Algebraic structures and their hardware–software implementation gain considerable attention in the field of information security and coding theory. Research progress in the applications of arithmetic properties of algebraic structures is being frequently made. These structures are mostly useful in improvement of the cryptographic algorithms. A novel technique is given to design a cryptosystem responsible for lossless for image encryption. The proposed scheme is for the RGB image whose pixels are considered as 24 binary bits, accordingly a unique arrangement for the construction of S-boxes over a Galois field $$ GF\left( {2^{9} } \right) $$ G F 2 9 is employed. Consequently, it generates multiple different S-boxes with excellent cryptographic characteristic and hence confusing process of the cryptosystem has been working. Whereas the diffusion process in this cryptosystem is based on Affine transformation over a unit elements of an integers modulo ring $$ {\mathbb{Z}}_{n} $$ Z n . The scrambling of the image data through the Affine transformation escalate the security asset, avoid computational effort and abbreviated the time complexity. In addition, the simulation test and comparative scrutinize illustrate that the proposed scheme is highly sensitive, large keyspace, excellent statistical properties and secure against differential attacks. Therefore, the proposed algorithm is valuable for confidential communication. Furthermore, due to the arithmetic properties of algebraic structures, the proposed scheme would be easily implemented, secure and fast enough to be utilized in real-world applications.

中文翻译：

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一种基于仿射变换与线性分数变换相结合的新型高效图像加密算法

代数结构及其硬件-软件实现在信息安全和编码理论领域得到了相当大的关注。代数结构算术性质的应用研究不断取得进展。这些结构主要用于改进密码算法。给出了一种新颖的技术来设计负责图像加密无损的密码系统。提议的方案是针对 RGB 图像，其像素被视为 24 个二进制位，因此在伽罗瓦域 $$ GF\left( {2^{9} } \right) $$ 上构造 S 盒的独特安排采用GF 2 9。因此，它产生了多个不同的具有优良密码特性的S-box，因此密码系统的混淆过程一直在起作用。而该密码系统中的扩散过程基于对整数模环 $$ {\mathbb{Z}}_{n} $$ Z n 的单位元素进行仿射变换。通过仿射变换对图像数据进行加扰可提升安全资产、避免计算工作并缩短时间复杂度。此外，仿真测试和对比研究表明，所提出的方案具有高度敏感、密钥空间大、统计特性优良、抗差分攻击安全等特点。因此，所提出的算法对于机密通信是有价值的。此外，由于代数结构的算术特性，所提出的方案将易于实现、安全且足够快，可以在实际应用中使用。