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• ALGORITHMS FOR REDUCING THE TIME REQUIRED TO PERFORM OPERATIONS OF THE DOMINGO-FERRER CRYPTOSYSTEM

  V.S. Starodubcev , L.К. Babenko

  150-159

  2026-09-10

  Abstract ▼

  An analysis of the literature on the topic of fully homomorphic encryption is carried out. A brief description of the completely homomorphic Domingo-Ferrer cryptographic system based on the number factorization problem is presented, and the time characteristics of the stages of an attack with a known plaintext on this cryptosystem are given. The time characteristics of cryptosystem operations are analyzed, methods and means of their practical implementation are described. New algorithms for implementing the operations of the Domingo-Ferrer cryptosystem are proposed to reduce their execution time. The justification of estimates of the time costs of cryptosystem operations is formed on the basis of theoretical calculations, as well as the results of experimental studies. The aim of the study is to reduce the execution time of the Domingo-Ferrer cryptosystem by developing algorithms for their modification, taking into account the specifics of practical implementation. The main result of this work is a reduction in the execution time of the following operations of the Domingo-Ferrer cryptosystem: encryption by 10-15%, decryption by 2 times, homomorphic multiplication by 64 times for a chain of 200 multiplications using the degree of polynomials of the ciphertext representation d=100 and a slight increase in the time spent on key generation. The conducted research represents a significant contribution to the development of a fully homomorphic Domingo-Ferrer cryptosystem based on the integer factorization problem. This work has practical significance because it significantly improves the performance of homomorphic calculations of this cryptosystem. The results obtained can become the basis for the development of efficient (in terms of required computing costs and the level of security provided) cloud computing software and hardware systems using a fully homomorphic Domingo-Ferrer cryptosystem to ensure the confidentiality of processed information

• ESTIMATION OF THE SEARCH TIME FOR KEY COMPONENTS IN A KNOWN PLAINTEXT ATTACK ON THE DOMINGO-FERRER CRYPTOSYSTEM

  L. К. Babenko , V. S. Starodubcev , N.B. Yelchaninova

  110-118

  2025-07-24

  Abstract ▼

  This paper provides a brief description of the fully homomorphic Domingo-Ferrer cryptographic system and describes the stages of an attack with a known plaintext on this cryptosystem. The stage of searching for the key components of the attack in question is analyzed, for which existing implementation methods are described, among which the method with minimal computational complexity is determined. The rationale for the computational complexity and time costs of the considered method for implementing the key component search stage is based on theoretical calculations, as well as experimental studies.
  The aim of the study is to evaluate the complexity of implementing the stage of searching for key components in an attack with a known plaintext on a fully homomorphic Domingo-Ferrer cryptographic system using the Gauss method, developed for solving systems of linear algebraic equations modulo a prime number. The main result of this work is an assessment of the computational complexity of the key component search stage in a known plaintext attack on the Domingo-Ferrer cryptographic system, implemented using the Gauss method. The complexity estimate is expressed in the number of basic mathematical operations and is confirmed by a number of experimental studies, which allows us to draw reasonable conclusions about the computational complexity of the method under consideration. The conducted research represents a significant contribution to the development of a fully homomorphic Domingo-Ferrer cryptosystem based on the integer factorization problem. It has practical significance, as it allows us to assess the criticality of an attack with a known plaintext on a given cryptosystem. The results obtained can serve as a basis for researchers and cryptographers to develop recommendations for choosing the parameters of the Domingo-Ferrer cryptosystem to ensure the necessary level of security in various applications.

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

  L.К. Babenko, V. S. Starodubcev

  6-15

  2024-11-10

  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.

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

  L.К. Babenko, V.S. Starodubcev

  2024-08-12

  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.