Short Comparable Encryption

The notion of comparable encryption is introduced in Esorics 2013 [18] which overcomes the weakness of order-preserving encryption (OPE). While an OPE enables to compare the numerical order of numbers from their corresponding ciphertexts alone, the comparable encryption enables to compare the numerical order of the pair of numbers from their ciphertexts if either of the ciphertexts is accompanied with the corresponding token. Hence, it significantly reduces the amount of disclosed knowledge with respect to encrypted numbers from their ciphertexts. Since an OPE is considered to be a key primitive for encrypted databases such as CryptDB [31] and Monomi [36], a comparable encryption has a potential to enhance the security of these applications. However, the previous comparable encryption requires large ciphertext length, which so severely spoils the performance of encrypted databases that it is no longer practical. We propose in this paper, a very short comparable encryption. While each bit is encrypted into a string of security parameter length, say 160 bits, in the previous works, ours encrypts each bit into 3-ary. This is even shorter than the ciphertext length of OPEs.