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 one­way permutations to one-way permutations with strong security preserv­ing properties that are simpler than previously known reductions.