Pseudo-random Generators from One-way Functions

Abstract

One of the basic primitives in cryptography and other areas of computer science is a pseudo-random generator. The usefulness of a pseudo-random generator is demonstrated by the fact that it can be used to construct a private key cryptosystem that is secure even against chosen plaintext attack. A pseudo-random generator can also be used to conserve random bits and allows reproducibility of results in Monte Carlo simulation experiments. Intuitively, a pseudo-random generator is a polynomial time computable function g that stretches a short random string x into a much longer string g(x) that “looks” just like a random string to any polynomial time adversary that is allowed to examine g(x)1. Thus, a pseudo-random number generator can be used to efficiently convert a small amount of true randomness into a much longer string that is indistinguishable from a truly random string of the same length to any polynomial time adversary.