MoniPoly—An Expressive $q$q-SDH-Based Anonymous Attribute-Based Credential System With Constant-Size Proofs

Modern anonymous attribute-based credential (ABC) systems benefit from expressive and efficient show proofs on logical statements. Camenisch and Groß pioneered such statements with an Strong RSA-based ABC system on a restricted message space that offers efficient $\mathsf{AND}$, $\mathsf{OR}$ and $\mathsf{NOT}$ proofs. While other ABC frameworks have adopted constructions in the same vein, the Camenisch-Groß ABC has been the most expressive and asymptotically most efficient proof system to date. Due to its use of prime numbers as message space, however, it is constrained by the requirement of a trusted message-space setup and an inherent restriction to pre-defined finite-set attributes. In this paper, we present a provably secure ABC system that supports show proofs for complex logical statements on an unrestricted message space. Our construction is founded on the commit-and-sign paradigm and offers a novel commitment scheme. This construction is not only more expressive than existing approaches, but also highly efficient. Its ECC protocols only require a constant number of bilinear pairings by the verifier; none by the prover. As the security models for the existing approaches do not capture the expressiveness of this scheme, we introduce strong security models for impersonation resilience and unlinkability under adaptive active and concurrent attacks. Based on the $q$-(co-)SDH assumption, we prove the scheme's security with respect to both properties with tight reductions.