Stateless and Non-Interactive Order-Preserving Encryption for Outsourced Databases through Subtractive Homomorphism
Dongfang Zhao
TL;DR
HOPE introduces a stateless, non-interactive order-preserving encryption scheme for outsourced databases by leveraging the additive property of Paillier to reveal only the sign of plaintext differences via a dedicated comparison key. It extends Paillier to support negative values and subtractive homomorphism, enabling homomorphic subtraction and a secure EvalCmp that preserves equality semantics. The security analysis grounds HOPE in the n-th residue hardness and CPA-based indistinguishability, while the simulation-based argument shows leakage is limited to the sign information comparable to plaintext Sgn. The approach promises zero client storage and zero client-server interaction, facilitating scalable indexing and range queries in DaaS with formal correctness and security proofs, and outlines future implementation efforts in MySQL and PostgreSQL environments.
Abstract
Order-preserving encryption (OPE) has been extensively studied for more than two decades in the context of outsourced databases because OPE is a key enabling technique to allow the outsourced database servers to sort encrypted tuples in order to build indexes, complete range queries, and so forth. The state-of-the-art OPE schemes require (i) a stateful client -- implying that the client manages the local storage of some mapping between plaintexts and ciphertexts, and/or (ii) the interaction between the client and the server during the query. In production systems, however, the above assumptions do not always hold (not to mention performance overhead): In the first case, the storage requirement could exceed the capability of the client; In the second case, the clients may not be accessible when the server executes a query involving sort or comparison. This paper proposes a new OPE scheme that works for stateless clients and requires no client-server interaction during the queries. The key idea of our proposed protocol is to leverage the underlying additive property of a homomorphic encryption scheme such that the sign of the difference between two plaintexts can be revealed by some algebraic operations with an evaluation key. We will demonstrate the correctness and security of the proposed protocol in this short paper; the implementation and experimental results will be presented in an extended report.