Formal Security Proof of CMAC and Its Variants

Abstract

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.