Lightweight MDS Involution Matrices
Lightweight MDS Involution Matrices
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DOI：
10.1007/978-3-662-48116-5_23
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发表时间：
2015-03
影响因子：
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通讯作者：
Siang Meng Sim;Khoongming Khoo;F. Oggier;Thomas Peyrin
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文献类型：
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作者：
Siang Meng Sim;Khoongming Khoo;F. Oggier;Thomas Peyrin
在这篇文章中，我们提供了新的方法来寻找轻量级MDS矩阵，特别是对合矩阵。通过证明许多新的性质和等价类的各种MDS矩阵的建设，如循环，阿达玛，柯西和阿达玛柯西，我们展示了新的搜索算法，大大减少了搜索空间，使轻量级的MDS矩阵，而高维可能找到。我们还解释了为什么不可约多项式的选择可能对轻量级产生显着影响，并且与经典观点相反，我们表明海明权没有直接影响。虽然我们的研究主要集中在对合MDS矩阵上，但我们也得到了非对合MDS矩阵的结果。总体而言，使用Hadamard或Hadamard-Cauchy结构，我们提供了（对合或非对合）MDS矩阵与最少可能的XOR门的经典尺寸，，andinand。与最知名的矩阵相比，我们的一些新候选矩阵节省了硬件实现所需的XOR门数量的50%。最后，我们的工作表明，对合MDS矩阵是非常有趣的积木设计师，因为它们可以实现几乎相同数量的异或门作为非对合MDS矩阵，后者通常是非轻量级的逆矩阵时，需要。
In this article, we provide new methods to look for lightweight MDS matrices, and in particular involutory ones. By proving many new properties and equivalence classes for various MDS matrices constructions such as circulant, Hadamard, Cauchy and Hadamard-Cauchy, we exhibit new search algorithms that greatly reduce the search space and make lightweight MDS matrices of rather high dimension possible to find. We also explain why the choice of the irreducible polynomial might have a significant impact on the lightweightness, and in contrary to the classical belief, we show that the Hamming weight has no direct impact. Even though we focused our studies on involutory MDS matrices, we also obtained results for non-involutory MDS matrices. Overall, using Hadamard or Hadamard-Cauchy constructions, we provide the (involutory or non-involutory) MDS matrices with the least possible XOR gates for the classical dimensions,,andinand. Compared to the best known matrices, some of our new candidates save up to 50 % on the amount of XOR gates required for an hardware implementation. Finally, our work indicates that involutory MDS matrices are really interesting building blocks for designers as they can be implemented with almost the same number of XOR gates as non-involutory MDS matrices, the latter being usually non-lightweight when the inverse matrix is required.