On the Security of Goldreich's One-Way Function

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On the Security of Goldreich's One-Way Function
Goldreich (ECCC 2000) suggested a simple construction of a candidate one-way function f : {0, 1}n → {0, 1}m where each bit of output is a fixed predicate P of a constant number d of (random) input bits. We investigate the security of this construction in the regime m = Dn, where D(d) is a sufficiently large constant. We prove that for any predicate P that correlates with either one or two of its variables, f can be inverted with high probability. We also prove an amplification claim regarding Goldreich’s construction. Suppose we are given an assignment x ∈ {0, 1}n that has correlation > 0 with the hidden assignment x ∈ {0, 1}n . Then, given access to x , it is possible to invert f on x with high probability, provided D = D(d, ε) is sufficiently large.
Andrej Bogdanov, Youming Qiao
Added 25 May 2010
Updated 25 May 2010
Type Conference
Year 2009
Authors Andrej Bogdanov, Youming Qiao
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