I.: Constant-round concurrent zero knowledge in the bounded player model (2013)

by V Goyal, A Jain, R Ostrovsky, S Richelson, Visconti
Venue:ASIACRYPT 2013, Part I. LNCS
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4-round resettably-sound zero knowledge, Theory of Cryptography

by Kai-min Chung, Rafail Ostrovsky, Rafael Pass, Muthuramakrishnan Venkitasubramaniam, Ivan Visconti - 11th Theory of Cryptography Conference, TCC 2014
"... Abstract. While 4-round constructions of zero-knowledge arguments are known based on the existence of one-way functions, constuctions of resettably-sound zero-knowledge arguments require either stronger as-sumptions (the existence of a fully-homomorphic encryption scheme), or more communication roun ..."
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Abstract. While 4-round constructions of zero-knowledge arguments are known based on the existence of one-way functions, constuctions of resettably-sound zero-knowledge arguments require either stronger as-sumptions (the existence of a fully-homomorphic encryption scheme), or more communication rounds. We close this gap by demonstrating a 4-round resettably-sound zero-knowledge argument for NP based on the existence of one-way functions. 1
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