Algorithm for generating S-box using trigonometric function
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Abstract
Substitution boxes, commonly known as S-boxes, are one of the most important nonlinear components of modern symmetric-key block encryption algorithms. Their main task is to introduce confusion and nonlinear transformation into the encryption process so that the relationship between plaintext, ciphertext, and secret key becomes difficult to analyze. In Feistel networks and substitution–permutation networks, the S-box plays a central role in strengthening the resistance of a cipher against linear, differential, and algebraic cryptanalysis. This paper presents an algorithm for generating cryptographically strong 8×8 S-boxes using trigonometric transformation. The proposed approach is based on nonlinear numerical behavior produced by trigonometric functions and parameter-controlled transformations. By selecting different values of the control parameters, a large number of candidate S-boxes can be generated. These candidates are then evaluated according to standard cryptographic criteria, including nonlinearity, Strict Avalanche Criterion, Differential Probability, Linear Approximation Probability, and Fixed Point Analysis. The experimental results show that the generated S-box achieves a minimum nonlinearity of 100, a maximum nonlinearity of 112, and an average nonlinearity of 105.5. In addition, the proposed S-box obtains a SAC value of 0.4922, a DP value of 10/256, a LAP value of 0.1328, and zero fixed points. These results indicate that trigonometric transformations can be used as a promising mathematical tool for constructing substitution boxes for block cipher algorithms.
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