Abstract

Assuming the inractability of factoring, we show that the output of the exponentiation modulo a composite function fN;g (x) = g x mod N (where N = P \Delta Q) is pseudorandom, even when its input is restricted to be half the size. This result is equivalent to the simultaneous hardness of the upper half of the bits of fN;g , proven by Hastad, Schrift and Shamir. Yet, we supply a different proof that is significantly simpler than the original one. In addition, we suggest a pseudorandom generator which is more efficient than all previously known factoring based pseudorandom generators. Keywords: Modular exponentiation, discrete logarithm, hard core predicates, simultaneous security, pseudorandom generator, factoring assumption. This write-up is based on the Master Thesis of the second author (supervised by the first author). 0 1 Introduction One-way functions play an extremely important role in modern cryptography. Loosely speaking, these are functions which are easy to evaluate bu...

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