## One-Way Functions and Balanced NP (0)

Venue: | Theoretical Computer Science |

Citations: | 2 - 1 self |

### BibTeX

@ARTICLE{Lutz_one-wayfunctions,

author = {Jack H. Lutz},

title = {One-Way Functions and Balanced NP},

journal = {Theoretical Computer Science},

year = {}

}

### OpenURL

### Abstract

The existence of cryptographically secure one-way functions is related to the measure of a subclass of NP. This subclass, called fiNP ("balanced NP"), contains 3SAT and other standard NP problems. The hypothesis that fiNP is not a subset of P is equivalent to the P 6= NP conjecture. A stronger hypothesis, that fiNP is not a measure 0 subset of E 2 = DTIME(2 polynomial ) is shown to have the following two consequences. 1. For every k, there is a polynomial time computable, honest function f that is (2 n k =n k )-one-way with exponential security. (That is, no 2 n k -time-bounded algorithm with n k bits of nonuniform advice inverts f on more than an exponentially small set of inputs. ) 2. If DTIME(2 n ) "separates all BPP pairs," then there is a (polynomial time computable) pseudorandom generator that passes all probabilistic polynomial-time statistical tests. (This result is a partial converse of Yao, Boppana, and Hirschfeld's theorem, that the existence of pseudorandom ge...