Zero-knowledge proofs of knowledge for group homomorphisms

Asimple zero-knowledge proof of knowledge protocol is presented ofwhichmany known protocols are instantiations. These include Schnorr’s protocol for proving knowledge of a discrete logarithm, the Fiat–Shamir andGuillou–Quisquater protocols for proving knowledge of a modular root, protocols for proving knowledge of representations (like Okamoto’s protocol), protocols for proving equality of secret values, a protocol for proving the correctness of a Diffie–Hellman key, protocols for proving the multiplicative relation of three commitments (as required in secure multi-party computation), and protocols used in credential systems. This unifies a substantial body of work and can also lead to instantiations of the protocol for new applications.