### On effective computations in special subsemigroups of polynomial transformations and protocol based multivariate cryptosystems

Vasyl Ustimenko

##### Abstract

Large semigroups and groups of transformations of finite affine space of dimension n with the option of computability of the composition of n arbitrarily chosen elements in polynomial time are described in the paper. Constructions of such families are given together with effectively computed homomorphisms between members of the family. These algebraic platforms allow us to define protocols for several generators of subsemigroup of affine Cremona semigroups with several outputs. Security of these protocols rests on the complexity of the word decomposition problem, It allows to introduce algebraic protocols expanded to cryptosystems of El Gamal type which are not a public key system. In particular symbiotic combination of these protocol of Noncommutative cryptography with one time pad encryption is given. Some of these nonclassical multivariate cryptosystems are implemented with platforms of cubical transformations.

Note: Some new applications of protocols of noncommutative cryptography to the area of postquantum solutions are suggested. Algorithms are partially implemented.

##### Metadata
Available format(s)
Category
Foundations
Publication info
Preprint. Minor revision.
Keywords
Post Quantum CrypographyComputer Algebramultiple composition propertysubgroups of affine Cremona groupcomputationally tame homomorphismkey exchange protocols.
Contact author(s)
vasylustimenko @ yahoo pl
History
2021-04-06: received
Short URL
https://ia.cr/2021/423
License

CC BY

BibTeX

@misc{cryptoeprint:2021/423,
author = {Vasyl Ustimenko},
title = {On effective computations in special subsemigroups of polynomial transformations and protocol based multivariate cryptosystems},
howpublished = {Cryptology ePrint Archive, Paper 2021/423},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/423}},
url = {https://eprint.iacr.org/2021/423}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.