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

Vasyl Ustimenko

##### Abstract

Noncommutative cryptography is based on the applications of algebraic structures like noncommutative groups, semigroups and noncommutative rings. Its intersection with 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=F_q or K=Z_m defined via multiplications of variables. Efficiently computed homomorphisms between such subsemigroups can be used in Post Quantum protocols schemes and 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. So the proposed algorithms are strong candidates for their usage in postquantum technologies.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint. Minor revision.
Keywords
Postquantum Cryptographykey exchange protocolsinverse protocolssemigroups of transformationsdecomposition problem
Contact author(s)
vasyl @ hektor umcs lublin pl
History
Short URL
https://ia.cr/2019/133

CC BY

BibTeX

@misc{cryptoeprint:2019/133,
author = {Vasyl Ustimenko},
title = {On semigroups of multiplicative Cremona transformations and  new solutions of Post Quantum Cryptography.},
howpublished = {Cryptology ePrint Archive, Paper 2019/133},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/133}},
url = {https://eprint.iacr.org/2019/133}
}

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