On Eulerian semigroups of multivariate transformations and their cryptographic applications-Reference-Cited by-同舟云学术

On Eulerian semigroups of multivariate transformations and their cryptographic applications

Published:2023-04-04 Issue: Volume: Page:
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Author:

Ustimenko Vasyl¹

Affiliation:

1. Royal Holloway University of London

Abstract

Abstract The intersection of Commutative and Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K. We consider special semigroups of transformations of the variety (K*)n, K=Fq or K=Zm defined via multiplications of variables. Efficiently computed homomorphisms between such subsemigroups can be used in Post Quantum key exchange protocols and in their inverse versions when correspondents elaborate mutually inverse transformations of (K*)n. The security of these schemes is based on a complexity of decomposition problem for element of the semigroup into product of given generators. We introduce combination of inverse versions of these schemes with cryptosystems based on stable subsemigroups of Cremona group which use encryption and decryption multivariate maps with the density gap. MSC 2010: 11T71, 14G50

Publisher

Research Square Platform LLC

Reference32 articles.

1. Anne Canteaut: François-Xavier Standaert (Eds.), Eurocrypt 2021}, LNCS 12696, 40th Annual International Conference on the Theory and Applications of Cryptographic Techniques Zagreb, Croatia, October 17–21, 2021, Proceedings, Part I, Springer, 839p. (2021)

2. Ding, J., Gower, J.E., Schmidt, D.S.: Multivariate Public Key Cryptosystems}, 260. Springer, Advances in Information Security, v. 25, (2006)

3. Goubin, L., Yang, J.P.B.-Y.: \{\em\ Multivariate\ Cryptography,\ Encyclopedia\ of\ Cryptography\ and\ Security\},\ \(2nd\ Ed\.\)\ \ 824–828\. (2011)

4. Ustimenko, V.: On new symbolic key exchange protocols and cryptosystems based on hidden tame hommorphism.Dopovidi. NAS of Ukraine, n 10, pp.26–36. (2018)

5. On the families of stable transformations of large order and their cryptographical applications;Ustimenko V;Tatra Mt. Math. Publ,2017