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2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
ISBN: 0-8186-2445-0
pp: 69-78
J. Boyar , Loyola Univ., Chicago, IL, USA
ABSTRACT
The communication complexity of zero-knowledge proof systems is improved. Let C be a Boolean circuit of size n. Previous zero-knowledge proof systems for the satisfiability of C require the use of Omega (kn) bit commitments in order to achieve a probability of undetected cheating not greater than 2/sup -k/. In the case k=n, the communication complexity of these protocols is therefore Omega (n/sup 2/) bit commitments. A zero-knowledge proof is given for achieving the same goal with only O(n/sup m/+k square root n/sup m/) bit commitments, where m=1+ epsilon /sub n/ and epsilon /sub n/ goes to zero as n goes to infinity. In the case k=n, this is O(n square root n/sup m/). Moreover, only O(k) commitments need ever be opened, which is interesting if committing to a bit is significantly less expensive than opening a commitment.
INDEX TERMS
protocols, subquadratic zero-knowledge, communication complexity, proof systems, Boolean circuit, satisfiability, probability
CITATION
R. Peralta, G. Brassard, J. Boyar, "Subquadratic zero-knowledge", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 69-78, 1991, doi:10.1109/SFCS.1991.185350
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