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.

翻译：在一般通货环上,双轨变形的家属为$G$n美元,平方块面积为$K$,在稳定特性下,这种变形将逐渐稳定,稳定意味着因度变形产生的圆环分组各要素的最大程度受美元的约束。如果是K=F$,这种变形可按指数顺序排列。我们引进了由二次变形和数字加密算法组成的大型群体,这些变形由非对称加密安全协议保护的二次变形和数字加密算法组成。变形的构造以双倍舒伯特图的行走方式呈现。