S.F. Krendelev - Ph.D. (Phys.-Math.), Novosibirsk State University professor. E-mail: s.f.krendelev@gmail.com

This paper presents the studies on order preserving encryption. There is an review on existing systems of order preserving encryption from unified point of view. There are two approaches on systems for order preserving encryption, first from calculus second from standard theoretic information theory. Some new variants of order preserving encryption presented. At the end of paper was presented the method of storage of encrypted data which allowed effective compare and decrypt data. This method also supports the simple arithmetic operations on encrypted data.