On the Construction of One-Way Functions from Average Case Hardness

In this paper we study the possibility of proving the existence of one-way functions based on average case hardness. It is well-known that if there exists a polynomial-time sampler that outputs instance-solution pairs such that the distribution on the instances is hard on average, then one-way functions exist. We study the possibility of constructing such a sampler based on the assumption that there exists a sampler that outputs only instances, where the distribution on the instances is hard on the average. Namely, we study the possibility of "modifying" an ordinary sampler S that outputs (only) hard instances of some search problem R, to a sampler that outputs instance-solution pairs of the same search problem R. We show that under some restriction, not every sampler can be so modified. That is, we show that if some hard problem with certain properties exists (which, in particular is implied by the existence of one-way permutations), then for every polynomial , there exists...

• Type: Conference
• Year: 2010
• Where: ICS
• Authors: Noam Livne
• Keywords: ICS 2010, Theoritical Computer Science