关于多元密码学中的双Schubert自动机和稳定映射的计算
On computations with Double Schubert Automaton and stable maps of Multivariate Cryptography
摘要：
构造了一般增阶交换环$K$上仿射空间$K^n$的具有稳定性质的双射变换族$G_n$.稳定性是指由$d$度变换生成的循环子群的元素的最大度由$d$有界。在$K=F_q$的情况下，$K^n$的这些变换可以是指数级的。介绍了由二次变换构成的大群和由非交换密码学安全协议保护的数字加密算法。变换的构造是以双Schubert图上的行走为基础的。
英文摘要：
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.
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