On Eulerian semigroups of multivariate transformations and their cryptographic applications

V Ustimenko - European Journal of Mathematics, 2023 - Springer
The intersection of Commutative and Multivariate Cryptography contains studies of
cryptographic applications of the subsemigroups and subgroups of the affine Cremona …

On semigroups of multiplicative Cremona transformations and new solutions of Post Quantum Cryptography.

V Ustimenko - Cryptology ePrint Archive, 2019 - eprint.iacr.org
Noncommutative cryptography is based on the applications of algebraic structures like
noncommutative groups, semigroups and noncommutative rings. Its intersection with …

Extremal algebraic graphs, quadratic multivariate public keys and temporal rules

V Ustymenko, A Wróblewska - 2023 18th Conference on …, 2023 - ieeexplore.ieee.org
We introduce large groups of quadratic transformations of a vector space over the finite
fields defined via symbolic computations with the usage of algebraic constructions of …

On computations with Double Schubert Automaton and stable maps of Multivariate Cryptography

V Ustimenko - arXiv preprint arXiv:2108.08288, 2021 - arxiv.org
The families of bijective transformations $ G_n $ of affine space $ K^ n $ over general
commutative ring $ K $ of increasing order with the property of stability will be constructed …

On semigroups of multivariate transformations constructed in terms of time dependent linguistic graphs and solutions of Post Quantum Multivariate Cryptography.

V Ustimenko - Cryptology ePrint Archive, 2021 - eprint.iacr.org
Time dependent linguistic graphs over abelian group H are introduced. In the case $ H= K*
$ such bipartite graph with point set $ P= H^ n $ can be used for generation of Eulerian …

On the implementations of new graph based cubic Multivariate Public Keys

V Ustimenko, T Chojecki… - 2023 18th Conference on …, 2023 - ieeexplore.ieee.org
Algebraic Constructions of Extremal Graph Theory were efficiently used for the construction
of Low Density Parity Check Codes for satellite communication, constructions of stream …

[PDF][PDF] Expanding graphs of the Extremal Graph Theory and expanded platforms of Post Quantum Cryptography.

V Ustimenko, U Romanczuk-Polubiec… - FedCSIS (Position …, 2019 - annals-csis.org
Explicit constructions in Extremal Graph Theory give appropriate lower bounds for Turan
type problems. In the case of prohibited cycles, the explicit constructions can be used for …

On Noncommutative Cryptography and homomorphism of stable cubical multivariate transformation groups of infinite dimensional affine spaces

V Ustimenko, M Klisowski - Cryptology ePrint Archive, 2019 - eprint.iacr.org
Noncommutative cryptography is based on applications of algebraic structures like
noncommutative groups, semigroups and non-commutative rings. Its inter-section with …

On the usage of postquantum protocols defined in terms of transformation semi-groups and their homomophisms

V Ustimenko - Theoretical and Applied Cybersecurity, 2020 - tacs.ipt.kpi.ua
We suggest new applications of protocols of Non-commutative cryptography defined in
terms of subsemigroups of Affine Cremona Semigroups over finite commutative rings and …

On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups

V Ustimenko, M Klisowski - Algebra and Discrete …, 2023 - admjournal.luguniv.edu.ua
Noncommutative cryptography is based on applications of algebraic structures like
noncommutative groups, semigroups, and noncommutative rings. Its intersection with …