Pseudo-random number generators based on discrete logarithm

Abstract

The mathematical model of pseudo-random number generator is given in the paper. The problems of discrete logarithm tasks solving and the concept of «hard bits» for discrete logarithm are considered in the paper. Constraints are imposed related to the absence of logarithm which can compute the discrete logarithm of y = gxmodp, where x ≤ 2c for polynomial time. The constraint is called the assumption on discrete logarithm with short с bit exponents (с – DLSE). As an example, the Sundaram- Patel’s generator is given, qualitative and quantitative characteristics of the generator resistance to the main types of attacks are proposed.\nThe paper gives the analysis of algorithms for generating pseudo-random numbers, such as the algorithm of Blum-Blum- Shub algorithm, Blum-Micali, Fortuna and Yarrow. Based on specified criteria, evaluation of algorithms is given, conclusions on the advantages and disadvantages of each algorithm are made.