Lectures 11–12 - One Way Permutations, Goldreich Levin Theorem, Commitments

Proof: Just pick g at random. For every particular 2 √ n-time algorithm A, the expected number of inputs on which A(x) = g(x) is one, and the probability that A computes g successfully on an at least 2−n/10 fraction of the total 2n inputs can be shown to be less than 2−2 −n/2 . But a 2 √ n algorithm can be described by about 2 √ n 2n/2 bits and so the total number of such algorithms is much smaller than 22 n/2 .