Search

Search Results

• 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.

• HYBRID ENCRYPTION BASED ON SYMMETRIC AND HOMOMORPHIC CIPHERS

  L. K. Babenko , Е.А. Tolomanenko

  6-18

  2021-07-18

  Abstract ▼

  The purpose of this work is to develop and research a hybrid encryption algorithm based on the joint application of the symmetric encryption algorithm Kuznyechik and homomorphic encryp-tion (Gentry scheme or BGV scheme). Such an encryption algorithm can be useful in situations with limited computing resources. The point is that with the correct expression of the basic operations of the symmetric encryption algorithm through Boolean functions, it becomes possible on the transmitting side to encrypt the data with a symmetric cipher, and the secret encryption key - with a homomorphic one. In this case, manipulations can be carried out on the receiving side so that the original encrypted message is also encrypted only with a homomorphic cipher. In this case, symmetric encryption is removed, but the information remains inaccessible to the node that pro-cesses it. This property of secrecy makes it possible to carry out resource-intensive operations on a powerful computing node, providing homomorphically encrypted data for a low-resource node for the purpose of their subsequent processing in encrypted form. The article presents the developed hybrid algorithm. As a symmetric encryption algorithm, Kuznyechik encryption algorithm is used, which is part of the GOST R34.12 - 2015 standard. In order to be able to apply homomorphic encryption to data encrypted with the Kuznyechik cipher, the Kuznyechik algorithm S-boxes is presented in a boolean form using the Zhegalkin polynomial. Also, the linear transformation L is presented in the sequence form of performing the simplest operations of addition and multiplication on the transformeddata. The primary modeling of the developed algorithm was carried out on a simplified version of the KuzchyechikS-KN1 algorithm.

• DEVELOPMENT OF HOMOMORPHIC DIVISION METHODS

  I.D. Rusalovsky, L.K. Babenko, О.B. Makarevich

  2022-11-01

  Abstract ▼

  The article deals with the problems of homomorphic cryptography. Homomorphic cryptography
  is one of the young areas of cryptography. Its distinguishing feature is that it is possible to
  process encrypted data without decrypting it first, so that the result of operations on encrypted
  data is equivalent to the result of operations on open data after decryption. Homomorphic encryption
  can be effectively used to implement secure cloud computing. To solve various applied problems,
  support for all mathematical operations, including the division operation, is required, but
  this topic has not been sufficiently developed. The ability to perform the division operation
  homomorphically will expand the application possibilities of homomorphic encryption and will
  allow performing a homomorphic implementation of many algorithms. The paper considers the
  existing homomorphic algorithms and the possibility of implementing the division operation within
  the 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 the
  expression of the division operation through the multiplication operation. As part of the second
  method, it is proposed to represent ciphertexts as an array of homomorphically encrypted bits, and
  all operations, including the division operation considered in this article, are implemented
  through binary homomorphic operations. Possible approaches to the implementation of division
  through binary operations are considered and an approach is chosen that is most suitable for a
  homomorphic implementation. The proposed methods are analyzed and their advantages and disadvantages
  are indicated.

• METHOD OF IMPLEMENTING HOMOMORPHIC DIVISION

  L. K. Babenko, I. D. Rusalovsky

  2020-11-22

  Abstract ▼

  The article deals with the problems of homomorphic cryptography. Homomorphic cryptography
  is one of the young directions of cryptography. Its peculiarity lies in the fact that it is possible
  to process encrypted data without preliminary decryption in such a way that the result of operations
  on encrypted data is equivalent, after decryption, to the result of operations on open data.
  The article provides a brief overview of the areas of application of homomorphic encryption. To
  solve various applied problems, support for all mathematical operations is required, including the
  division operation, and the ability to perform this operation homomorphically will expand the
  possibilities of using homomorphic encryption. The paper proposes a method of homomorphic
  division based on an abstract representation of the ciphertext in the form of an ordinary fraction.
  The paper describes in detail the proposed method. In addition, the article contains an example of
  the practical implementation of the proposed method. It is proposed to divide the levels of data
  processing into 2 levels – cryptographic and mathematical. At the cryptographic level, a completely homomorphic encryption algorithm is used and the basic homomorphic mathematical operations
  are performed – addition, multiplication and difference. The mathematical level is a superstructure
  on top of the cryptographic level and expands its capabilities. At the mathematical level,
  the ciphertext is represented as a simple fraction and it becomes possible to perform the
  homomorphic division operation. The paper also provides a practical example of applying the
  homomorphic division method based on the Gentry algorithm for integers. Conclusions and possible
  ways of further development are given.

• THE LIBRARY OF FULLY HOMOMORPHIC ENCRYPTION OVER THE INTEGERS

  L.K. Babenko, I.D. Rusalovsky

  2020-07-20

  Abstract ▼

  The article discusses one of the new directions of cryptography, a homomorphic cryptography.
  Its distinctive feature is that this type of cryptography allows you to process encrypted data
  without first decrypting it in such a way that the result of operations on encrypted data is equivalent
  after decryption to the result of operations on open data. The paper describes the main areas
  of application of homomorphic encryption. The analysis of existing developments in the field of
  homomorphic encryption is performed. The analysis showed that existing library implementations
  only allow processing of bits or arrays of bits and do not support the division operation. However,
  to solve applied problems, support for performing integer operations is necessary. The analysis
  revealed the need to implement the operation of homomorphic division, as well as the relevance of
  developing your own implementation of a library of homomorphic encryption over integers. The
  ability to perform four operations (addition, difference, multiplication and division) on encrypted
  data will expand the field of application of homomorphic encryption. A method of homomorphic
  division is proposed, which allows performing the division operation on homomorphically encrypted
  data. A library architecture of completely homomorphic operations on integers is proposed.
  The library supports the basic homomorphic operations on integers, as well as the division
  operation, thanks to the method of homomorphic division. Based on the proposed method of
  homomorphic division and library architecture, a library of homomorphic operations on integers
  was implemented. The article also provides measurements of the time required to perform certain
  operations on encrypted data and analyzes the effectiveness of the developed library implementation.
  Conclusions and possible ways of further development are given.