Several dynamic substitution box (S-box) generators have been proposed in recent years. Some of the existing S-box generators can generate an S-box with good cryptographic properties. However, no analysis has been performed for almost all generators to confirm if they can output highly dynamic S-boxes in a reasonable computational complexity. This article aims to propose an S-box generator that can efficiently generate highly dynamic S-boxes with good cryptographic properties. For this purpose, we use elliptic curves over finite rings. To create randomness in the points on the curves, we define two families of total orders. We then use these ordered curves to generate an S-box of size m using the y-coordinates of an ordered subset of size m of the underlying curve. We performed a rigorous analysis to show that our proposed generator can efficiently generate dynamic S-boxes with good cryptographic properties. Compared to some of the existing generators, it is shown that the proposed S-box generator is more suitable for cryptographic purposes.

近年来，已经提出了几种动态替代盒（S-box）发生器。一些现有的S-box生成器可以生成具有良好加密特性的S-box。但是，尚未对几乎所有生成器进行分析，以确认它们是否可以以合理的计算复杂度输出高度动态的S盒。本文旨在提出一种S-box生成器，它可以有效地生成具有良好加密特性的高度动态的S-box。为此，我们在有限环上使用椭圆曲线。为了在曲线上的点上创建随机性，我们定义了两个总阶数族。然后，我们使用这些命令的曲线，产生的大小的S-box米使用Ÿ的大小有序子集的坐标-米基础曲线的 我们进行了严格的分析，以表明我们提出的生成器可以有效地生成具有良好加密特性的动态S盒。与某些现有的生成器相比，表明所提出的S-box生成器更适合于加密目的。