Decentralized multi-authority anonymous credential system with bundled languages on identifiers in bilinear groups

We propose a multi-show decentralized multi-authority attribute-based anonymous credential system (dACS). Referring to previous work, we give a new syntax and three security notions: unforgeability, anonymity and unlinkability. Especially, corruption of authorities is considered to reflect a real scenario. Then we give a generic construction of dACS. In our $$ \textsf{dACS} $$ , an attribute authority who issues a private secret key to an entity only has to sign the entity's identifier. Then, according to the principle of "commit-to-identifier", the entity generates a proof of knowing credentials. There are two building blocks: the structure-preserving signature scheme and the Groth-Sahai non-interactive proof system, both of which are in asymmetric bilinear groups. The principle is realized with a bundled language that is simultaneous pairing-product equations on the identifier. There, the bundled language works for preventing collusion attacks . Finally, we instantiate our generic $$ \textsf{dACS} $$ under the Symmetric External Diffie-Hellman (SXDH) assumption, compare the instantiated scheme with previous work, and evaluate the performance.