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• W1588934224 abstract "The exponentiation function in a finite field of order p (a prime number) is believed to be a one-way function. It is well known that O(log log p) bits are simultaneously hard for this function. We consider a special case of this problem, the discrete logarithm with short exponents, which is also believed to be hard to compute. Under this intractibility assumption we show that discrete exponentiation modulo a prime p can hide n − Ω(log n) bits (n = [log p] and p=2q+1, where q is also a prime). We prove simultaneous security by showing that any information about the n − Ω(log n) bits can be used to discover the discrete log of g s mod p where s has Ω(log n) bits. For all practical purposes, the size of s can be a constant c bits. This leads to a very efficient pseudo-random number generator which produces n − c bits per iteration. For example, when n = 1024 bits and c = 128 bits our pseudo-random number generator produces a little less than 900 bits per exponentiation." @default.
• W1588934224 created "2016-06-24" @default.
• W1588934224 creator A5010421733 @default.
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• W1588934224 date "1998-01-01" @default.
• W1588934224 modified "2023-09-26" @default.
• W1588934224 title "An efficient discrete log pseudo random generator" @default.
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• W1588934224 doi "https://doi.org/10.1007/bfb0055737" @default.
• W1588934224 hasPublicationYear "1998" @default.
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