DEVELOPMENT OF HOMOMORPHIC DIVISION METHODS

Abstract

The article deals with the problems of homomorphic cryptography. Homomorphic cryptographyis one of the young areas of cryptography. Its distinguishing feature is that it is possible toprocess encrypted data without decrypting it first, so that the result of operations on encrypteddata is equivalent to the result of operations on open data after decryption. Homomorphic encryptioncan be effectively used to implement secure cloud computing. To solve various applied problems,support for all mathematical operations, including the division operation, is required, butthis topic has not been sufficiently developed. The ability to perform the division operationhomomorphically will expand the application possibilities of homomorphic encryption and willallow performing a homomorphic implementation of many algorithms. The paper considers theexisting homomorphic algorithms and the possibility of implementing the division operation withinthe 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 theexpression of the division operation through the multiplication operation. As part of the secondmethod, it is proposed to represent ciphertexts as an array of homomorphically encrypted bits, andall operations, including the division operation considered in this article, are implementedthrough binary homomorphic operations. Possible approaches to the implementation of divisionthrough binary operations are considered and an approach is chosen that is most suitable for ahomomorphic implementation. The proposed methods are analyzed and their advantages and disadvantagesare indicated.

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