A message authentication code (MAC) scheme allows the holder of a secret key to produce a MAC witnessing the integrity of the message, which they can verify using the same secret key. This is the symmetric-cryptography analogue of a public-key signature scheme, in which the holder of a secret key can produce a signature witnessing the integrity of the message, which anyone can verify using the corresponding public key.
MACs allow the construction of keyed-verification credential systems, which the issuer of a credential uses a MAC to witness the integrity of a credential and later checks it on presentation. Most famously, this is the idea underlying Macaroons, which support other interesting features such as delegation and attenuation.
In their 2013 paper, Algebraic MACs and Keyed-Verification Anonymous Credentials, Chase, Meiklejohn, and Zaverucha apply this idea to anonymous credentials, introducing the concept of a keyed-verification anonymous credential (KVAC), where the issuer of an anonymous credential is also the verifier of the credential, and then showed how to construct anonymous credentials using algebraic MACs, i.e., MACs defined in some group rather than using bitwise operations.
The insight of keyed-verification credentials is that while most anonymous credential systems are built to allow a user to present credentials to third parties, in many cases, particularly resource access control, it's sufficient for verification to be restricted to the issuer of the credential. This functional restriction allows much more efficient constructions, because the credential can use symmetric-style rather than public-key-style cryptography.
This section reviews the CMZ'13 construction, describing key generation, blinded issuance, and credential presentation.
TODO: rewrite this section to make it more clear.