On computations with Double Schubert Automaton and stable maps of Multivariate Cryptography
This work addresses secure encryption protocols in multivariate cryptography, but appears incremental as it builds on existing graph-based methods.
The authors constructed families of bijective transformations of affine spaces over commutative rings with a stability property, where the maximal degree in cyclic subgroups is bounded by the transformation's degree, and introduced a numerical encryption algorithm protected by noncommutative cryptography.
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.