Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
J. Boyar , Loyola Univ., Chicago, IL, USA
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.
protocols, subquadratic zero-knowledge, communication complexity, proof systems, Boolean circuit, satisfiability, probability
R. Peralta, G. Brassard and J. Boyar, "Subquadratic zero-knowledge,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 69-78.