Symmetric Authentication within a Simulatable Cryptographic Library

Proofs of security protocols typically employ simple abstractions of cryptographic operations, so that large parts of such proofs are independent of cryptographic details. The typical abstraction is the Dolev-Yao model, which treats cryptographic operations as a specific term algebra. However, there is no cryptographic semantics, i.e., no theorem that says what a proof with the Dolev-Yao abstraction implies for the real protocol, even if provably secure cryptographic primitives are used. Recently we introduced an extension to the Dolev-Yao model for which such a cryptographic semantics exists, i.e., where security is preserved if the abstractions are instantiated with provably secure cryptographic primitives. Only asymmetric operations (digital signatures and public-key encryption) are considered so far. Here we extend this model to include a first symmetric primitive, message authentication, and prove that the extended model still has all desired properties. The proof is a combination of a probabilistic, imperfect bisimulation with cryptographic reductions and static information-flow analysis. Considering symmetric primitives adds a major complication to the original model: we must deal with the exchange of secret keys, which might happen any time before or after the keys have been used for the first time. Without symmetric primitives only public keys need to be exchanged.