How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
The complexity of promise problems with applications to public-key cryptography
Information and Control
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
Demonstrating possession of a discrete logarithm without revealing it
Proceedings on Advances in cryptology---CRYPTO '86
Cryptographic capsules: a disjunctive primitive for interactive protocols
Proceedings on Advances in cryptology---CRYPTO '86
Gradual and Verifiable Release of a Secret
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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
Perfect zero-knowledge languages can be recognized in two rounds
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Random self-reducibility and zero knowledge interactive proofs of possession of information
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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An interactive proof is called perfect zero-knowledge if the probability distribution generated by any probabilistic polynomial-time verifier interacting with the prover on input a theorem 驴, can be generated by another probabilistic polynomial time machine which only gets 驴 as input (and interacts with nobody!).In this paper we present a perfect zero-knowledge proof system for a decision problem which is computationally equivalent to the Discrete Logarithm Problem. Doing so we provide additional evidence to the belief that perfect zero-knowledge proofs exist in a non-trivial manner (i.e. for languages not in BPP). Our results extend to the logarithm problem in any finite Abelian group.