On computations with Double Schubert Automaton and stable maps of Multivariate Cryptography

TL;DR

This paper constructs stable bijective transformations over affine spaces using Double Schubert Graphs, introduces large groups of quadratic transformations, and proposes a secure encryption algorithm based on noncommutative cryptography.

Contribution

It introduces a novel method for constructing stable transformations via walks on Double Schubert Graphs and develops a new encryption protocol in noncommutative cryptography.

Findings

Transformations can be of exponential order over finite fields.

Large groups of quadratic transformations are constructed.

A secure encryption algorithm based on these transformations is proposed.

Abstract

The families of bijective transformations $G_n$ of affine space $K^n$ over general commutative ring $K$ of increasing order with the property of stability will be constructed. Stability means that maximal degree of elements of cyclic subgroup generated by the transformation of degree $d$ is bounded by $d$. In the case $K=F_q$ these transformations of $K^n$ can be of an exponential order. We introduce large groups formed by quadratic transformations and numerical encryption algorithm protected by secure protocol of Noncommutative Cryptography. The construction of transformations is presented in terms of walks on Double Schubert Graphs.