МЕТОД РЕАЛИЗАЦИИ ГОМОМОРФНОГО ДЕЛЕНИЯ

Abstract

The article deals with the problems of homomorphic cryptography. Homomorphic cryptographyis one of the young directions of cryptography. Its peculiarity lies in the fact that it is possibleto process encrypted data without preliminary decryption in such a way that the result of operationson 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. Tosolve various applied problems, support for all mathematical operations is required, including thedivision operation, and the ability to perform this operation homomorphically will expand thepossibilities of using homomorphic encryption. The paper proposes a method of homomorphicdivision 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 ofthe practical implementation of the proposed method. It is proposed to divide the levels of dataprocessing into 2 levels – cryptographic and mathematical. At the cryptographic level, a completely homomorphic encryption algorithm is used and the basic homomorphic mathematical operationsare performed – addition, multiplication and difference. The mathematical level is a superstructureon 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 thehomomorphic division operation. The paper also provides a practical example of applying thehomomorphic division method based on the Gentry algorithm for integers. Conclusions and possibleways of further development are given.