Order-Preserving Encryption Using Approximate Integer Common Divisors

TL;DR

This paper introduces a simple, efficient order-preserving encryption scheme based on the approximate common divisor problem, offering strong security properties and superior performance compared to existing methods.

Contribution

It is the first OPE scheme grounded in a computational hardness primitive, providing optimal information leakage and fast encryption/decryption operations.

Findings

Scheme requires only O(1) arithmetic operations

Achieves optimal information leakage under uniform distribution

Demonstrates faster execution times than existing OPE schemes

Abstract

We present a new, but simple, randomised order-preserving encryption (OPE) scheme based on the general approximate common divisor problem (GACDP). This appears to be the first OPE scheme to be based on a computational hardness primitive, rather than a security game. This scheme requires only $O(1)$ arithmetic operations for encryption and decryption. We show that the scheme has optimal information leakage under the assumption of uniformly distributed plaintexts, and we indicate that this property extends to some non-uniform distributions. We report on an extensive evaluation of our algorithms. The results clearly demonstrate highly favourable execution times in comparison with existing OPE schemes.