Efficient Secure Comparison Protocols

A secure comparison protocol allows players to evaluate the greater-than predicate on hidden values; it addresses a problem that belongs to the field of multiparty computation, in which players wish to jointly and privately evaluate a function on secret inputs. Introduced by Yao under the name millionaires’ problem, secure comparison has received a great deal of attention. It has proven to be a fundamental building block in a variety of multiparty computation protocols. However, due to their inherent non-arithmetic structure, existing constructions often remain a major efficiency bottleneck in multiparty computation. In this work, we design new two-party protocols for the greater-than functionality, improving over the state of the art. We prove the security of our protocols in the UC model with respect to passive corruption, assuming only oblivious transfers. Our constructions can readily be used in a variety of protocols in which secure comparisons constitute the main efficiency bottleneck. We construct our protocols in the preprocessing model, with an extremely efficient information-theoretically secure online phase. We use oblivious transfer extensions to get rid of all but a constant amount of expensive computations. Toward our goal of secure comparison, we also design protocols for testing equality between private inputs, which improve similarly over the state of the art. The latter contribution is of independent interest.