Department of Political Sciences, Communication and International Relations, University of Macerata, Via Crescimbeni, 30/32, 62100 Macerata, Italy.
Department of Information and Communication Systems Security, Faculty of Comupter Science, V. N. Karazin Kharkiv National University, 4 Svobody Sq., 61022 Kharkiv, Ukraine.
Sensors (Basel). 2022 Aug 14;22(16):6073. doi: 10.3390/s22166073.
Cryptographic algorithms are used to ensure confidentiality, integrity and authenticity of data in information systems. One of the important areas of modern cryptography is that of symmetric key ciphers. They convert the input plaintext into ciphertext, representing it as a random sequence of characters. S-boxes are designed to complicate the input-output relationship of the cipher. In other words, S-boxes introduce nonlinearity into the encryption process, complicating the use of different methods of cryptanalysis (linear, differential, statistical, correlation, etc.). In addition, S-boxes must be random. This property means that nonlinear substitution cannot be represented as simple algebraic constructions. Random S-boxes are designed to protect against algebraic methods of cryptanalysis. Thus, generation of random S-boxes is an important area of research directly related to the design of modern cryptographically strong symmetric ciphers. This problem has been solved in many related works, including some using the simulated annealing (SA) algorithm. Some works managed to generate 8-bit bijective S-boxes with a nonlinearity index of 104. However, this required enormous computational resources. This paper presents the results of our optimization of SA via various parameters. We were able to significantly reduce the computational complexity of substitution generation with SA. In addition, we also significantly increased the probability of generating the target S-boxes with a nonlinearity score of 104.
密码算法用于确保信息系统中数据的机密性、完整性和真实性。现代密码学的一个重要领域是对称密钥密码。它们将输入的明文转换为密文，表示为随机字符序列。S-盒旨在使密码的输入-输出关系复杂化。换句话说，S-盒为加密过程引入了非线性，使不同的密码分析方法（线性、差分、统计、相关等）的使用变得复杂。此外，S-盒必须是随机的。该属性意味着非线性替换不能表示为简单的代数构造。随机 S-盒旨在防止针对代数密码分析方法的攻击。因此，随机 S-盒的生成是与现代密码强度强的对称密码设计直接相关的重要研究领域。在许多相关工作中已经解决了这个问题，包括一些使用模拟退火（SA）算法的工作。一些工作设法生成了具有 104 非线性度指数的 8 位双射 S-盒。然而，这需要巨大的计算资源。本文介绍了我们通过各种参数对 SA 进行优化的结果。我们能够通过 SA 显著降低代换生成的计算复杂度。此外，我们还显著提高了生成具有 104 非线性得分的目标 S-盒的概率。
