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 inputs, f can be inverted with high probability.