On secure two-party integer division

Abstract

We consider the problem of secure integer division: given two Paillier encryptions of ℓ-bit values n and d, determine an encryption of ⌊n/d⌋ without leaking any information about n or d. We propose two new protocols solving this problem. The first requires arithmetic operations on encrypted values (secure addition and multiplication) in rounds. This is the most efficient constant-rounds solution to date. The second protocol requires only arithmetic operations in rounds, where κ is a correctness parameter. Theoretically, this is the most efficient solution to date as all previous solutions have required Ω(ℓ) operations. Indeed, the fact that an o(ℓ) solution is possible at all is highly surprising. © 2012 Springer-Verlag.