One-Round Secure Comparison of Integers

We consider the problem of securely evaluating the Greater Than (GT) predicate and its extension -- transferring one of two secrets, depending on the result of comparison. We generalize our solutions and show how to securely decide membership in the union of a set of intervals. We then consider the related problem of comparing two {em encrypted} numbers. We show how to efficiently apply our solutions to practical settings, such as auctions with the semi-honest auctioneer, proxy selling, etc. All of our protocols are one round. We propose new primitives, {em Strong Conditional Oblivious Transfer} (SCOT) and {em Conditional Encrypted Mapping} (CEM), which capture common security properties of one round protocols in a variety of settings, which may be of independent interest.