Abstract

Rafail Ostrovsky z Quadratic residuosity and graph isomorphism are classic problems and the canonical examples of zero-knowledge languages. However, despite much research e ort, all previous zeroknowledge proofs for them required either cryptography (and thus unproven assumptions) or an unbounded number of rounds of message exchange. For both (and similar) languages, we exhibit zero-knowledge proofs that require 5 rounds and no unproven assumptions. Our solution is essentially optimal, in this setting, due to a recent lowerbound argument of Goldreich and Krawzcyk. 1

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