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• 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.

• 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.

• 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.

• A MODEL OF A SUBSYSTEM FOR GENERATING CRYPTOGRAPHIC KEYS OF THE CYBERPHYSICAL SYSTEM INFORMATION PROTECTION SYSTEM

  V. А. Golovskoy, А. V. Vinokurov

  2025-04-27

  Abstract ▼

  The study is devoted to improving the subsystem of information protection in the radio channels of a
  cyberphysical system using the example of a robotic complex (RTC). Modern and promising critical conditions
  for the use of RTCs are considered, which determine the sets of requirements for the characteristics
  of both RTCs and their subsystems, such as the radio data transmission system (RS) and the information
  security subsystem. One of the approaches to meeting the requirements is the unification of theseRTC subsystems, which can be divided conditionally into two scientific and technical tasks: unification of
  radio protocols and unification of information security tools in RS radio channels. The paper presents the
  practical problems obtained as a result of the analysis, which lie at the intersection of two areas of research
  – RS and information security subsystems. A hypothesis has been formed about the potential for
  effective resolution of one of these practical problems – providing an information protection system with
  cryptographic keys - by including a cryptographic key generation subsystem (CKGS) from biometric data
  used as the initial key information in the RTC information protection system. The proposed improvement
  has several aspects – regulatory, economic, and technical. The paper examines only the scientific and
  technical side of the issue, as a result of which a functional model of the CKGS is proposed, which provides
  a study of the possibilities of the modeled subsystem for the implementation of the formulated principles
  of functioning. The purpose of the work is to develop a model of the CKGS functioning for the cryptographic
  information protection system in the RS RTC radio channels and the formation of its algorithmic
  content. The object of research is a system of cryptographic information protection in RS radio channels.
  The subject of the research is an algorithm for generating cryptographic keys for a cryptographic information
  protection system in RS RTC radio channels. To achieve this goal, a class of abstractions involved
  and a methodological apparatus are substantiated that uses the provisions of the theory of algorithms to
  prove the existence of an algorithm that solves a formulated mass problem and has specified non-trivial
  semantic properties. Research methods – analysis, analogy, synthesis, decomposition, abstraction. The
  main mass problem and the hypothesis of its solvability are formulated. In order to test the hypothesis, the
  corresponding theorem is formulated and proved. The proposed model makes it possible to prove the joint
  effective feasibility of various information processing algorithms