Formal Verification of Security Proofs of Cryptographic Schemes Using Probabilistic Hoare Logic

Abstract

Cryptographic schemes must be presented with a security proof based on complexity theory. However, security proofs tend to be complex and difficult to verify, because an adversary can access various kinds of oracles. The use of formal methods is a way to tame such complexity. Hoare logic has been used to verify properties of programs and its probabilistic extension has also been provided. In this paper, we introduce a probabilistic Hoare logic and its application to verification of security proofs of public key encryption schemes. Adversarial attacks are formalized as programs with probabilistic execution and security properties are formalized as first-order logic formulae.