Pseudorandom Vector Generation Using Elliptic Curves And Applications to Wiener Processes

Abstract

Using the arithmetic of elliptic curves over finite fields, we present an algorithm for the efficient generation of sequences of uniform pseudorandom vectors in high dimension, that simulate sample sequences of a sequence of independent identically distributed random variables, with values in the hypercube $[0,1]^d$ with uniform distribution. As an application, we obtain, in the discrete-time simulation, an efficient algorithm to simulate, uniformly distributed sample path sequences of a sequence of independent standard Wiener processes. Applications include Monte Carlo numerical computations of high dimensional integrals and Feynman-Kac formulas.