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