Practical and Proven Zero-Knowledge Constant Round Variants of GQ and Schnorr

SUMMARY In 1992 Burmester studied how to adapt the Guillou-Quisquater identiication scheme to a proven zero-knowledge proof without signiicantly increasing the communication complexity and computational overhead. He proposed an almost constant round version of Guillou-Quisquater. Di Crescenzo and Persiano presented a 4-move constant round zero-knowledge interactive proof of membership for the corresponding language. A straightforward adaptation of the ideas of Bellare-Micali-Ostrovsky will also give a constant round protocol. However, these protocols signiicantly increase the communication and computational complexity of the scheme. In this paper we present constant round variants of the protocols of Guillou-Quisquater and Schnorr with the same (order-wise) communication and computational complexity as the original schemes. Note that in our schemes the probability that a dishonest prover will fool a honest veriier may be exponentially small, while it can only be one over a superpolynomial in Burmester's scheme. Our protocols are perfect zero-knowledge under no cryptographic assumptions.

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