815.14847.96
    Journal articles | 2003
    Professor Igor Shparlinski
    Pappalardi F; Saidak F; Shparlinski IE, 2003, 'Square-free values of the Carmichael function', Journal of Number Theory, vol. 103, pp. 122 - 131, http://dx.doi.org/10.1016/S0022-314X(03)00110-0
    Journal articles | 2003
    Professor Igor Shparlinski
    Nguyen PQ; Shparlinski IE, 2003, 'The insecurity of the digital signature algorithm with partially known nonces', Journal of Cryptology, vol. 15, pp. 151 - 176, http://dx.doi.org/10.1007/s00145-002-0021-3
    Journal articles | 2003
    Professor Igor Shparlinski
    Konyagin S; Lange T; Shparlinski I, 2003, 'Linear complexity of the discrete logarithm', Designs, Codes, and Cryptography, vol. 28, pp. 135 - 146, http://dx.doi.org/10.1023/A:1022584306676
    Journal articles | 2003
    Professor Igor Shparlinski
    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), vol. 2898, pp. 183 - 189, http://dx.doi.org/10.1007/978-3-540-40974-8_15
    Journal articles | 2003
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski I; Sinclair A, 2003, 'Finding points on curves over finite fields', SIAM Journal on Computing, vol. 32, pp. 1436 - 1448, http://dx.doi.org/10.1137/S0097539799351018
    Journal articles | 2003
    Professor Igor Shparlinski
    Banks WD; Harcharras A; Shparlinski IE, 2003, 'Short Kloosterman sums for polynomials over finite fields', Canadian Journal of Mathematics, vol. 55, pp. 225 - 246, http://dx.doi.org/10.4153/CJM-2003-010-0
    Journal articles | 2003
    Professor Igor Shparlinski
    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, vol. 35, pp. 522 - 528, http://dx.doi.org/10.1112/S002460930300198X
    Journal articles | 2003
    Professor Igor Shparlinski
    Nguyen PQ; Shparlinski IE, 2003, 'The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces', Designs, Codes, and Cryptography, vol. 30, pp. 201 - 217, http://dx.doi.org/10.1023/A:1025436905711
    Journal articles | 2003
    Professor Igor Shparlinski
    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, vol. 12, pp. 23 - 47, http://dx.doi.org/10.1007/s00037-003-0176-9
    Journal articles | 2003
    Professor Igor Shparlinski
    Shparlinski IE, 2003, '', Periodica Mathematica Hungarica, vol. 46, pp. 215 - 222, http://dx.doi.org/10.1023/a:1025996312037
    Journal articles | 2003
    Professor Igor Shparlinski
    Gutierrez J; Shparlinski IE; Winterhof A, 2003, 'On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators', IEEE Transactions on Information Theory, vol. 49, pp. 60 - 64, http://dx.doi.org/10.1109/TIT.2002.806144
    Journal articles | 2003
    Professor Igor Shparlinski
    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), vol. 2898, pp. 264 - 275, http://dx.doi.org/10.1007/978-3-540-40974-8_21
    Journal articles | 2003
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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), vol. 2567, pp. 62 - 70, http://dx.doi.org/10.1007/3-540-36288-6_5
    Journal articles | 2003
    Professor Igor Shparlinski
    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), vol. 2643, pp. 6 - 17, http://dx.doi.org/10.1007/3-540-44828-4_2
    Journal articles | 2002
    Professor Igor Shparlinski
    Friedlander JB; Konyagin S; Shparllnski IE, 2002, 'Some doubly exponential sums over ℤm', Acta Arithmetica, vol. 105, pp. 349 - 370, http://dx.doi.org/10.4064/aa105-4-4
    Journal articles | 2002
    Professor Igor Shparlinski
    Shparlinski IE, 2002, 'On a question of Erdos and Graham', Archiv der Mathematik, vol. 78, pp. 445 - 448, http://dx.doi.org/10.1007/s00013-002-8269-2
    Journal articles | 2002
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2002, 'Average normalisations of elliptic curves', Bulletin of the Australian Mathematical Society, vol. 66, pp. 353 - 358, http://dx.doi.org/10.1017/s0004972700040211
    Journal articles | 2002
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', Journal of Number Theory, vol. 95, pp. 340 - 350, http://dx.doi.org/10.1016/S0022-314X(01)92775-1
    Journal articles | 2002
    Professor Igor Shparlinski
    Mans B; Pappalardi F; Shparlinski I, 2002, 'On the spectral Ádám property for circulant graphs', Discrete Mathematics, vol. 254, pp. 309 - 329, http://dx.doi.org/10.1016/S0012-365X(01)00374-0
    Journal articles | 2002
    Professor Igor Shparlinski
    Shparlinski IE, 2002, 'On the distribution of the Diffie-Hellman pairs', Finite Fields and their Applications, vol. 8, pp. 131 - 141, http://dx.doi.org/10.1006/ffta.2000.0321
    Journal articles | 2002
    Professor Igor Shparlinski
    Niederreiter H; Shparlinski IE, 2002, 'On the average distribution of inversive pseudorandom numbers', Finite Fields and their Applications, vol. 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358
    Journal articles | 2002
    Professor Igor Shparlinski
    Banks WD; Conflitti A; Shparlinski IE, 2002, 'Character sums over integers with restricted g-ary digits', Illinois Journal of Mathematics, vol. 46, pp. 819 - 836, http://dx.doi.org/10.1215/ijm/1258130986
    Journal articles | 2002
    Professor Igor Shparlinski
    Vasco MIG; Shparlinski IE, 2002, 'Security of the most significant bits of the Shamir message passing scheme', Mathematics of Computation, vol. 71, pp. 333 - 342, http://dx.doi.org/10.1090/S0025-5718-01-01358-8
    Journal articles | 2002
    Professor Igor Shparlinski
    Codenotti B; Shparlinski IE; Winterhof A, 2002, 'On the hardness of approximating the permanent of structured matrices', Computational Complexity, vol. 11, pp. 158 - 170, http://dx.doi.org/10.1007/s00037-002-0174-3
    Journal articles | 2002
    Professor Igor Shparlinski
    El Mahassni E; Shparlinski I, 2002, 'On the uniformity of distribution of the elliptic curve ElGamal signature', Finite Fields and their Applications, vol. 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366
    Journal articles | 2002
    Professor Igor Shparlinski
    Shparlinski IE, 2002, 'Security of most significant bits of gx(2)', Information Processing Letters, vol. 83, pp. 109 - 113, http://dx.doi.org/10.1016/S0020-0190(01)00315-5
    Journal articles | 2002
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', JOURNAL OF NUMBER THEORY, vol. 95, pp. 340 - 350, http://dx.doi.org/10.1006/jnth.2001.2775
    Journal articles | 2002
    Professor Igor Shparlinski
    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, vol. 71, pp. 1803 - 1806, http://dx.doi.org/10.1090/S0025-5718-02-01519-3
    Journal articles | 2002
    Professor Igor Shparlinski
    Shparlinski IE, 2002, 'On the uniformity of distribution of the EIGamal signature', Applicable Algebra in Engineering, Communications and Computing, vol. 13, pp. 9 - 16, http://dx.doi.org/10.1007/s002000100087
    Journal articles | 2002
    Professor Igor Shparlinski
    Niederreiter H; Shparlinski IE, 2002, 'On the Average Distribution of Inversive Pseudorandom Numbers', Finite Fields and Their Applications, vol. 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358
    Journal articles | 2002
    Professor Igor Shparlinski
    El Mahassni E; Shparlinski I, 2002, 'On the Uniformity of Distribution of the Elliptic Curve ElGamal Signature', Finite Fields and Their Applications, vol. 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366
    Journal articles | 2001
    Professor Igor Shparlinski
    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, vol. 13, pp. 53 - 63, http://dx.doi.org/10.5802/jtnb.303
    Journal articles | 2001
    Professor Igor Shparlinski
    Niederreiter H; Shparlinski IE, 2001, 'On the distribution of inversive congruential pseudorandom numbers in parts of the period', Mathematics of Computation, vol. 70, pp. 1569 - 1574, http://dx.doi.org/10.1090/S0025-5718-00-01273-4
    Journal articles | 2001
    Professor Igor Shparlinski
    Shparlinski I, 2001, 'On the Linear Complexity of the Power Generator', Designs, Codes, and Cryptography, vol. 23, pp. 5 - 10, http://dx.doi.org/10.1023/A:1011264815860
    Journal articles | 2001
    Professor Igor Shparlinski
    Shparlinski IE, 2001, 'On the Uniformity of Distribution of the Naor-Reingold Pseudo-Random Function', Finite Fields and their Applications, vol. 7, pp. 318 - 326, http://dx.doi.org/10.1006/ffta.2000.0291
    Journal articles | 2001
    Professor Igor Shparlinski
    Friedlander JB; Pomerance C; Shparlinski IE, 2001, 'Period of the power generator and small values of Carmichael's function', Mathematics of Computation, vol. 70, pp. 1591 - 1605, http://dx.doi.org/10.1090/S0025-5718-00-01282-5
    Journal articles | 2001
    Professor Igor Shparlinski
    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 | 2001
    Professor Igor Shparlinski
    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), vol. 2139 LNCS, pp. 201 - 212, http://dx.doi.org/10.1007/3-540-44647-8_12
    Journal articles | 2001
    Professor Igor Shparlinski
    Shparlinski IE; Silverman JH, 2001, 'On the Linear Complexity of the Naor-Reingold Pseudo-random Function from Elliptic Curves', Designs, Codes, and Cryptography, vol. 24, pp. 279 - 289, http://dx.doi.org/10.1023/A:1011223204345
    Journal articles | 2001
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 2001, 'Distribution of inverses in polynomial rings', Indagationes Mathematicae, vol. 12, pp. 303 - 315, http://dx.doi.org/10.1016/S0019-3577(01)80012-4
    Journal articles | 2001
    Professor Igor Shparlinski
    El Mahassni E; Shparlinski I, 2001, 'Polynomial representations of the Diffie-Hellman mapping', Bulletin of the Australian Mathematical Society, vol. 63, pp. 467 - 473, http://dx.doi.org/10.1017/s0004972700019547
    Journal articles | 2001
    Professor Igor Shparlinski
    Friedlander JB; Shparlinski IE, 2001, 'Double exponential sums over thin sets', Proceedings of the American Mathematical Society, vol. 129, pp. 1617 - 1621, http://dx.doi.org/10.1090/s0002-9939-00-05921-9
    Journal articles | 2001
    Professor Igor Shparlinski
    Friedlander JB; Shparlinski IE, 2001, 'On the distribution of the power generator', Mathematics of Computation, vol. 70, pp. 1575 - 1589, http://dx.doi.org/10.1090/S0025-5718-00-01283-7
    Journal articles | 2001
    Professor Igor Shparlinski
    Friedlander JB; Shparlinsk IE, 2001, 'On the distribution of Diffie-Hellman triples with sparse exponents', SIAM Journal on Discrete Mathematics, vol. 14, pp. 162 - 169, http://dx.doi.org/10.1137/S0895480199361740
    Journal articles | 2001
    Professor Igor Shparlinski
    Shparlinski I, 2001, 'On the Multiplicative Orders of γ and γ+γ-1 over finite fields', Finite Fields and their Applications, vol. 7, pp. 327 - 331, http://dx.doi.org/10.1006/ffta.2000.0292
    Journal articles | 2001
    Professor Igor Shparlinski
    Bernasconi A; Damm C; Shparlinski I, 2001, 'Circuit and decision tree complexity of some number theoretic problems', Information and Computation, vol. 168, pp. 113 - 124, http://dx.doi.org/10.1006/inco.2000.3017
    Journal articles | 2001
    Professor Igor Shparlinski
    Shparlinski IE, 2001, 'On the uniformity of distribution of the RSA pairs', Mathematics of Computation, vol. 70, pp. 801 - 808, http://dx.doi.org/10.1090/S0025-5718-00-01274-6
    Journal articles | 2001
    Professor Igor Shparlinski
    Shparlinski I, 2001, 'On Some Properties of the Shrinking Generator', Designs, Codes, and Cryptography, vol. 23, pp. 147 - 156, http://dx.doi.org/10.1023/A:1011256430812
    Journal articles | 2001
    Professor Igor Shparlinski
    Lieman D; Shparlinski I, 2001, 'On a new exponential sum', Canadian Mathematical Bulletin, vol. 44, pp. 87 - 92, http://dx.doi.org/10.4153/CMB-2001-010-1
    Journal articles | 2001
    Professor Igor Shparlinski
    El Mahassni E; Shparlinski I, 2001, 'On Some Uniformity of Distribution Properties of ESIGN', Electronic Notes in Discrete Mathematics, vol. 6, pp. 132 - 139, http://dx.doi.org/10.1016/S1571-0653(04)00164-7
    Journal articles | 2000
    Professor Igor Shparlinski
    Karpinski M; Van Der Poorten A; Shparlinski I, 2000, 'Zero testing of p-adic and modular polynomials', Theoretical Computer Science, vol. 233, pp. 309 - 317, http://dx.doi.org/10.1016/S0304-3975(99)00133-4
    Journal articles | 2000
    Professor Igor Shparlinski
    Gutierrez J; Niederreiter H; Shparlinski IE, 2000, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatshefte fur Mathematik, vol. 129, pp. 31 - 36, http://dx.doi.org/10.1007/s006050050004
    Journal articles | 2000
    Professor Igor Shparlinski
    Friedlander JB; Hansen J; Shparlinski IE, 2000, 'Character sums with exponential functions', Mathematika, vol. 47, pp. 75 - 85, http://dx.doi.org/10.1112/S0025579300015734
    Journal articles | 2000
    Professor Igor Shparlinski
    Niederreiter H; Shparlinski IE, 2000, 'Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus', Acta Arithmetica, vol. 92, pp. 89 - 98, http://dx.doi.org/10.4064/aa-92-1-89-98
    Journal articles | 2000
    Professor Igor Shparlinski
    Niederreiter H; Shparlinski IE, 2000, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Applicable Algebra in Engineering, Communications and Computing, vol. 10, pp. 189 - 202, http://dx.doi.org/10.1007/s002000050124
    Journal articles | 2000
    Professor Igor Shparlinski
    Shparlinski IE, 2000, 'Linear complexity of the Naor-Reingold pseudo-random function', Information Processing Letters, vol. 76, pp. 95 - 99, http://dx.doi.org/10.1016/S0020-0190(00)00133-2
    Journal articles | 2000
    Professor Igor Shparlinski
    Coppersmith D; Shparlinski I, 2000, 'On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping', JOURNAL OF CRYPTOLOGY, vol. 13, pp. 339 - 360, http://dx.doi.org/10.1007/s001450010002
    Journal articles | 2000
    Professor Igor Shparlinski
    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, vol. 120, pp. 23 - 46, http://dx.doi.org/10.1007/s11856-000-1270-1
    Journal articles | 2000
    Professor Igor Shparlinski
    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), vol. 1776 LNCS, pp. 259 - 268, http://dx.doi.org/10.1007/10719839_27
    Journal articles | 2000
    Professor Igor Shparlinski
    Shparlinski IE, 2000, 'On the Naor-Reingold pseudo-random function from elliptic curves', Applicable Algebra in Engineering, Communications and Computing, vol. 11, pp. 27 - 34, http://dx.doi.org/10.1007/s002000000023
    Journal articles | 2000
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski IE, 2000, 'CREW PRAM complexity of modular inversion', SIAM Journal on Computing, vol. 29, pp. 1839 - 1857, http://dx.doi.org/10.1137/S0097539797328070
    Journal articles | 2000
    Professor Igor Shparlinski
    Griffin F; Shparlinski IE, 2000, 'On the linear complexity profile of the power generator', IEEE Transactions on Information Theory, vol. 46, pp. 2159 - 2162, http://dx.doi.org/10.1109/18.868485
    Journal articles | 2000
    Professor Igor Shparlinski
    Shparlinski IE, 2000, 'Computing Jacobi Symbols modulo Sparse Integers and Polynomials and Some Applications', Journal of Algorithms, vol. 36, pp. 241 - 252, http://dx.doi.org/10.1006/jagm.2000.1091
    Journal articles | 2000
    Professor Igor Shparlinski
    Bernasconi A; Damm C; Shparlinski I, 2000, 'The average sensitivity of square-freeness', Computational Complexity, vol. 9, pp. 39 - 51, http://dx.doi.org/10.1007/PL00001600
    Journal articles | 2000
    Professor Igor Shparlinski
    El Mahassni E; Shparlinski I, 2000, 'On some uniformity of distribution properties of ESIGN', Electronic Notes in Discrete Mathematics, vol. 6, pp. 1 - 8
    Journal articles | 1999
    Professor Igor Shparlinski
    Friedlander J; Larsen M; Lieman D; Shparlinski I, 1999, 'On the Correlation of Binary M-sequences', Designs, Codes, and Cryptography, vol. 16, pp. 249 - 256, http://dx.doi.org/10.1023/A:1008383811226
    Journal articles | 1999
    Professor Igor Shparlinski
    Niederreiter H; Shparlinski IE, 1999, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and their Applications, vol. 5, pp. 246 - 253, http://dx.doi.org/10.1006/ffta.1999.0257
    Journal articles | 1999
    Professor Igor Shparlinski
    Canetti R; Friedlander J; Shparlinski I, 1999, 'On certain exponential sums and the distribution of Diffie-Hellman triples', Journal of the London Mathematical Society, vol. 59, pp. 799 - 812, http://dx.doi.org/10.1112/S002461079900736X
    Journal articles | 1999
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski I, 1999, 'Computing components and projections of curves over finite fields', SIAM Journal on Computing, vol. 28, pp. 822 - 840, http://dx.doi.org/10.1137/s009753979427741x
    Journal articles | 1999
    Professor Igor Shparlinski
    Everest GR; Shparlinski IE, 1999, 'Counting the values taken by algebraic exponential polynomials', Proceedings of the American Mathematical Society, vol. 127, pp. 665 - 675, http://dx.doi.org/10.1090/s0002-9939-99-04728-0
    Journal articles | 1998
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski I, 1998, 'Orders of Gauss periods in finite fields', Applicable Algebra in Engineering, Communications and Computing, vol. 9, pp. 15 - 24, http://dx.doi.org/10.1007/s002000050093
    Journal articles | 1996
    Professor Igor Shparlinski
    Von Zur Gathen J; Karpinski M; Shparlinski I, 1996, 'Counting curves and their projections', Computational Complexity, vol. 6, pp. 64 - 99, http://dx.doi.org/10.1007/BF01202042
    Journal articles | 1996
    Professor Igor Shparlinski
    Shparlinski I, 1996, 'On finding primitive roots in finite fields', Theoretical Computer Science, vol. 157, pp. 273 - 275, http://dx.doi.org/10.1016/0304-3975(95)00164-6
    Journal articles | 1996
    Professor Igor Shparlinski
    Van Der Poorten AJ; Shparlinski IE, 1996, 'On linear recurrence sequences with polynomial coefficients', Glasgow Mathematical Journal, vol. 38, pp. 147 - 155, http://dx.doi.org/10.1017/s0017089500031372
    Journal articles | 1996
    Professor Igor Shparlinski
    Karpinski M; Shparlinski I, 1996, 'On some approximation problems concerning sparse polynomials over finite fields', Theoretical Computer Science, vol. 157, pp. 259 - 266, http://dx.doi.org/10.1016/0304-3975(95)00162-X
    Journal articles | 1996
    Professor Igor Shparlinski
    Shparlinski I, 1996, 'On exponential sums with sparse polynomials and rational functions', Journal of Number Theory, vol. 60, pp. 233 - 244, http://dx.doi.org/10.1006/jnth.1996.0121
    Journal articles | 1996
    Professor Igor Shparlinski
    Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', Applicable Algebra in Engineering, Communications and Computing, vol. 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260
    Journal articles | 1996
    Professor Igor Shparlinski
    Everest GR; Shparlinski IE, 1996, 'Divisor sums of generalised exponential polynomials', Canadian Mathematical Bulletin, vol. 39, pp. 35 - 46, http://dx.doi.org/10.4153/CMB-1996-005-5
    Journal articles | 1996
    Professor Igor Shparlinski
    Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol. 7, pp. 427 - 431, http://dx.doi.org/10.1007/s002000050043
    Journal articles | 1995
    Professor Igor Shparlinski
    Pappalardi F; Shparlinski I, 1995, 'On artin′s conjecture over function fields', Finite Fields and Their Applications, vol. 1, pp. 399 - 404, http://dx.doi.org/10.1006/ffta.1995.1030
    Journal articles | 1993
    Professor Igor Shparlinski
    Shparlinski IE, 1993, 'On parameters of some graphs from finite fields', European Journal of Combinatorics, vol. 14, pp. 589 - 591, http://dx.doi.org/10.1006/eujc.1993.1061
    Journal articles | 1993
    Professor Igor Shparlinski
    Shparlinski IE, 1993, 'Finding irreducible and primitive polynomials', Applicable Algebra in Engineering, Communication and Computing, vol. 4, pp. 263 - 268, http://dx.doi.org/10.1007/BF01200150
    Journal articles | 1993
    Professor Igor Shparlinski
    MULLEN GL; SHPARLINSKI I, 1993, 'VALUES OF LINEAR RECURRING SEQUENCES OF VECTORS OVER FINITE-FIELDS', ACTA ARITHMETICA, vol. 65, pp. 221 - 226, http://dx.doi.org/10.4064/aa-65-3-221-226
    Journal articles | 1993
    Professor Igor Shparlinski
    Shparlinski IE, 1993, 'On bivariate polynomial factorization over finite fields', Mathematics of Computation, vol. 60, pp. 787 - 791, http://dx.doi.org/10.1090/S0025-5718-1993-1176716-3
    Journal articles | 1992
    Professor Igor Shparlinski
    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, vol. 39, pp. 151 - 163, http://dx.doi.org/10.1016/0377-0427(92)90126-I
    Journal articles | 1992
    Professor Igor Shparlinski
    SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1992, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', LECTURE NOTES IN MATHEMATICS, vol. 1518, pp. 145 - 169, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KR02000014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 1992
    Professor Igor Shparlinski
    Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'Distances from differences of roots of polynomials to the nearest integers', Information Processing Letters, vol. 43, pp. 143 - 146, http://dx.doi.org/10.1016/0020-0190(92)90006-H
    Journal articles | 1992
    Professor Igor Shparlinski
    Van Der Poorten AJ; Shparlinski IE, 1992, 'On the number of zeros of exponential polynomials and related questions', Bulletin of the Australian Mathematical Society, vol. 46, pp. 401 - 412, http://dx.doi.org/10.1017/S0004972700012065
    Journal articles | 1992
    Professor Igor Shparlinski
    Shparlinskiĭ IE, 1992, 'On primitive elements in finite fields and on elliptic curves', Mathematics of the USSR - Sbornik, vol. 71, pp. 41 - 50, http://dx.doi.org/10.1070/SM1992v071n01ABEH001389
    Journal articles | 1992
    Professor Igor Shparlinski
    Shparlinski IE, 1992, 'A deterministic test for permutation polynomials', Computational Complexity, vol. 2, pp. 129 - 132, http://dx.doi.org/10.1007/BF01202000
    Journal articles | 1992
    Professor Igor Shparlinski
    Journal articles | 1992
    Professor Igor Shparlinski
    Stepanov SA; Shparlinskii IE, 1992, 'An estimate of incomplete multiplicative character sum of polynomials', Discrete Mathematics and Applications, vol. 2, pp. 169 - 174, http://dx.doi.org/10.1515/dma.1992.2.2.169
    Journal articles | 1991
    Professor Igor Shparlinski
    Shparlinskii IE, 1991, 'Estimates of Gaussian sums', Mathematical Notes of the Academy of Sciences of the USSR, vol. 50, pp. 740 - 746, http://dx.doi.org/10.1007/BF01156612
    Journal articles | 1991
    Professor Igor Shparlinski
    Shparlinskiy IE, 1991, 'On the Distribution of Values of Recurring Sequences and the Bell Numbers in Finite Fields', European Journal of Combinatorics, vol. 12, pp. 81 - 87, http://dx.doi.org/10.1016/S0195-6698(13)80010-8
    Journal articles | 1990
    Professor Igor Shparlinski
    Stepanov SA; Shparlinskii IE, 1990, 'On the construction of a primitive normal basis in a finite field', Mathematics of the USSR - Sbornik, vol. 67, pp. 527 - 533, http://dx.doi.org/10.1070/SM1990v067n02ABEH001369
    Journal articles | 1990
    Professor Igor Shparlinski
    Shparlinskiĭ IE; Skorobogatov AN, 1990, 'Exponential sums and rational points on complete intersections', Mathematika, vol. 37, pp. 201 - 208, http://dx.doi.org/10.1112/S0025579300012912
    Journal articles | 1990
    Professor Igor Shparlinski
    Shparlinskii IE, 1990, 'Some arithmetic properties of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 47, pp. 612 - 617, http://dx.doi.org/10.1007/BF01170895
    Journal articles | 1990
    Professor Igor Shparlinski
    Perel'muter GI; Shparlinskii IE, 1990, 'The distribution of primitive roots in finite fields', Russian Mathematical Surveys, vol. 45, pp. 223 - 224, http://dx.doi.org/10.1070/RM1990v045n01ABEH002330
    Journal articles | 1990
    Professor Igor Shparlinski
    Shparlinskii IE, 1990, 'Generalization of Chebyshev polynomials', Siberian Mathematical Journal, vol. 31, pp. 183 - 185, http://dx.doi.org/10.1007/BF00971170
    Journal articles | 1989
    Professor Igor Shparlinski
    Shparlinskii IE, 1989, 'Dimension of BCH codes', Problems of information transmission, vol. 25, pp. 77 - 80
    Journal articles | 1989
    Professor Igor Shparlinski
    Shparlinskiĭ IE, 1989, 'On polynomials of prescribed height in finite fields', Mathematics of the USSR - Sbornik, vol. 63, pp. 247 - 255, http://dx.doi.org/10.1070/SM1989v063n01ABEH003271
    Journal articles | 1989
    Professor Igor Shparlinski
    Shparlinskii IE, 1989, 'On arithmetical properties of solutions of norm equations', Russian Mathematical Surveys, vol. 44, pp. 216 - 217, http://dx.doi.org/10.1070/RM1989v044n03ABEH002131
    Journal articles | 1989
    Professor Igor Shparlinski
    Shparlinskii IE, 1989, 'On distribution of values of recurrence sequences', Problems of information transmission, vol. 25, pp. 120 - 125
    Journal articles | 1988
    Professor Igor Shparlinski
    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, vol. 43, pp. 249 - 252, http://dx.doi.org/10.1007/BF01139128
    Journal articles | 1987
    Professor Igor Shparlinski
    Shparlinskii IE, 1987, 'Number of different prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 42, pp. 773 - 780, http://dx.doi.org/10.1007/BF01138309
    Journal articles | 1986
    Professor Igor Shparlinski
    Shparlinskii IE, 1986, 'WEIGHT SPECTRA OF SOME CODES.', Problems of information transmission, vol. 22, pp. 111 - 116
    Journal articles | 1985
    Professor Igor Shparlinski
    Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1985, 'On one sequence of iteration parameters', USSR Computational Mathematics and Mathematical Physics, vol. 25, pp. 89 - 93, http://dx.doi.org/10.1016/0041-5553(85)90046-1
    Journal articles | 1985
    Professor Igor Shparlinski
    Shparlinskii IE, 1985, 'Number of prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 38, pp. 529 - 532, http://dx.doi.org/10.1007/BF01137461
    Journal articles | 1985
    Professor Igor Shparlinski
    Shparlinskii IE, 1985, 'Coefficients of primitive polynomials', Mathematical Notes of the Academy of Sciences of the USSR, vol. 38, pp. 951 - 954, http://dx.doi.org/10.1007/BF01157011
    Journal articles | 1984
    Professor Igor Shparlinski
    Kosachevskaya LL; Shparlinskii IE, 1984, 'The rate of convergence of some iterational processes', USSR Computational Mathematics and Mathematical Physics, vol. 24, pp. 81 - 84, http://dx.doi.org/10.1016/0041-5553(84)90088-0
    Journal articles | 1984
    Professor Igor Shparlinski
    Shparlinskii IE, 1984, 'On a multiplicative generator of pseudorandom numbers', USSR Computational Mathematics and Mathematical Physics, vol. 24, pp. 79 - 81, http://dx.doi.org/10.1016/0041-5553(84)90159-9
    Journal articles | 1984
    Professor Igor Shparlinski
    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, vol. 39, pp. 199 - 200, http://dx.doi.org/10.1070/RM1984v039n02ABEH003150
    Journal articles | 1983
    Professor Igor Shparlinski
    Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE, 1983, 'On the spline-based method for experimental data deconvolution', Computer Physics Communications, vol. 29, pp. 227 - 230, http://dx.doi.org/10.1016/0010-4655(83)90002-4
    Journal articles | 1983
    Professor Igor Shparlinski
    Shparlinskii IE, 1983, 'On one property of a multiplicative transducer of pseudo-random numbers', USSR Computational Mathematics and Mathematical Physics, vol. 23, pp. 158 - 159, http://dx.doi.org/10.1016/S0041-5553(83)80030-5
    Journal articles | 1982
    Professor Igor Shparlinski
    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, vol. 27, pp. 87 - 89, http://dx.doi.org/10.1016/0010-4655(82)90011-X
    Journal articles | 1982
    Professor Igor Shparlinski
    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, vol. 22, pp. 232 - 237, http://dx.doi.org/10.1016/0041-5553(82)90114-8
    Journal articles | 1981
    Professor Igor Shparlinski
    Shparlinskii IE, 1981, 'The distribution of the fractional parts of recurrent sequences', USSR Computational Mathematics and Mathematical Physics, vol. 21, pp. 231 - 235, http://dx.doi.org/10.1016/0041-5553(81)90169-5
    Journal articles | 1979
    Professor Igor Shparlinski
    Levin MB; Shparlinskii IE, 1979, 'The uniform distribution of fractional parts of recurrent sequences', Russian Mathematical Surveys, vol. 34, pp. 207 - 208, http://dx.doi.org/10.1070/RM1979v034n03ABEH003995
    Journal articles | 1979
    Professor Igor Shparlinski
    Shparlinskii IE, 1979, 'On a completely uniform distribution', USSR Computational Mathematics and Mathematical Physics, vol. 19, pp. 249 - 253, http://dx.doi.org/10.1016/0041-5553(79)90117-4
    Journal articles | 1978
    Professor Igor Shparlinski
    Shparlinskii IE, 1978, 'Distribution of nonresidues and primitive roots in recurrent sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 24, pp. 823 - 828, http://dx.doi.org/10.1007/BF01141537
    Journal articles |
    Professor Igor Shparlinski
    Kerr B; Mérai L; Shparlinski IE, 'On digits of Mersenne numbers', , http://arxiv.org/abs/2001.03380v4
    Journal articles |
    Professor Igor Shparlinski
    Sha M; Shparlinski IE; Stewart CL, 'On the distribution of multiplicatively dependent vectors', , http://arxiv.org/abs/1903.09796v2
    Journal articles |
    Professor Igor Shparlinski
    Shparlinski IE; Thuswaldner JM, 'Weyl sums over integers with digital restrictions', , http://arxiv.org/abs/2105.04835v1
    Journal articles |
    Professor Igor Shparlinski
    Blackburn SR; Ostafe A; Shparlinski IE, '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 |
    Professor Igor Shparlinski
    Munsch M; Shparlinski IE, 'Additive energy and a large sieve inequality for sparse sequences', , http://arxiv.org/abs/2103.12659v1
    Journal articles |
    Professor Igor Shparlinski
    Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 'Energy bounds for modular roots and their applications', , http://arxiv.org/abs/2103.09405v1
    Journal articles |
    Professor Igor Shparlinski
    Pomerance C; Shparlinski IE, '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 |
    Professor Igor Shparlinski
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 'On sparsity of representations of polynomials as linear combinations of exponential functions', , http://arxiv.org/abs/2102.01949v1
    Journal articles |
    Professor Igor Shparlinski
    Brandes J; Shparlinski IE, 'Two-dimensional Weyl sums failing square-root cancellation along lines', , http://arxiv.org/abs/2012.08877v1
    Journal articles |
    Professor Igor Shparlinski
    Chen C; Kerr B; Shparlinski I, 'Metric theory of lower bounds on Weyl sums', , http://arxiv.org/abs/2004.02539v3
    Journal articles |
    Professor Igor Shparlinski
    Chen C; Kerr B; Maynard J; Shparlinski I, 'Metric theory of Weyl sums', , http://arxiv.org/abs/2011.09306v1
    Journal articles |
    Professor Igor Shparlinski
    Shkredov ID; Shparlinski IE; Zaharescu A, 'On the distribution of modular square roots of primes', , http://arxiv.org/abs/2009.03460v1
    Journal articles |
    Professor Igor Shparlinski
    Konyagin SV; Shparlinski IE; Vyugin IV, 'Polynomial Equations in Subgroups and Applications', , http://arxiv.org/abs/2005.05315v1
    Journal articles |
    Professor Igor Shparlinski
    Kerr B; Mello J; Shparlinski IE, 'An effective local--global principle for algebraic varieties and the sum product problem in finite fields', , http://arxiv.org/abs/2005.02923v1
    Journal articles |
    Professor Igor Shparlinski
    Shparlinski IE; Stewart CL, 'Counting solvable $S$-unit equations', , http://arxiv.org/abs/2007.15170v1
    Journal articles |
    Professor Igor Shparlinski
    Chen C; Shparlinski IE, 'Hybrid bounds on two-parametric family Weyl sums along smooth curves', , http://arxiv.org/abs/2003.02419v1
    Journal articles |
    Professor Igor Shparlinski
    Li R; Shparlinski IE, 'Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers', , http://arxiv.org/abs/2001.09721v1
    Journal articles |
    Professor Igor Shparlinski
    Sha M; Shparlinski IE, 'Möbius Randomness Law for Frobenius Traces', , http://arxiv.org/abs/1909.00969v3
    Journal articles |
    Professor Igor Shparlinski
    Dietmann R; Ostafe A; Shparlinski IE, 'Discriminants of Fields Generated by Polynomials of Given Height', , http://arxiv.org/abs/1909.00135v1
    Journal articles |
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, '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 |
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, 'Integers with a large smooth divisor', Integers with a large smooth divisor, http://arxiv.org/abs/math/0601460v1
    Journal articles |
    Professor Igor Shparlinski
    Konyagin SV; Shparlinski IE, '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 |
    Professor Igor Shparlinski
    Naccache D; Shparlinski IE, 'Divisibility, Smoothness and Cryptographic Applications', Divisibility, Smoothness and Cryptographic Applications, http://arxiv.org/abs/0810.2067v3
    Journal articles |
    Professor Igor Shparlinski
    Shparlinski IE, 'On a Generalised Lehmer Problem for Arbitrary Powers', On a Generalised Lehmer Problem for Arbitrary Powers, http://arxiv.org/abs/0803.3487v2
    Journal articles |
    Professor Igor Shparlinski
    Banks WD; Shparlinski IE, '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
  • Working Papers | 2021
    Professor Igor Shparlinski
    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 | 2020
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Conference Papers | 2016
    Professor Igor Shparlinski
    Kohel D; Shparlinski I, 2016, 'Preface', in Contemporary Mathematics, pp. vii - viii
    Conference Papers | 2016
    Professor Igor Shparlinski
    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
    Conference Papers | 2016
    Professor Igor Shparlinski
    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
    Conference Papers | 2008
    Professor Igor Shparlinski
    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, Kinki Univ, Higashiosaka, JAPAN, pp. 222 - 242, presented at 5th China-Japan Seminar on Number Theory, Kinki Univ, Higashiosaka, JAPAN, 27 August 2008 - 31 August 2008, http://dx.doi.org/10.1142/9789814289924_0010
    Conference Papers | 2008
    Professor Igor Shparlinski
    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
    Conference Papers | 2007
    Professor Igor Shparlinski
    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, Ctr Int Rencontres Math, Marseilles, FRANCE, pp. 163 - 167, presented at 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, Ctr Int Rencontres Math, Marseilles, FRANCE, 05 November 2007 - 09 November 2007, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267679700010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2007
    Professor Igor Shparlinski
    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, Melbourne, AUSTRALIA, pp. 111 - 118, presented at 8th International Conference on Finite Fields and Applications, Melbourne, AUSTRALIA, 09 July 2007 - 13 July 2007, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000257880200009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2007
    Professor Igor Shparlinski
    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, Fujian Normal Univ, Wuui Mt, PEOPLES R CHINA, pp. 226 - 232, presented at 1st International Workshop on Coding and Cryptology, Fujian Normal Univ, Wuui Mt, PEOPLES R CHINA, 11 June 2007 - 15 June 2007, http://dx.doi.org/10.1142/9789812832245_0017
    Conference Papers | 2006
    Professor Igor Shparlinski
    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, Weihai, PEOPLES R CHINA, pp. 155 - 189, presented at 4th China-Japan Seminar on Number Theory, Weihai, PEOPLES R CHINA, 30 August 2006 - 03 September 2006, http://dx.doi.org/10.1142/9789812770134_0007
    Conference Papers | 2005
    Professor Igor Shparlinski
    Shparlinski IE, 2005, 'Pseudorandom Number Generators from Elliptic Curves', in Luengo I (ed.), RECENT TRENDS IN CRYPTOGRAPHY, AMER MATHEMATICAL SOC, Real Soc Mat Espanola, Santander, SPAIN, pp. 121 - 141, presented at Summer School on Recent Trends in Cryptography, Real Soc Mat Espanola, Santander, SPAIN, 11 July 2005 - 15 July 2005, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000263678500005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2003
    Professor Igor Shparlinski
    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 | 2003
    Professor Igor Shparlinski
    Shparlinski IE, 2003, 'Orders of points on elliptic curves', in Gutierrez J; Shpilrain V; Yu JT (eds.), AFFINE ALGEBRAIC GEOMETRY, AMER MATHEMATICAL SOC, Seville, SPAIN, pp. 245 - 251, presented at 1st RSME-AMS Joint Meeting, Seville, SPAIN, 19 June 2003 - 21 June 2003, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000227464800015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2003
    Professor Igor Shparlinski
    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, Baltimore, MD, pp. 153 - 177, presented at Joint Annual Meeting of the American-Mathematical-Society/Mathematical-Association-of-America, Baltimore, MD, 17 January 2003, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000235211700007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2003
    Professor Igor Shparlinski
    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, Banff, CANADA, pp. 49 - 59, presented at Conference in Number Theory in Honour of Hugh C Williams, Banff, CANADA, 24 May 2003 - 30 May 2003, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000223282500004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2003
    Professor Igor Shparlinski
    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, Banff, CANADA, pp. 29 - 47, presented at Conference in Number Theory in Honour of Hugh C Williams, Banff, CANADA, 24 May 2003 - 30 May 2003, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000223282500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2002
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Conference Papers | 2002
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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 | 2002
    Professor Igor Shparlinski
    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 | 2001
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, BERGEN, NORWAY, pp. 257 - 264, presented at International Conference on Sequences and their Applications (SETA 01), BERGEN, NORWAY, 13 May 2001 - 17 May 2001, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000174706300019&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2001
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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 | 2001
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, OAXACA, MEXICO, pp. 286 - 298, presented at 6th International Conference on Finite Fields and Applications (Fq6), OAXACA, MEXICO, 21 May 2001 - 26 May 2001, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000179469500023&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2001
    Professor Igor Shparlinski
    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 | 2000
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, HONG KONG BAPTIST UNIV, HONG KONG, PEOPLES R CHINA, pp. 86 - 102, presented at 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2000), HONG KONG BAPTIST UNIV, HONG KONG, PEOPLES R CHINA, 27 November 2000 - 01 December 2000, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000175526000006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2000
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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, Piscataway, NJ, pp. 71 - 79, presented at DIMACS Workshop on Unusual Applications of Number Theory, Piscataway, NJ, 10 January 2000 - 14 January 2000, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000224833300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1999
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Vasco MIG; Shparlinski IE, 1999, 'On the security of Diffie-Hellman bits', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 257 - 268, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800019&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1999
    Professor Igor Shparlinski
    Nguyen PQ; Shparlinski IE; Stern J, 1999, 'Distribution of modular sums and the security of the server aided exponentiation', in Lam KY; Shparlinski I; Wang H; Xing CP (eds.), CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, BIRKHAUSER VERLAG AG, SINGAPORE, SINGAPORE, pp. 331 - 342, presented at Workshop on Cryptography and Computational Number Theory (CCNT 99), SINGAPORE, SINGAPORE, 22 November 1999 - 26 November 1999, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800024&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1999
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski I, 1999, 'Constructing elements of large order in finite fields', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 404 - 409, http://dx.doi.org/10.1007/3-540-46796-3_38
    Conference Papers | 1999
    Professor Igor Shparlinski
    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, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169016800004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1999
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    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
    Professor Igor Shparlinski
    von zur Gathen J; Shparlinski I, 1999, 'Gauss periods in finite fields', in Jungnickel D; Niederreiter H (ed.), FINITE FIELDS AND APPLICATIONS, SPRINGER-VERLAG BERLIN, UNIV AUGSBURG, DEPT MATH, AUGSBURG, GERMANY, pp. 162 - 177, presented at 5th International Conference on Finite Fields and Applications, UNIV AUGSBURG, DEPT MATH, AUGSBURG, GERMANY, 02 August 1999 - 06 August 1999, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000169087900014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1998
    Professor Igor Shparlinski
    Mans B; Pappalardi F; Shparlinski I, 1998, 'On the ádám conjecture on circulant graphs', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 251 - 260, http://dx.doi.org/10.1007/3-540-68535-9_29
    Conference Papers | 1998
    Professor Igor Shparlinski
    Grant D; Krastev K; Lieman D; Shparlinski I, 1998, 'A public key cryptosystem based on sparse polynomials', in Buchmann J; Hoholdt T; Stichtenoth H; TapiaRecillas H (eds.), CODING THEORY, CRYPTOGRAPHY AND RELATED AREAS, SPRINGER-VERLAG BERLIN, GUANAJUATO, MEXICO, pp. 114 - 121, presented at International Conference on Coding Theory, Cryptography and Related Areas, GUANAJUATO, MEXICO, 20 April 1998 - 24 April 1998, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000085321900010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1998
    Professor Igor Shparlinski
    Gathen JVZ; Shparlinski I, 1998, 'The crew pram complexity of modular inversion', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 305 - 315
    Conference Papers | 1995
    Professor Igor Shparlinski
    van der Poorten AJ; Shparlinski I; Zimmer HG, 1995, 'Number Theoretic and Algebraic Methods in Computer Science', in Number Theoretic and Algebraic Methods in Computer Science, WORLD SCIENTIFIC, presented at International Conference on NTAMCS '93, http://dx.doi.org/10.1142/9789814532532
    Conference Papers | 1995
    Professor Igor Shparlinski
    vonzurGathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields', in 36TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, PROCEEDINGS, I E E E, COMPUTER SOC PRESS, MILWAUKEE, WI, pp. 284 - 292, presented at 36th Annual Symposium on Foundations of Computer Science (FOCS 95), MILWAUKEE, WI, 23 October 1995 - 25 October 1995, http://dx.doi.org/10.1109/SFCS.1995.492484
    Conference Papers | 1995
    Professor Igor Shparlinski
    von zur Gathen J; Shparlinski I, 1995, 'Orders of gauss periods in finite fields', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 208 - 215, http://dx.doi.org/10.1007/bfb0015425
    Conference Papers | 1995
    Professor Igor Shparlinski
    von zur Gathen J; Shparlinski I, 1995, 'Finding points on curves over finite fields extended abstract', in Annual Symposium on Foundations of Computer Science - Proceedings, pp. 284 - 292
    Conference Papers | 1994
    Professor Igor Shparlinski
    Shparlinski IE, 1994, 'On some applications of finitely generated semi-groups', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 265 - 279, http://dx.doi.org/10.1007/3-540-58691-1_66
    Conference Papers | 1994
    Professor Igor Shparlinski
    Von Zur Gathen J; Shparlinski I, 1994, 'Components and projections of curves over finite fields', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 297 - 305, http://dx.doi.org/10.1007/3-540-58325-4_193
    Conference Papers | 1993
    Professor Igor Shparlinski
    Von Zur Gathen J; Karpinski M; Shparlinski I, 1993, 'Counting curves and their projections', in Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 805 - 812, http://dx.doi.org/10.1145/167088.167292
    Conference Papers | 1992
    Professor Igor Shparlinski
    Shparlinski IE, 1992, 'On Gaussian sums for finite fields and elliptic curves', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 5 - 15, http://dx.doi.org/10.1007/bfb0034335
    Conference Papers | 1991
    Professor Igor Shparlinski
    SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1991, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', in Stichtenoth H; Tsfasman MA (ed.), CODING THEORY AND ALGEBRAIC GEOMETRY, SPRINGER-VERLAG BERLIN, CTR INT RENCONTRES MATH, LUMINY, FRANCE, pp. 145 - 169, presented at WORKSHOP ON ALGEBRAIC GEOMETRY AND CODING THEORY - 3 ( AGCT-3 ), CTR INT RENCONTRES MATH, LUMINY, FRANCE, 17 June 1991 - 21 June 1991, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992BX67L00014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1991
    Professor Igor Shparlinski
    STEPANOV SA; SHPARLINSKI IE, 1991, 'ON NORMAL BASES OF ALGEBRAIC NUMBER-FIELDS', in Schweiger F; Manstavicius E (ed.), NEW TRENDS IN PROBABILITY AND STATISTICS, VOL 2, VSP BV, PALANGA, LITHUANIA, pp. 369 - 378, presented at INTERNATIONAL CONF ON ANALYTIC AND PROBABILISTIC METHODS IN NUMBER THEORY, IN HONOUR OF JONAS KUBILIUS ON THE OCCASION OF HIS 70TH BIRTHDAY, PALANGA, LITHUANIA, 24 September 1991 - 28 September 1991, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992BY41L00033&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 1987
    Professor Igor Shparlinski
    Stepanov SA; Shparlinskiy IE, 1987, 'On structure complexity of normal basis of finite field', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 414 - 416, http://dx.doi.org/10.1007/3-540-18740-5_90
    Working Papers |
    Professor Igor Shparlinski
    Chen C; Shparlinski IE, 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 |
    Professor Igor Shparlinski
    Dąbrowski A; Pomykała J; Shparlinski IE, On oracle factoring of integers, http://dx.doi.org, http://arxiv.org/abs/1912.00345v2
    Working Papers |
    Professor Igor Shparlinski
    Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 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

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