METHOD OF IMPLEMENTING HOMOMORPHIC DIVISION

Abstract

The article deals with the problems of homomorphic cryptography. Homomorphic cryptography is one of the young directions of cryptography. Its peculiarity lies in the fact that it is possible to process encrypted data without preliminary decryption in such a way that the result of operations on encrypted data is equivalent, after decryption, to the result of operations on open data. The article provides a brief overview of the areas of application of homomorphic encryption. To solve various applied problems, support for all mathematical operations is required, including the division operation, and the ability to perform this operation homomorphically will expand the possibilities of using homomorphic encryption. The paper proposes a method of homomorphic division based on an abstract representation of the ciphertext in the form of an ordinary fraction. The paper describes in detail the proposed method. In addition, the article contains an example of the practical implementation of the proposed method. It is proposed to divide the levels of data processing into 2 levels – cryptographic and mathematical. At the cryptographic level, a completely homomorphic encryption algorithm is used and the basic homomorphic mathematical operations are performed – addition, multiplication and difference. The mathematical level is a superstructure on top of the cryptographic level and expands its capabilities. At the mathematical level, the ciphertext is represented as a simple fraction and it becomes possible to perform the homomorphic division operation. The paper also provides a practical example of applying the homomorphic division method based on the Gentry algorithm for integers. Conclusions and possible ways of further development are given.