On Pseudo-Random Number Generators Using Elliptic Curves and Chaotic Systems

Abstract

Elliptic Curve Cryptography (ECC) is a relatively recent branch of cryptography which is based on the arithmetic on elliptic curves and security of the hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Elliptic curve cryptographic schemes are public-key mechanisms that provide encryption, digital signature and key exchange capabilities. Elliptic curve a lgorithms are also applied to generation of sequences of pseudo-random numbers. Another recent branch of cryptography is chaotic dynamical systems where security is based on high sensitivity of iterations of maps to initial conditions and parameters. In the present work, we give a short survey describing state-of-the-art of several sugge sted constructions for generating sequences of pseudorandom number generators based on elliptic curves (ECPRNG) over finite fields of prime o rder. In the second part of the paper we propose a method of generating sequences of pseudorandom points on elliptic curves over fin ite fields which is driven by a chaotic map. Such a constructio n improves randomness of the sequence generated since it combines good statistical properties of an ECPRNG and a CPRNG (Chaotic Pseudo- Random Number Generator). The algorithm proposed in this work is of interest for both classical and elliptic curve crypt ography.