computational complexity

, Volume 21, Issue 1, pp 83–127 | Cite as

On the security of Goldreich’s one-way function

Article

Abstract

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 inputs, f can be inverted with high probability.

We also prove an amplification claim regarding Goldreich’s construction. Suppose we are given an assignment \({x' \in \{0, 1\}^n}\) that has correlation \({\varepsilon > 0}\) with the hidden assignment \({x \in \{0, 1\}^n}\) . Then, given access to x′, it is possible to invert f on x with high probability, provided \({D = D(d, \varepsilon)}\) is sufficiently large.

Keywords

One-way function parallel cryptography 

Subject classification

68Q17 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of CSE and ITCSCChinese University of Hong KongShatinHong Kong
  2. 2.ITCS, Tsinghua UniversityBeijingChina

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