FEATURES OF THE IMPLEMENTATION OF THE CRYPTANALYSIS SYSTEM OF HOMOMORPHIC CIPHERS BASED ON THE PROBLEM OF FACTORIZATION OF NUMBERS

Abstract

This article discusses homomorphic cryptosystems based on the problem of factorization of numbers. In comparison with Gentry-type cryptosystems, their implementation is less laborious, but it requires careful verification of durability. The Domingo-Ferrer symmetric cryptosystem is considered as an example of a homomorphic cryptosystem based on the number factorization problem. For this cryptosystem, the processes of key generation, encryption, decryption, and performing homomorphic operations are presented. A description of an attack with a known plaintext on the Domingo-Ferrer cryptosystem is given, as well as a demonstration example of such an attack with a small value of the degree of the polynomials of the ciphertext representation. For the system architecture under development, the basic requirements and a general scheme are presented with a brief description of the area of responsibility of individual modules and their interrelationships. The aim of the study is to identify approaches, techniques and tactics common to specific cryptanalysis methods of homomorphic cryptosystems based on the problem of factorization of numbers, and to create a system architecture that would simplify cryptanalysis by providing the cryptanalyst with a convenient environment and tools for implementing his own cryptanalysis methods. The main result of this work is the architecture of the cryptanalysis system, which allows for a comprehensive analysis of vulnerabilities for various attacks and to assess the level of cryptographic strength of the cipher in question, based on the problem of factorization of numbers, as well as the justification for the use of such an architecture for the analysis of homomorphic ciphers using the example of the Domingo-Ferrer cryptosystem. The implementation of a cryptanalysis system based on the proposed architecture will help researchers and cryptography specialists to study in more detail possible weaknesses in homomorphic ciphers based on the problem of factorization of numbers and develop appropriate measures to strengthen their durability. Thus, the ongoing research is important for the development of cryptographic systems based on the problem of factorization of numbers and provides new tools for cryptanalysts in the field of analysis of homomorphic cryptosystems. The results obtained can be used to increase the strength of existing ciphers and develop new cryptographic methods.