Algebraic MACs and Keyed-Verification Anonymous Credentials

We consider the problem of constructing anonymous credentials for use in a setting where the issuer of credentials is also the verifier, or more generally where the issuer and verifier have a shared key. In this setting we can use message authentication codes (MACs) instead of public key signatures as the basis for the credential system. To this end, we construct two algebraic MACs in prime-order groups, along with efficient protocols for issuing credentials, asserting possession of a credential, and proving statements about hidden attributes (e.g., the age of the credential owner). We prove the security of the first scheme in the generic group model, and prove the security of the second scheme-using a dual system based approach-under decisional Diffie-Hellman (DDH). Our MACs are of independent interest, as they are the only uf-cmva-secure MACs with efficient proofs of knowledge. Finally, we compare the efficiency of our new systems to two existing constructions of anonymous credentials: U-Prove and Idemix. We show that the performance of the new schemes is competitive with U-Prove (which does not have multi-show unlinkability), and many times faster than Idemix.