论文标题
构建相关性免疫功能来自相互正交蜂窝自动机的集合
Building Correlation Immune Functions from Sets of Mutually Orthogonal Cellular Automata
论文作者
论文摘要
相关免疫布尔功能在实施有效的掩蔽对策中对密码学中的侧通道攻击起着重要作用。在本文中，我们研究了一种通过相互正交的细胞自动机（MOCA）家族构建相关免疫功能的方法。首先，我们表明，与MOCA家族相关的正交阵列（OA）至少可以扩展到强度的二元OA。为了证明这一结果，我们根据DE Bruijn图上的正交标记来利用MOCA的表征。然后，我们使用所得的二进制OA来定义二阶相关免疫功能的支持。接下来，我们执行一些计算实验，以构建最高$ n = 12 $变量的所有此类功能，并观察到它们的相关免疫顺序实际上更大，至少至少3个。我们通过讨论这些结果如何为未来的研究开辟有趣的观点，并在搜索新的相关性 - 微这些功能和Binary Orthogonal and orthogogonal arreays。
Correlation immune Boolean functions play an important role in the implementation of efficient masking countermeasures for side-channel attacks in cryptography. In this paper, we investigate a method to construct correlation immune functions through families of mutually orthogonal cellular automata (MOCA). First, we show that the orthogonal array (OA) associated to a family of MOCA can be expanded to a binary OA of strength at least 2. To prove this result, we exploit the characterization of MOCA in terms of orthogonal labelings on de Bruijn graphs. Then, we use the resulting binary OA to define the support of a second-order correlation immune function. Next, we perform some computational experiments to construct all such functions up to $n=12$ variables, and observe that their correlation immunity order is actually greater, always at least 3. We conclude by discussing how these results open up interesting perspectives for future research, with respect to the search of new correlation-immune functions and binary orthogonal arrays.
