Fast Order-Preserving Encryption from Uniform Distribution Sampling

Abstract

Order-preserving encryption (OPE) is a symmetric encryption that ciphertexts preserve numerical ordering of the corresponding plaintexts. It allows various applications to search or sort the order of encrypted data (e.g., range queries in database) efficiently. In this paper, we study OPE for more practical use. We first discuss the elements of previous schemes considered as obstacles in practical applications and propose a new construction by eliminating them (especially probabilistic random variate generation functions such as hypergeometric and binomial distributions). We propose a new OPE whose encryption and decryption are much faster than those of the previous schemes by employing uniform distribution sampling. Furthermore, we provide a batch decryption algorithm to support concurrent decryption of numerical values within the specific range, which is firstly observed in the OPE research literature. It can be very efficiently applied for the encrypted range query processing of database systems. The security of our scheme is proven under the weak variants of notions proposed by Teranishi et al. in Asiacrypt 2014, which yield partial indistinguishability and one-wayness.