A substitution box (S-box) is the only non-linear component in many cryptosystems. Recently, S-box generators have been used intensively in many modern cryptosystems to obtain ciphertext that is secure against modern cryptanalysis. The purpose of these generators is to (i) efficiently generate (ii) dynamic S-boxes (iii) with optimal cryptographic properties (iv) that can be used as a group to create a secure ciphertext. However, no formal methods have been introduced that can analyze if an S-box generator can satisfy conditions (i), (ii) and (iv). The aim of this paper is fourfold: we formally discuss five methods to test if an S-box generator satisfies (i), (ii) and (iv). In the second part, we propose a new S-box generator based on isomorphic ordered elliptic curves that satisfies conditions (i)-(iv). In the third part, we conduct a detailed comparison of our S-box generator with some of the state-of-the-art S-box generators. From the comparison, we conclude that our generator is more secure and suitable for encryption. In the fourth part, we discuss an application of the proposed S-box generator for image encryption. Experimental results reveal that our S-box generator can generate a highly secure ciphertext for a plain text with a high correlation.

替换盒（S-box）是许多密码系统中唯一的非线性组件。近年来，S-box生成器已在许多现代密码系统中得到广泛使用，以获取对现代密码分析安全的密文。这些生成器的目的是（i）有效地生成（ii）具有最佳加密特性的动态S盒（iii）（iv）可以用作创建安全密文的组。但是，尚未引入可以分析S-box生成器是否满足条件（i），（ii）和（iv）的正式方法。本文的目的是四个方面：我们正式讨论测试S-box发生器是否满足（i），（ii）和（iv）的五种方法。在第二部分中，我们提出了一种新的S-box生成器，它基于满足条件（i）-（iv）的同构有序椭圆曲线。第三部分 我们将S-box生成器与一些最新的S-box生成器进行了详细的比较。通过比较，我们可以得出结论，我们的生成器更安全并且更适合加密。在第四部分中，我们讨论了所提出的S-box生成器在图像加密中的应用。实验结果表明，我们的S-box生成器可以为具有高相关性的纯文本生成高度安全的密文。