Automorphic Signatures in Bilinear Groups

We introduce the notion of automorphic signatures, which satisfy the following properties: the verification keys lie in the message space, messages and signatures consist of group elements only, and verification is done by evaluating a set of pairing-product equations. These signatures make a perfect counterpart to the powerful proof system by Groth and Sahai (Eurocrypt 2008). We provide practical instantiations of automorphic signatures under appropriate assumptions and an extension yielding blind signatures. We then use them in combination with Groth-Sahai proofs to efficiently instantiate several cryptographic primitives, such as group signatures, non-interactive anonymous credentials and anonymous proxy signatures.