Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms

Abstract. Goldreich (ECCC 2000) proposed a candidate one-way function construction which is parameterized by the choice of a small predicate (over d = O(1) variables) and of a bipartite expanding graph of right-degree d. The function is computed by labeling the n vertices on the left with the bits of the input, labeling each of the n vertices on the right with the value of the predicate applied to the neighbors, and outputting the n-bit string of labels of the vertices on the right. Inverting Goldreich's one-way function is equivalent to finding solutions to a certain constraint satisfaction problem (which easily reduces to SAT) having a "planted solution," and so the use of SAT solvers constitutes a natural class of attacks. We perform an experimental analysis using MiniSat, which is one of the best publicly available algorithms for SAT. Our experiment shows that the running time required to invert the function grows exponentially with the length of the input, and that ...

• Type: Conference
• Year: 2009
• Where: TCC
• Authors: James Cook, Omid Etesami, Rachel Miller, Luca Trevisan
• Keywords: 3-ary Parity Predicate, Cryptography, One-way Function Construction, SAT Solvers, TCC 2009