Quasi - Cryptography

We propose the study of quasi-cryptographic primitives and protocols. These are relaxed versions of standard cryptographic primitives and protocols where the adversary may be given more resources than some of the honest parties. The purpose of this study is to obtain a better understanding of some of the obstacles in basing cryptography on NP-hardness, as well as the relations between various cryptographic primitives. We make a first step in this direction by investigating the simplest quasi-cryptographic primitive: quasi-one-way functions. Extending an approach proposed by Gutfreund, Shaltiel, and Ta-Shma (CCC 2005), we construct an “infinitely often” version of this primitive, partially answering an open question asked by these authors. On the negative side, we show that constructing a length-doubling quasi-pseudorandom generator from a quasi-one-way function (even a quasi-one-way permutation) is impossible via fully-black-box reductions. This contrasts the standard cryptographic setting where such constructions are possible.