This study explores the application of genetic algorithms in generating highly nonlinear substitution boxes (S-boxes) for symmetric key cryptography. We present a novel implementation that combines a genetic algorithm with the Walsh-Hadamard Spectrum (WHS) cost function to produce 8x8 S-boxes with a nonlinearity of 104. Our approach achieves performance parity with the best-known methods, requiring an average of 49,399 iterations with a 100% success rate. The study demonstrates significant improvements over earlier genetic algorithm implementations in this field, reducing iteration counts by orders of magnitude. By achieving equivalent performance through a different algorithmic approach, our work expands the toolkit available to cryptographers and highlights the potential of genetic methods in cryptographic primitive generation. The adaptability and parallelization potential of genetic algorithms suggest promising avenues for future research in S-box generation, potentially leading to more robust, efficient, and innovative cryptographic systems. Our findings contribute to the ongoing evolution of symmetric key cryptography, offering new perspectives on optimizing critical components of secure communication systems.

翻译：本研究探索了遗传算法在对称密钥密码学中生成高度非线性代换盒（S盒）的应用。我们提出了一种新颖的实现方法，将遗传算法与沃尔什-哈达玛谱（WHS）成本函数相结合，以生成非线性度为104的8×8 S盒。我们的方法实现了与已知最佳方法相当的性能，平均需要49,399次迭代且成功率达到100%。该研究表明，相较于该领域早期的遗传算法实现，本方法取得了显著改进，将迭代次数降低了数个数量级。通过采用不同的算法路径达到同等性能，我们的工作扩展了密码学家可用的工具集，并凸显了遗传方法在密码原语生成中的潜力。遗传算法的适应性和并行化潜力为S盒生成的未来研究指明了有前景的方向，可能催生更稳健、高效和创新的密码系统。我们的发现有助于推动对称密钥密码学的持续发展，为优化安全通信系统的关键组件提供了新的视角。