We present a high-assurance and high-speed implementation of the SHA-3 hash function. Our implementation is written in the Jasmin programming language, and is formally verified for functional correctness, provable security and timing attack resistance in the EasyCrypt proof assistant. Our implementation is the first to achieve simultaneously the four desirable properties (efficiency, correctness, provable security, and side-channel protection) for a non-trivial cryptographic primitive. Concretely, our mechanized proofs show that: 1) the SHA-3 hash function is indifferentiable from a random oracle, and thus is resistant against collision, first and second preimage attacks; 2) the SHA-3 hash function is correctly implemented by a vectorized x86 implementation. Furthermore, the implementation is provably protected against timing attacks in an idealized model of timing leaks. The proofs include new EasyCrypt libraries of independent interest for programmable random oracles and modular indifferentiability proofs.

The CMAC standard, when initially proposed by Iwata and Kurosawa as OMAC1, was equipped with a complex game-based security proof. Following recent advances in formal verification for game-based security proofs, we formalize a proof of unforgeability for CMAC in EasyCrypt. A side effects of this proof are improvements of EasyCrypt libraries. This formal proof obtains security bounds very similar to Iwata and Kurosawa's for CMAC, but also proves secure a certain number of intermediate constructions of independent interest, including ECBC, FCBC and XCBC. This work represents one more step in the direction of obtaining a reliable set of independently verifiable evidence for the security of international cryptographic standards.