Applied Mathematics & Information Sciences

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Order preserving encryption is a type of homomorphic encryption in which the homomorphic operation is order comparison. This means that comparing encrypted data returns the same result than comparing the original data. This allows to order encrypted data without the need of decryption. A possible use for this kind of cryptosystems is in databases, where a record field may be encrypted and still permit range queries. An important problem is determining how good a particular order preserving encryption scheme is. In fact, characteristics of order preserving cryptosystems make traditional security analysis useless. In this paper, we propose two different methodologies, applicable to most order preserving schemes, that can be used to determine their security by analyzing their randomness. The first one relies on techniques of noise analysis by converting the encryption function into a noise signal whose power distribution will be considered. The second one relies on techniques of error analysis. It is based on the computation of the mean absolute errors between the encryption function and several approximations defined by small sets of plaintext-ciphertext pairs. As a derived result of the first of these methodologies, a new order preserving cryptosystem is proposed.

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