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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

• COMPUTATIONALLY EFFICIENT METHOD FOR DETERMINING THE AVERAGE LINEAR PROPERTIES OF PSEUDO-DYNAMIC SUBSTITUTIONS

  S.V. Polikarpov, V.A. Prudnikov, K.E. Rumyantsev

  2021-01-19

  Abstract ▼

  Pseudo-dynamic substitutions PD-sbox can become an effective replacement for fixed substitutions
  in pseudo-random functions, since they have the positive properties of both fixed substitutions
  (low consumption of computational resources) and dynamic substitutions (which can radically complicate
  the application of statistical cryptanalysis methods). The problem of active implementation of
  pseudo-dynamic substitutions is, inter alia, the absence of a computationally efficient method for
  determining the averaged linear properties for the entire set of equivalent substitutions generated
  using PD-sbox, while in most cases, only the determination of the maximum values of the prevalence
  (bias) bias (α, β) from the ideal value 1/2. To solve this problem, an original method is proposed,
  which consists in the fact that the maximum dominance values are calculated only for relatively small
  fixed substitutions included in the PD-sbox, and the resulting maximum dominance values are obtained
  by iterative calculation using a logical-probabilistic expression for the Exclusive OR operation
  -NO (XNOR). The effect of using the proposed method is a dramatic reduction in computational
  operations and, accordingly, the possibility of determining on a typical personal computer the maximum
  values of the prevalence bias (α, β) for 16-element PD-sboxes consisting of 8-bit fixed substitutions
  (which is unattainable when using a trivial method).

• 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.