关于密码S盒中Boomerang一致性的演化
On the Evolution of Boomerang Uniformity in Cryptographic S-boxes
摘要：
S盒是一种重要的原语，它帮助密码算法抵御各种攻击。对特定攻击的抵抗力可以与S盒的某种属性联系起来，属性值越好，算法越安全。这种属性的一个例子是所谓的回飞棒均匀性，这有助于抵御回飞棒攻击。如何构造具有良好回飞棒一致性的S盒并不总是清楚的。有一些代数技巧可以产生良好的回飞棒均匀性，但结果仍然很少。在这项工作中，我们探讨了具有良好的回旋镖均匀性值的S盒的演化。我们考虑三种不同的编码和五个S盒大小。对于尺寸$4\times 4$和$5\times 5$，我们设法获得最佳解决方案。对于$6\times 6$，我们得到了非APN函数的最优回飞棒均匀性。对于更大的尺寸，结果表明问题是非常困难的（甚至比演化微分均匀性更困难，这可以被认为是一个研究得很好的问题）。
英文摘要：
S-boxes are an important primitive that help cryptographic algorithms to be resilient against various attacks. The resilience against specific attacks can be connected with a certain property of an S-box, and the better the property value, the more secure the algorithm. One example of such a property is called boomerang uniformity, which helps to be resilient against boomerang attacks. How to construct S-boxes with good boomerang uniformity is not always clear. There are algebraic techniques that can result in good boomerang uniformity, but the results are still rare. In this work, we explore the evolution of S-boxes with good values of boomerang uniformity. We consider three different encodings and five S-box sizes. For sizes $4\times 4$ and $5\times 5$, we manage to obtain optimal solutions. For $6\times 6$, we obtain optimal boomerang uniformity for the non-APN function. For larger sizes, the results indicate the problem to be very difficult (even more difficult than evolving differential uniformity, which can be considered a well-researched problem).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
