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 tradition al 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 enc ryption 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.

Santi Martinez

Josep M. Miret

Rosana Tomas

Magda Valls

Applied Mathematics & Information Sciences

Applied Mathematics and Information Sciences is a journal focused on the field of applied mathematics and information sciences, aiming to provide researchers with a platform to communicate and share the latest research findings.

《Applied Mathematics and Information Sciences》是一个专注于应用数学和信息科学领域的期刊，旨在为研究者提供一个交流和分享最新研究成果的平台。

Applied Mathematics and Information Sciences

Security Analysis of Order Preserving Symmetric Cryptography

This paper proposes two different methodologies, applicable to most order preserving schemes, that can be used to determine their security by analyzing their randomness, and a new order preserving cryptosystem is proposed.

Security Analysis of Order Preserving Symmetric Cryptography

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info