A hard-core predicate for all one-way functions (1989)
| Venue: | In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing |
| Citations: | 292 - 4 self |
BibTeX
@INPROCEEDINGS{Goldreich89ahard-core,
author = {Oded Goldreich and Leonid A. Levint},
title = {A hard-core predicate for all one-way functions},
booktitle = {In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing},
year = {1989},
pages = {25--32}
}
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Abstract
Abstract rity of f. In fact, for inputs (to f*) of practical size, the pieces effected by f are so small A central tool in constructing pseudorandom that f can be inverted (and the “hard-core” generators, secure encryption functions, and bit computed) by exhaustive search. in other areas are “hard-core ” predicates b In this paper we show that every oneof functions (permutations) f, discovered in way function, padded to the form f(p,z) = [Blum Micali $21. Such b ( 5) cannot be effi- (P,9(X)), llPl / = 11z//, has bY itself a hard-core ciently guessed (substantially better than SO- predicate of the same (within a polynomial) 50) given only f(z). Both b, f are computable security. Namely, we prove a conjecture of in polynomial time. [Levin 87, sec. 5.6.21 that the sca1a.r product [Yao 821 transforms any one-way function of boolean vectors p, x is a hard-core of every f into a more complicated one, f*, which has one-way function f(p, x) = (p,g(x)). The rea hard-core predicate. The construction ap- sult extends to multiple (up to the logarithm plies the original f to many small pieces of of security) such bits and to any distribution the input to f * just to get one “hard-core ” on the z’s for which f is hard to invert.
