Order-Preserving Encryption (OPE) is an encryption preserving the order relationship of the plaintexts to support efficient range query on ciphertexts. Other than traditional symmetric encryption aiming at absolute security, OPE sacrifices some security for the ability to search on ciphertext. In this paper, we propose a new cryptographic primitive, Probability-p Order-Preserving Encryption (p-OPE), which preserves the order of plaintexts with probability p. When p = 1, p-OPE becomes OPE, thus p-OPE is an extension of OPE. We define and analyse the security and precision of the novel primitive, then we propose a construction of p-OPE and conduct experiments to show its performance. As shown in the theoretical analysis and experiment results, p-OPE can improve the security at the cost of some precision sacrifice.
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