论文标题
二进制正交阵列的简单条件
Simplicity conditions for binary orthogonal arrays
论文作者
论文摘要
众所周知，在侧通道攻击框架中使用的相关 - 免疫（CI）布尔功能需要具有较低的锤击权重。当CI函数的支持是（等效地）简单的正交数组时，当它们的元素被写成数组的行时。然后，CI函数的最小锤子重量与简单正交数组中的最小行数相同。在本文中，我们使用Rao的义务在行数上提供足够的条件，使二进制正交阵列（OA）简单。我们将此结果应用于确定所有简单的二元正交阵列2和3中的最小行数；我们表明，在所有OA的情况下，此最低限度是相同的，我们将此观察结果扩展到了一些优势的OA $ 4 $和5美元。在强度2和3的情况下，这使我们能够对第一作者和X. Chen提出的一个问题对2-CI布尔功能的最小锤重量的单调性提出的问题进行积极回答，并在优势4和5的情况下对同一问题进行了积极回答。
It is known that correlation-immune (CI) Boolean functions used in the framework of side-channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays when their elements are written as rows of an array. The minimum Hamming weight of a CI function is then the same as the minimum number of rows in a simple orthogonal array. In this paper, we use Rao's Bound to give a sufficient condition on the number of rows, for a binary orthogonal array (OA) to be simple. We apply this result for determining the minimum number of rows in all simple binary orthogonal arrays of strengths 2 and 3; we show that this minimum is the same in such case as for all OA, and we extend this observation to some OA of strengths $4$ and $5$. This allows us to reply positively, in the case of strengths 2 and 3, to a question raised by the first author and X. Chen on the monotonicity of the minimum Hamming weight of 2-CI Boolean functions, and to partially reply positively to the same question in the case of strengths 4 and 5.
