Public Randomness in Cryptography

Abstract

The main contribution of this paper is the introduction of a formal notion of public randomness in the context of cryptography. We show how this notion affects the definition of the security of a cryptographic primitive and the definition of how much security is preserved when one cryptographic primitive is reduced to another. Previous works considered the public random bits as a part of the input, and security was parameterized in terms of the total length of the input. We parameterize security solely in terms of the length of the private input, and treat the public random bits as a separate resource. This separation allows us to independently address the important issues of how much security is preserved by a reduction and how many public random bits are used in the reduction.

To exemplify these new definitions, we present reductions from weak one-way permutations to one-way permutations with strong security preserving properties that are simpler than previously known reductions.

Research supported in part by National Science Foundation operating grant CCR-9016468 and grant No. 89-00312 from the United States-Israel Binational Science Foundation (BSF)

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