About polynomial-time 'unpredictable' generators

Abstract

So-called perfect or unpredictable pseudorandom generators have been recently proposed by cryptologists. These generators are usually based on nonlinear recurrences modulo some integer m. Under some (yet unproven) complexity assumptions, it has been proven that no polynomial-time statistical test can distinguish a sequence of bits produced by such a generator from a sequence of truly random bits. Theoretical background concerning this class of generators is given, and the practicality of using them for simulation applications is considered. An examination is made of their ease of implementation, their efficiency, their periodicity, the ease of jumping ahead in the sequence, the minimum size of modulus that should be used, etc.