Private Coins versus Public Coins in Zero-Knowledge Proof Systems
- Rafael PassAffiliated withCornell University
- , Muthuramakrishnan VenkitasubramaniamAffiliated withCornell University
Goldreich-Krawczyk (Siam J of Comp’96) showed that only languages in BPP have constant-round public-coin black-box zero-know-ledge protocols. We extend their lower bound to “fully black-box” private-coin protocols based on one-way functions. More precisely, we show that only languages in BPP Sam —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 near-linear lower bounds on the round complexity of fully black-box concurrent zero-knowledge proofs (or arguments with sublinear verifier communication) for languages outside BPP Sam .
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 on one-way functions, this transformation preserves zero knowledge, round complexity and communication complexity.
- Private Coins versus Public Coins in Zero-Knowledge Proof Systems
- Book Title
- Theory of Cryptography
- Book Subtitle
- 7th Theory of Cryptography Conference, TCC 2010, Zurich, Switzerland, February 9-11, 2010. Proceedings
- pp 588-605
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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