Synthesis of sets of non-symmetric two-operand two-bit crypto operations within the permutation accuracy

Authors

DOI:

https://doi.org/10.15587/2706-5448.2020.202099

Keywords:

computer cryptography, asymmetric crypto operations, multiple operations, variability of crypto algorithms.

Abstract

The object of research is the processes of building operations for cryptographic protection of information, as the requirements for information security are constantly increasing. Increasing the stability of cryptographic transformations directly depends on the complexity and variability of the crypto algorithm. It is possible to increase variability by increasing the range of crypto operations. Significantly increasing the number of crypto operations is possible through the synthesis of asymmetric operations. This paper is devoted to the creation of methodological support for the synthesis and analysis of sets of two-operand two-bit cryptographic operations with precision permutation. The conducted researches are based on the results of a computational experiment, which consists in the synthesis of two-operand two-bit crypto operations based on single-operand, with the subsequent search for pairs of operations of direct and correct inverse crypto transformation on the basis of complete search. In the course of the computational experiment, pairs of two-operand operations were presented, represented by tuples of four single-operand operations. The formalization of the results provided a mathematical representation of operations, suitable for practical implementation. To simplify the complexity of practical implementation, the synthesized operations are divided into 24 sets of 24 operations. Separation of operations occurred due to the use of templates of tables of truth of sets of operations with precision to permutation of operands. It is established that the entire set of operations can be constructed with the precision of permutation based on the use of the template of any operation. In addition, the analysis of the synthesized sets showed that the sets of symmetric and asymmetric operations do not intersect. 20 sets of asymmetric two-operand two-bit operations, as well as 4 sets of symmetric operations are obtained. Further investigation of each synthesized set of asymmetric crypto operations will allow for the relationship between the operands of the operation and between the operations as a whole. The use of synthesized asymmetric operations will improve the reliability of crypto algorithms for streaming encryption of information by significantly increasing the variability of cryptographic transformations. In turn, the use of synthesized sets of operations will simplify practical implementation in computer cryptography

Author Biographies

Nataliia Lada, Cherkasy State Technological University, 17, Shevchenko str., Cherkasy, Ukraine, 18006

PhD

Department of Information Security and Computer Engineering

Viktoriya Dzyuba, Cherkasy branch of the private higher educational institution "European University", 83, Smilyanskaya str., Cherkasy, Ukraine, 18000

Senior Lecturer, Postgraduate Student

Department of Economics, Finance, Accounting, Mathematical and Information Sciences

Roksolana Breus, Cherkasy State Technological University, 17, Shevchenko str., Cherkasy, Ukraine, 18006

Assistant

Department of Information Security and Computer Engineering

Serhii Lada, Department of the State Emergency Service of Ukraine in Cherkassy region, 1, prykordonnyka Lazarenka str., Cherkasy, Ukraine, 18010

Specialist of first category

Department of Information Technology of the Operations Center, Telecommunication Systems and Information Technologies

References

  1. Rudnytskyi, V. M., Opirskyi, I. R., Melnyk, O. H., Pustovit, M. O. (2018). Syntez hrupy operatsii strohoho stiikoho kryptohrafichnoho koduvannia dlia pobudovy potokovykh shyfriv. Bezpeka informatsii, 24 (3), 195–200.
  2. Pustovit, M. O., Melnyk, O. H., Sysoienko, S. H. (2017). Syntez operatsii obernenoho hrupovoho matrychnoho kryptohrafichnoho peretvorennia informatsii. Visnyk Cherkaskoho derzhavnoho tekhnolohichnoho universytetu. Seriia: Tekhnichni nauky, 4, 118–124.
  3. Bernstein, D., Buchmann, J., Dahmen, E. (2009). Post-quantum cryptography. Berlin: Springer, 246. doi: http://doi.org/10.1007/978-3-540-88702-7
  4. Lada, N. V., Kozlovska, S. H. (2018). Applying cryptographic addition operations by module twowith accuracy of permutation in stream ciphers. Control, Navigation and Communication Systems. Academic Journal, 1 (47), 127–130. doi: http://doi.org/10.26906/sunz.2018.1.127
  5. Adki, V., Hatkar, S. (2016). A Survey on Cryptography Techniques. International Journal of Advanced Research in Computer Science and Software Engineering, 6 (6), 469–475.
  6. Rudnytskyi, V., Opirskyy, I., Melnyk, O., Pustovit, M. (2019). The implementation of strict stable cryptographic coding operations. Advanced Information Systems, 3 (3), 109–112. doi: http://doi.org/10.20998/2522-9052.2019.3.15
  7. Ferguson, N., Schneier, B. (2003). Practical Cryptography: Designing and Implementing Secure Cryptographic Systems. Wiley, 432.
  8. Kozlovska, S. H. (2018). Syntez hrup dvokhoperandnykh operatsii kryptoperetvorennia na osnovi perestanovochnykh skhem. Suchasna spetsialna tekhnika, 4 (55), 44–50.
  9. Rudnitsky, V., Berdibayev, R., Breus, R., Lada, N., Pustovit, M. (2019). Synthesis of reverse two-bit dual-operated strictly straight cryptographic coding on the basis of another operation. Advanced Information Systems, 3 (4), 109–114. doi: http://doi.org/10.20998/2522-9052.2019.4.16
  10. Rudnytskyi, V. M., Lada, N. V., Babenko, V. H. (2018). Kryptohrafichne koduvannia: syntez operatsii potokovoho shyfruvannia z tochnistiu do perestanovky. Kharkiv: TOV «DISA PLIuS», 184.
  11. Lada, N., Kozlovska, S., Rudnitskaya, Y. (2019). Researching and Synthesizing a Group of Symmetric Modified Modulo-4 Addition Operations. Central Ukrainian Scientific Bulletin. Technical Sciences, 2 (33), 181–189. doi: http://doi.org/10.32515/2664-262x.2019.2(33).181-189
  12. Hoffstein, J., Pipher. J., Silverman. J. H. (2008). An Introduction to Mathematical Cryptography. Springer, 523. doi: http://doi.org/10.1007/978-1-4939-1711-2
  13. Mao, W. (2003). Modern Cryptography: Theory and Practice. Prentice Hall PTR, 648.
  14. Melnyk, R. P. (2012). Zastosuvannia operatsii rozshyrenoho matrychnoho kryptohrafichnoho peretvorennia dlia zakhystu informatsii. Systemy obrobky informatsii, 9 (107), 145–147.
  15. Rudnytskyi, V. M. (Ed.) (2018). Kryptohrafichne koduvannia: obrobka ta zakhyst informatsii. Kharkiv: TOV «DISA PLIuS», 139.

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Published

2020-03-05

How to Cite

Lada, N., Dzyuba, V., Breus, R., & Lada, S. (2020). Synthesis of sets of non-symmetric two-operand two-bit crypto operations within the permutation accuracy. Technology Audit and Production Reserves, 2(2(52), 28–31. https://doi.org/10.15587/2706-5448.2020.202099

Issue

Vol. 2 No. 2(52) (2020): Information and control systems

Section

Reports on research projects

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Copyright (c) 2020 Nataliia Lada, Viktoriya Dzyuba, Roksolana Breus, Serhii Lada

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