Secure Database Using Order-Preserving Encryption Scheme Based on Arithmetic Coding and Noise Function

Abstract : Order-preserving symmetric encryption (OPE) is a deterministic encryption scheme which encryption function preserves numerical order of the plaintexts. That allows comparison operations to be directly applied on encrypted data in case, for example, decryption takes too much time or cryptographic key is unknown. That’s why it is successfully used in cloud databases as effective range queries can be performed based on. This paper presents order-preserving encryption scheme based on arithmetic coding. In the first part of it we review principles of arithmetic coding, which formed the basis of the algorithm, as well as changes that were made. Then we describe noise function approach, which makes algorithm cryptographically stronger and show modifications that can be made to obtain order-preserving hash function. Finally we analyze resulting vulnerability to chosen-plaintext attack.