How to construct random functions
Journal of the ACM (JACM)
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
SIAM Journal on Computing
Special Uses and Sbuses of the Fiat-Shamir Passport Protocol
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Multiple non-interactive zero knowledge proofs based on a single random string
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Non-interactive circuit based proofs and non-interactive perfect zero-knowledge with preprocessing
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Cryptographic voting protocols: a systems perspective
SSYM'05 Proceedings of the 14th conference on USENIX Security Symposium - Volume 14
Conditional Computational Entropy, or Toward Separating Pseudoentropy from Compressibility
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient rational secret sharing in standard communication networks
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Round-optimal composable blind signatures in the common reference string model
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Ciphertext-Auditable public key encryption
IWSEC'06 Proceedings of the 1st international conference on Security
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We introduce Fair Zero-Knowledge, a multi-verifier ZK system where every proof is guaranteed to be “zero-knowledge for all verifiers.” That is, if an honest verifier accepts a fair zero-knowledge proof, then he is assured that all other verifiers also learn nothing more than the verity of the statement in question, even if they maliciously collude with a cheating prover. We construct Fair Zero-Knowledge systems based on standard complexity assumptions (specifically, the quadratic residuosity assumption) and an initial, one-time use of a physically secure communication channel (specifically, each verifier sends the prover a private message in an envelope). All other communication occurs (and must occur) on a broadcast channel. The main technical challenge of our construction consists of provably removing any possibility of using steganography in a ZK proof. To overcome this technical difficulty, we introduce tools —such as Unique Zero Knowledge— that may be of independent interest.