论文标题
关于加密S盒中回旋镖均匀性的演变
On the Evolution of Boomerang Uniformity in Cryptographic S-boxes
论文作者
论文摘要
S框是一个重要的原始性，可帮助加密算法对各种攻击具有弹性。针对特定攻击的弹性可以与S-box的某个属性连接，并且属性值越好，算法越安全。这种属性的一个例子称为Boomerang统一性，这有助于抵抗回旋镖攻击。如何以良好的飞旋镖统一性构建S盒并不总是很清楚。有一些代数技术可以导致良好的飞旋镖均匀性，但结果仍然很少见。在这项工作中，我们探讨了具有良好价值的Boomerang均匀性值的S框的演变。我们考虑三种不同的编码和五个S-box尺寸。对于$ 4 \ times 4 $和$ 5 \ times 5 $的尺寸，我们设法获得了最佳解决方案。对于$ 6 \ times 6 $，我们获得了非APN功能的最佳回旋镖均匀性。对于较大的尺寸，结果表明问题非常困难（甚至比不断发展的差异均匀性更加困难，这可以被视为一个经过充分研究的问题）。
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).
