On the power of nonuniformity in proofs of security

Authors:
Kai-Min Chung;Huijia Lin;Mohammad Mahmoody;Rafael Pass
Affiliations:
Cornell, Ithaca, NY, USA;MIT and Boston University, Cambridge and Boston, MA, USA;Cornell, Ithaca, NY, USA;Cornell, Ithaca, NY, USA
Venue:
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Year:
2013

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Abstract

Nonuniform proofs of security are common in cryptography, but traditional black-box separations consider only uniform security reductions. In this paper, we initiate a formal study of the power and limits of nonuniform black-box proofs of security. We first show that a known protocol (based on the existence of one-way permutations) that uses a nonuniform proof of security, and it cannot be proven secure through a uniform security reduction. Therefore, nonuniform proofs of security are indeed provably more powerful than uniform ones. We complement this result by showing that many known black-box separations in the uniform regime actually do extend to the nonuniform regime. We prove our results by providing general techniques for extending certain types of black-box separations to handle nonuniformity.