Order-preserving encryption for non-uniformly distributed plaintexts

Abstract

Order-preserving encryption (OPE) is a deterministic encryption scheme whose encryption function preserves numerical ordering of the plaintexts. While the concept of OPE was introduced in 2004, the first provably-secure OPE scheme was constructed by Boldyreva, Chenette, Lee, and O'Neill at Eurocrypt 2009. The BCLO scheme uses a sampling algorithm for the hypergeometric distribution as a subroutine and maps the Euclidean middle range gap to a domain gap. We study how to utilize the (non-uniform) distribution of the plaintext-space to reduce the number of sampling algorithm invocations in the BCLO scheme. Instead of the Euclidean middle range gap, we map the probabilistic middle range gap to a domain gap. Our simulation shows that the proposed method is effective for various distributions and especially for distributions with small variance. © 2012 Springer-Verlag Berlin Heidelberg.