Aslam Mazzamal, Beg Saira, Anjum Adeel, Qadir Zakria, Khan Shawal, Malik Saif Ur Rehman, Mahmud Ma Parvez
Computer Science, COMSATS Institute of Information Technology, Islamabad, Pakistan.
Department of Information Technology, Quaid e Azam University, Islamabad, Pakistan.
PeerJ Comput Sci. 2022 Sep 9;8:e892. doi: 10.7717/peerj-cs.892. eCollection 2022.
The substitution box (S-box) plays a vital role in creating confusion during the encryption process of digital data. The quality of encryption schemes depends upon the S-box. There have been several attempts to enhance the quality of the S-box by using fractal chaotic mechanisms. However, there is still weakness in the robustness against cryptanalysis of fractal-based S-boxes. Due to their chaotic behavior, fractals are frequently employed to achieve randomness by confusion and diffusion process. A complex number-based S-box and a chaotic map diffusion are proposed to achieve high nonlinearity and low correlation. This study proposed a Mandelbrot set S-box construction based on the complex number and Chen chaotic map for resisting cryptanalytic attacks by creating diffusion in our proposed algorithm. The cryptosystem was built on the idea of substitution permutation networks (SPN). The complex nature of the proposed S-box makes it more random than other chaotic maps. The robustness of the proposed system was analyzed by different analysis properties of the S-box, such as nonlinearity, strict avalanche criterion, Bit independent criterion, and differential and linear probability. Moreover, to check the strength of the proposed S-box against differential and brute force attacks, we performed image encryption with the proposed S-box. The security analysis was performed, including statistical attack analysis and NIST analysis. The analysis results show that the proposed system achieves high-security standards than existing schemes.
替换盒（S盒）在数字数据加密过程中产生混淆方面起着至关重要的作用。加密方案的质量取决于S盒。已经有几次尝试通过使用分形混沌机制来提高S盒的质量。然而，基于分形的S盒在抵抗密码分析方面的鲁棒性仍然存在弱点。由于其混沌行为，分形经常被用于通过混淆和扩散过程来实现随机性。提出了一种基于复数的S盒和一种混沌映射扩散方法，以实现高非线性和低相关性。本研究提出了一种基于复数和陈氏混沌映射的曼德勃罗集S盒构造方法，通过在我们提出的算法中创建扩散来抵抗密码分析攻击。该密码系统基于替换置换网络（SPN）的思想构建。所提出的S盒的复杂性质使其比其他混沌映射更具随机性。通过S盒的不同分析属性，如非线性、严格雪崩准则、比特独立准则以及差分和线性概率，对所提出系统的鲁棒性进行了分析。此外，为了检验所提出的S盒抵抗差分和暴力攻击的强度，我们使用所提出的S盒进行了图像加密。进行了安全分析，包括统计攻击分析和美国国家标准与技术研究院（NIST）分析。分析结果表明，所提出的系统比现有方案达到了更高的安全标准。
