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On Eulerian semigroups of multivariate transformations and their cryptographic applications

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Abstract

The intersection of Commutative and Multivariate Cryptography contains studies of cryptographic applications of the subsemigroups and subgroups of the affine Cremona semigroups defined over the finite commutative ring K. We consider the special semigroups of transformations of the variety \((K^{*})^n\), \(K=F_q\) or \(K=Z_m\), defined via multiplications of the variables. Efficiently computed homomorphisms between such subsemigroups can be used in the Post-Quantum key exchange protocols and in their inverse versions when the correspondents elaborate the mutually inverse transformations of \((K^{*})^n\). The security of these schemes is based on the complexity of the decomposition problem for an element of the semigroup into the product of the given generators.

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Authors and Affiliations

  1. Royal Holloway, University of London, Egham, TW20 0EX, UK

    Vasyl Ustimenko

  2. Institute of Telecommunications and Global Information Space of the NAS of Ukraine, Kiev, 03110, Ukraine

    Vasyl Ustimenko

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  1. Vasyl Ustimenko
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Correspondence to Vasyl Ustimenko.

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To the memory of Irina Suprunenko whose life was an inspirational example of devoted service to algebra and algebraists’ community.

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This research is supported by British Academy Fellowship for Researchers at Risk 2022.

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Ustimenko, V. On Eulerian semigroups of multivariate transformations and their cryptographic applications. European Journal of Mathematics 9, 93 (2023). https://doi.org/10.1007/s40879-023-00685-2

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