DEVELOPMENT OF HOMOMORPHIC DIVISION METHODS

Abstract

The article deals with the problems of homomorphic cryptography. Homomorphic cryptography is one of the young areas of cryptography. Its distinguishing feature is that it is possible to process encrypted data without decrypting it first, so that the result of operations on encrypted data is equivalent to the result of operations on open data after decryption. Homomorphic encryption can be effectively used to implement secure cloud computing. To solve various applied problems, support for all mathematical operations, including the division operation, is required, but this topic has not been sufficiently developed. The ability to perform the division operation homomorphically will expand the application possibilities of homomorphic encryption and will allow performing a homomorphic implementation of many algorithms. The paper considers the existing homomorphic algorithms and the possibility of implementing the division operation within the framework of these algorithms. The paper also proposes two methods of homomorphic division. The first method is based on the representation of ciphertexts as simple fractions and the expression of the division operation through the multiplication operation. As part of the second method, it is proposed to represent ciphertexts as an array of homomorphically encrypted bits, and all operations, including the division operation considered in this article, are implemented through binary homomorphic operations. Possible approaches to the implementation of division through binary operations are considered and an approach is chosen that is most suitable for a homomorphic implementation. The proposed methods are analyzed and their advantages and disadvantages are indicated.