On extremal graphs, affine Cremona semigroups and new solutions of Post Quantum Cryptography.

Authors

  • V. Ustimenko Department of Mathematics, Physics and Informatics, University of Marie Curie-Sklodowska, Lublin, Poland
  • O. Pustovit Department of ontological systems and applied algebraic combinatorics, Institute of Telecommunications and the Global Information Space of the National Academy of Sciences of Ukraine (ITGIP NAS of Ukraine), Kyiv, Ukraine

Keywords:

Extremal graphs, Information Security, Post Quantum Cryptography, Message Authentication Codes

Abstract

Explicit constructions in Extremal graph theory give appropriate lower bound for Turan type problems. In the case of prohibited cycles explicit constructions can be used for various problems of Information Security.

References

F. Lazebnik, V. Ustimenko, A. J.Woldar, A new series of dense graphs of high girth, Bull. Amer. Math. Soc. (N.S.) 32 (1995), no. 1, 73–79.

M. Polak, U. Romanczuk, V. Ustimenko A. Wroblewska, On the applications of Extremal Graph Theory to Coding Theory and Cryptography, Electronic Notes in Discrete Mathema Discrete Mathematics, (2017), no. 43, 329–342.

V. Ustimenko, U. Romanczuk-Polubiec, A. Wroblewska, M. Polak, E. Zhupa, On the constructions of new symmetric ciphers based on non-bijective multivariate maps of pre-scribed degree, Security and Communication Networks , Volume (2019), Article ID 2137561, 15 pp., https://doi.org/10.1155/2019/2137561.

V. Ustimenko, On new multivariate cryptosystems based on hidden Eulerian equations, Dopov. Nath Acad of Sci, Ukraine (2017), no. 5, 17–24.

V. Ustimenko, On the families of stable transformations of large order and their cryptographical applications, Tatra Mt. Math. Publ. 70 (2017), 107–117.

V. Ustimenko, On new symbolic key exchange protocols and cryptosystems based on hidden tame homomorphism, Dopov. Nath Acad of Sci, Ukraine (2018), no. 10, 26–36.

V. Ustimenko, M. Klisowski , On Noncommutative Cryptography with cubical multivariate maps of predictable density, Proceedings of ”Computing 2019” conference, London, 16-17, July,to appear in in Springer series "Advances in Intelligent Systems and Computing".

V. Ustimenko , On semigroups of multiplicative Cremona transformations and new solutions of Post Quantum Cryptography, Cryptology ePrint Archive, 133, (2019).

Ustimenko V. O., Pustovit O.S., On new algorithms for the audit of digital documents, their implementation and cybersecurity applications, Collective monographs of proceedings of XVI, International conference, Kyiv (Puscha-Vodytsa) (2018), 170–174.

Ustimenko V. O., Pustovit O.S., On new stream algorithms of generating of digests of digital documents with high avalanch effect, Collective monograph ”Mathematics and Computer modelling”, ser. of physic.-math., Proceedings of International symposium ”Problems of computational optimisations, Kyiv, Institute of Cybernetics of acad. V. M. Glushkov, September 24-27, 2019 (to appear).

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