One-round secure comparison of integers

Ian F. Blake 1  and Vladimir Kolesnikov 2
  • 1 Department of Electrical and Computer Engineering, University of Toronto, Canada. Email:
  • 2 Bell Laboratories, Alcatel-Lucent, 600 Mountain Ave., Murray Hill, NJ 07974, USA. Email:


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 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, Strong Conditional Oblivious Transfer (SCOT) and Conditional Encrypted Mapping (CEM), which capture common security properties of one round protocols in a variety of settings, which may be of independent interest.

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JMC is a forum for original research articles in the area of mathematical cryptology. Works in the theory of cryptology and articles linking mathematics with cryptology are welcome. Submissions from all areas of mathematics significant for cryptology are published, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes.