An Improved Pseudorandom Generator Based on Hardness of Factoring

Nenad Dedic, Leonid Reyzin, 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 Hastad, 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 [PS98a] using our technique.


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