In this article, we have developed an encryption technique to encrypt any kind of digital information. The main work is to construct the component of the block ciphers namely the substitution boxes (S-boxes) over an algebraic structure of finite chain ring; and then use these S-boxes in image encryption applications. The present formation is based on the finite commutative chain ring R₉ = ℤ₂ + uℤ₂ + … + u^k − 1ℤ₂ (module over itself) which is exactly twice of 256. The multiplicative group of unit elements of R₉ precisely has 256 elements and the set of all nonunit elements in R₉ forms a submodule of module R₉ consisting of 256 elements. By using this point we initiate a new 8 × 8 S-box triplet generation technique which addresses the group of units of R₉ and the submodule of R₉. This new construction technique of S-boxes ensures random values in the area of the initial domain of transformation. The proposed S-boxes have been examined by algebraic, statistical and texture analyses. A comparison of the expected and existing S-boxes reveals that the proposed S-boxes are comparatively better and can be used in the well known ciphers. Another goal of this work is to suggest an encryption technique for colored (RGB) images based on permutation keys and triplet of newly generated S-boxes. The outcomes of the security, statistical and the differential analyses have proved that our scheme is better for the image encryption.

在本文中，我们开发了一种加密技术来对任何类型的数字信息进行加密。主要工作是在有限链环的代数结构上构造分组密码的组成部分，即替换盒（S-box）。然后在图像加密应用程序中使用这些S盒。本形成是基于有限交换链环- [R ₉  =  ℤ ₂  +  uℤ ₂  + ... +  Ü ^{ķ  - 1个}ℤ ₂（模块在其自身上），这是完全两次256的R单元元件的乘法群₉精确具有256个元素，并且R _9中的所有非单位元素集形成由256个元素组成的模块R ₉的子模块。通过使用这一点，我们发起新的8×8的S盒三重代技术，其地址的组的的R单元₉ 和R的子模块₉。这种新的S盒构造技术可确保在转换的初始域范围内具有随机值。提议的S盒已通过代数，统计和纹理分析进行了检查。对预期的S-box和现有的S-box进行比较后发现，所建议的S-box相对更好，可以在众所周知的密码中使用。这项工作的另一个目标是建议一种基于置换密钥和新生成的S盒的三元组的彩色（RGB）图像加密技术。安全性，统计和差异分析的结果证明，我们的方案更适合图像加密。