Chapter

Advances in Cryptology — CRYPTO 2000

Volume 1880 of the series Lecture Notes in Computer Science pp 469-481

Date:

An Improved Pseudo-random Generator Based on Discrete Log

  • Rosario GennaroAffiliated withIBM T.J.Watson Research Center

Abstract

Under the assumption that solving the discrete logarithm problem modulo an n-bit prime p is hard even when the exponent is a small c-bit number, we construct a new and improved pseudo-random bit generator. This new generator outputs n - c - 1 bits per exponentiation with a c-bit exponent.

Using typical parameters, n = 1024 and c = 160, this yields roughly 860 pseudo-random bits per small exponentiations. Using an implementation with quite small precomputation tables, this yields a rate of more than 20 bits per modular multiplication, thus much faster than the the squaring (BBS) generator with similar parameters.