An Improved Pseudo-random Generator Based on Discrete Log

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.

• Type: Conference
• Year: 2000
• Where: CRYPTO
• Authors: Rosario Gennaro
• Keywords: CRYPTO 2000, Cryptology, Logarithm Problem Modulo, Pseudo-random Bit Generator, Pseudo-random Bits