Vladimir Kolesnikov Bell Laboratories TITLE: How to tell which of the encrypted numbers is greater? ABSTRACT: We consider the problem of comparing two encrypted numbers and its extension -- transferring one of the two secrets, depending on the result of comparison. Our constructions can be efficiently used in practice, e.g. in auctions with semi-honest auctioneer or purchasing digital goods, such as music or movies. We also define new primitives, which capture common security properties of one round protocols and computing on encrypted data in a variety of settings, which may be of independent interest.