Paradigms for Unconditional Pseudorandom Generators (Foundations and Trends® in Theoretical Computer Science)

In this comprehensive survey of unconditional pseudorandom generators (PRGs), the authors present the reader with an intuitive introduction to some of the most important frameworks and techniques for constructing unconditional PRGs for restricted models of computation. The authors discuss four major paradigms for designing PRGs: several PRGs based on k-wise uniform generators, small-bias generators, and simple combinations thereof, several PRGs based on “recycling” random bits to take advantage of communication Bottlenecks, connections between PRGs and computational hardness, and PRG frameworks based on random restrictions. The authors explain how to use these paradigms to construct PRGs that work unconditionally, with no unproven mathematical assumptions. The PRG constructions use ingredients such as finite field arithmetic, expander graphs, and randomness extractors. The analyses use techniques such as Fourier analysis, sandwiching approximators, and simplification-under-restrictions lemmas. Paradigms for Unconditional Pseudorandom Generators offers the reader a grounding in an important topic widely used in theoretical computer science and cryptography.