Security Preserving Amplification of Hardness (1990)
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BibTeX
@MISC{Goldreich90securitypreserving,
author = {Oded Goldreich and Russell Impagliazzo and Leonid Levin and Ramarathnam Venkatesan and David Zuckerman},
title = {Security Preserving Amplification of Hardness},
year = {1990}
}
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Abstract
We consider the task of transforming a weak one-way function (which may be easily inverted on all but a polynomial fraction of the range) into a strong one-way function (which can be easily inverted only on a negligible fraction of the range). The previous known transformation [Yao 82] does not preserve the security (i.e., the running-time of the inverting algorithm) within any polynomial. Its resulting function F (x) applies the weak oneway function to many small (of length jxj " , " ! 1) pieces of the input. Consequently, the function can be inverted for reasonable input lengths by exhaustive search. Using random walks on constructive expanders, we transform any regular (e.g., oneto -one) weak one-way function into a strong one, while preserving security. The resulting Supported by grant #86-00301 by US-Israel Binational Science Foundation, Jerusalem, Israel. y Supported by CCR-88-13632 z Supported by NSF grant DCR-8607492, MIT and Sun Microsystems. x Dept. of Computer Sc...
