The complexity of promise problems with applications to public-key cryptography
Information and Control
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Zero-knowledge proofs of identity
Journal of Cryptology
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Journal of the ACM (JACM)
The Complexity of Decision Versus Search
SIAM Journal on Computing
On being incoherent without being very hard
Computational Complexity
THE COMPLEXITY OF DECISION VERSUS SEARCH
THE COMPLEXITY OF DECISION VERSUS SEARCH
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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A notion of "competitive" interactive proof systems is defined by Bellare and Goldwasser as a natural extension of a problem whether computing a witness w of x 驴 L is harder than deciding x 驴 L for a language L 驴 NP. It is widely believed that quadratic residuosity (QR) does not have a competitive interactive proof system. Bellare and Goldwasser however introduced a notion of "representative" of ZN* and showed that there exists a competitive interactive proof system for promised QR, i.e., the moduli N is guaranteed to be the product of k = O(log log |N|) distinct odd primes. In this paper, we consider how to reduce the communication complexity of a competitive interactive proof system for promised QR and how to relax the constraint on k from O(log log|N|) to O(log |N|). To do this, we introduce a notion of "dominant" of ZN* and show that promised QR with the constraint that k = O(log |N|) has a competitive interactive proof system with considerably low communication complexity.