An Improved Pseudorandom Generator Based on Hardness of Factoring

by Nenad Dedić, Leonid Reyzin and Salil Vadhan

We present a simple to implement and efficient pseudorandom generator based on the factoring assumption. It outputs more than pn/2 pseudorandom bits per p exponentiations, each with the same base and an exponent shorter than n/2 bits. Our generator is based on results by Håstad, Schrift and Shamir [HSS93], but unlike their generator and its improvement by Goldreich and Rosen [GR00], it does not use hashing or extractors, and is thus simpler and somewhat more efficient.

In addition, we present a general technique that can be used to speed up pseudorandom generators based on iterating one-way permutations. We construct our generator by applying this technique to results of [HSS93]. We also show how the generator given by Gennaro [Gen00] can be simply derived from results of Patel and Sundaram [PS98] using our technique.

This work appears in Security in Communication Networks, Third International Conference, SCN 2002, Cimato, Galdi, Persiano, editors, Lecture Notes in Computer Science 2576, © Springer-Verlag, 2003.