Private Coins versus Public Coins in Zero-Knowledge Proof Systems

Goldreich-Krawczyk (Siam J of Comp’96) showed that only languages in BPP have constant-round public-coin black-box zero-knowledge protocols. We extend their lower bound to “fully black-box” privatecoin protocols based on one-way functions. More precisely, we show that only languages in BPPSam —where Sam is a “collision-finding” oracle in analogy with Simon (Eurocrypt’98) and Haitner et. al (FOCS’07)—can have constant-round fully black-box zero-knowledge proofs; the same holds for constant-round fully black-box zero-knowledge arguments with sublinear verifier communication complexity. We also establish nearlinear lower bounds on the round complexity of fully black-box concurrent zero-knowledge proofs (or arguments with sublinear verifier communication) for languages outside BPPSam . The technique used to establish these results is a transformation from private-coin protocols into Sam-relativized public-coin protocols; for the case of fully black-box protocols based ...

• Type: Conference
• Year: 2010
• Where: TCC
• Authors: Rafael Pass, Muthuramakrishnan Venkitasubramaniam
• Keywords: Black-box Zero-knowledge Arguments, Black-box Zero-knowledge Proofs, Black-box Zero-knowledge Protocols, Cryptography, TCC 2010