Formal verification of cryptographic security proofs

Verifying cryptographic security proofs manually is inherently tedious and error-prone. The game-playing technique for cryptographic proofs advocates a modular proof design where cryptographic programs called games are transformed stepwise such that each step can be analyzed individually. This code-based approach has rendered the formal verification of such proofs using mechanized tools feasible. In the first part of this dissertation we present Verypto: a framework to formally verify game-based cryptographic security proofs in a machineassisted manner. Verypto has been implemented in the Isabelle proof assistant and provides a formal language to specify the constructs occurring in typical cryptographic games, including probabilistic behavior, the usage of oracles, and polynomial-time programs. We have verified the correctness of several game transformations and demonstrate their applicability by verifying that the composition of 1-1 one-way functions is one-way and by verifying the IND-CPA security of the ElGamal encryption scheme. In a related project Barthe et al. developed the EasyCrypt toolset, which employs techniques from automated program verification to validate game transformations. In the second part of this dissertation we use EasyCrypt to verify the security of the Merkle-Damg̊ard construction – a general design principle underlying many hash functions. In particular we verify its collision resistance and prove that it is indifferentiable from a random oracle.