**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.

**Category / Keywords: **foundations / Post Quantum Crypography, Computer Algebra, multiple composition property, subgroups of affine Cremona group, computationally tame homomorphism, key exchange protocols.

**Date: **received 31 Mar 2021

**Contact author: **vasylustimenko at yahoo pl

**Available format(s): **PDF | BibTeX Citation

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

**Version: **20210406:070917 (All versions of this report)

**Short URL: **ia.cr/2021/423

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