Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
A Digital Signature Based on a Conventional Encryption Function
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
On the Randomness of Legendre and Jacobi Sequences
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Necessary and Sufficient Conditions For Collision-Free Hashing
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Mercurial commitments with applications to zero-knowledge sets
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
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Zero-Knowledge sets, proposed by Micali et al. in FOCS'03, allow the owner of a set S to publish a very short commitment CS to S, so that the owner can later prove or disprove, against CS, the membership of any (potential infinity many) elements chosen by the verifier, without leaking more about S than the membership of the elements. This new secure primitive is proved to be useful in private data queries, and other similar scenarios where depends on the trust and privacy. We investigate the theoretical primitives underline this new secure notion. The main contribution of this paper is to present a generic scheme for zero-knowledge sets which is as efficient as that in [1]. The new scheme is constructed by adopting the Merkle type of commitment under the assumption of existence of claw free pairs of trapdoor pseudo-permutations.