Demonstrating that a public predicate can be satisfied without revealing any information about how
Proceedings on Advances in cryptology---CRYPTO '86
Cryptographic capsules: a disjunctive primitive for interactive protocols
Proceedings on Advances in cryptology---CRYPTO '86
Zero-knowledge simulation of Boolean circuits
Proceedings on Advances in cryptology---CRYPTO '86
Minimum disclosure proofs of knowledge
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Zero-knowledge proofs of identity
Journal of Cryptology
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Designing programs that check their work
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Relations Among Complexity Measures
Journal of the ACM (JACM)
Direct Minimum-Knowledge Computations
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Multiparty Computations Ensuring Privacy of Each Party's Input and Correctness of the Result
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
A discrete logarithm implementation of zero-knowledge blobs
A discrete logarithm implementation of zero-knowledge blobs
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
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The fact that there are zero-knowledge proofs for all languages in NP has, potentially, enormous implications to cryptography. For cryptographers, the issue is no longer "which languages in NP have zero-knowledge proofs" but rather "which languages in NP have practical zero-knowledge proofs". Thus, the concrete complexity of zero-knowledge proofs for different languages must be established.In this paper, we study the concrete complexity of the known general methods for constructing zero-knowledge proofs. We establish that circuit-based methods have the potential of producing proofs which can be used in practice. Then we introduce several techniques which greatly reduce the concrete complexity of circuit-based proofs. In order to show that our protocols yield proofs of knowledge, we show how to extend the Feige-Fiat-Shamir definition for proofs of knowledge to the model of Brassard-Chaum-Cr茅peau. Finally, we present techniques for improving the efficiency of protocols which involve arithmetic computations, such as modular addition, subtraction, and multiplication, and greatest common divisor.