A General Zero-Knowledge Scheme

There is a great similarity between the zero-knowledge proof of quadratic residuocity presented by Goldwasser-Micali-Rackoff and the graph isomorphism proof presented by Goldreich-Micali-Wigderson. There is also a resemblance between the zero-knowledge proofs of Fiat-Shamir, Chaum-Evertse-van de Graaf, Beth and Guillou-Quisquater. A similar observation holds for zero-knowledge proofs based on encryption: the 3-colourability proofs and the Hamiltonian-circuit proofs of Blum and Goldreich-Micali-Wigderson, and the Brassard-Chaum-Crepeau proof for SAT. Feige, Fiat and Shamir introduced the concept of zero-knowledge proofs of knowledge. In this paper we present a general zero-knowledge scheme which unifies all these Arthur-Merlin proofs.