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首页> 外文期刊>IEEE Transactions on Information Theory >Constructions of Resilient S-Boxes With Strictly Almost Optimal Nonlinearity Through Disjoint Linear Codes
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Constructions of Resilient S-Boxes With Strictly Almost Optimal Nonlinearity Through Disjoint Linear Codes

机译：通过不相交的线性码构造具有几乎最佳非线性的弹性S盒

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摘要

In this paper, a novel approach of finding disjoint linear codes is presented. The cardinality of a set of $[u, m, t+1]$ disjoint linear codes largely exceeds all the previous best known methods used for the same purpose. Using such sets of disjoint linear codes, not necessarily of the same length, we have been able to provide a construction technique of $t$-resilient S-boxes $F:BBF_{2}^{n}mapstoBBF_{2}^{m}$ ($n$ even, $1< mleqlfloor n/4rfloor$) with strictly almost optimal nonlinearity $>2^{n-1}-2^{n/2}$. This is the first time that the bound $2^{n-1}-2^{n/2}$ has been exceeded by multiple output resilient functions. Actually, the nonlinearity of our functions is in many cases equal to the best known nonlinearity of balanced Boolean functions. A large class of previously unknown cryptographic resilient S-boxes is obtained, and several improvements of the original approach are proposed. Some other relevant cryptographic properties are also briefly discussed. It is shown that these functions may reach Siegenthaler's bound $n-t-1$, and can be either of optimal algebraic immunity or of slightly suboptimal algebraic immunity, which was confirmed by simulations.
机译：本文提出了一种寻找不相交线性码的新颖方法。一组$ [u，m，t + 1] $不相交的线性代码的基数大大超过了以前用于同一目的的所有最著名方法。使用这样的不相交的线性代码集（不一定长度相同），我们已经能够提供$ t $弹性S盒$ F：BBF_ {2} ^ {n} mapstoBBF_ {2} ^ { m} $（偶数$ n $，$ 1 2 ^ {n-1} -2 ^ {n / 2} $。这是多个输出弹性函数第一次超过绑定的$ 2 ^ {n-1} -2 ^ {n / 2} $。实际上，在许多情况下，我们函数的非线性等于平衡布尔函数的最著名的非线性。获得了大量以前未知的密码弹性S盒，并提出了对原始方法的一些改进。还简要讨论了其他一些相关的密码属性。结果表明，这些函数可以达到Siegenthaler的$ n-t-1 $，并且可以是最佳代数免疫性或次优免疫性，这已通过仿真得到了证实。

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