A Note for the Ideal Order-Preserving Encryption Object and Generalized Order-Preserving Encryption
Order-Preserving Encryption (OPE) preserves the order of data in their ciphertexts and, hence, allows range search on the encrypted data without needing to decrypt them. Security analysis of OPE schemes is very important because OPE is not a perfect encryption algorithm (the ciphertexts leak the ordering information of the plaintexts). Most of the existing security analysis for the OPE schemes are informal: they are either based on author-defined attacks or experiments. The authors initiates the cryptographic study of the OPE scheme. They define the security notion POPF-CCA to qualify the security of OPE.