ESTIMATION OF THE EXECUTION TIME OF ENCRYPTION, DECRYPTION, AND HOMOMORPHIC CALCULATIONS USING THE DOMINGO-FERRER CRYPTOSYSTEM

Abstract

This article considers a symmetric probabilistic homomorphic Domingo-Ferrer cryptosystem based
on the problem of number factorization. Currently, homomorphic cryptosystems of two types are relevant:
the Gentry type and those based on the problem of factorization of numbers. A distinctive feature of the
latter, in comparison with Gentry-type cryptosystems, is the lower complexity of performing homomorphic
operations, which significantly expands the scope of their application in practice. However, since
homomorphic cryptosystems based on the number factorization problem have not been widely used and
have not been sufficiently analyzed, unlike Gentry-type cryptosystems, their thorough comprehensive study
is required. For the considered symmetric homomorphic Domingo-Ferrer cryptosystem, descriptions of
key generation, encryption, decryption, and homomorphic computing operations are given. For encryption,
decryption, and homomorphic computing operations, a complexity estimate is given, expressed in the
number of basic mathematical operations, as well as graphs illustrating the dependence of the number of
operations on the selected parameters of the cryptosystem. The aim of the study is to assess the complexity
of performing encryption, decryption and homomorphic calculations by a symmetric probabilistic
homomorphic Domingo-Ferrer cryptosystem based on the number factorization problem. The main result
of this work is an assessment of the complexity and determination of the most time-consuming stages of
encryption, decryption and performing homomorphic calculations using the Domingo-Ferrer cipher, confirmed
by a number of experimental studies. The conducted research represents an important step in the
development of the Domingo-Ferrer cryptographic system based on the problem of factorization of numbers
and has the practical significance of implementing algorithms with the ability to determine the time
costs of encryption, decryption and performing homomorphic calculations. The results obtained can be
used by researchers and programmers in the development of implementations of the Domingo-Ferrer
cryptosystem in programming languages.