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Construction of MDS block diffusion matrices for block ciphers and hash functions

用于分组密码和哈希函数的MDS分块扩散矩阵的构造

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摘要

创新点

  1. 1、

    本文主要讨论每个块都是某一个内层快的多项式的分块扩散矩阵。与前人工作不同的是: 我们从内层块出发, 由里及外地构造MDS分块扩散层。 这使得我们最后能给出找到MDS分块矩阵的明确算法。

  2. 2、

    我们采用了新方法来验证分块扩散矩阵的MDS性。 新方法基于内层块的极小多项式, 只需检验外层矩阵的子矩阵 (多项式矩阵) 的行列式与此极小多项式是否互素。 这比带入内层块然后计算大尺寸行列式要高效得多。

  3. 3、

    我们发现了一种新的用于外层矩阵的变换。 这种变换可以从一个MDS分块矩阵得出多个MDS分块矩阵。 更重要的是, 我们可以利用这种变换导出所有外层矩阵上的一个等价关系, 并且MDS性是这种等价关系下的不变量。 因而我们可以把所有外层矩阵分类, 每一类或者都是MDS的或者都不是MDS的, 只需检验一个即可。 这样就大大减小了寻找MDS分块矩阵时的搜索空间。

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Ruoxin Zhao, Rui Zhang, Yongqiang Li & Baofeng Wu

  2. University of Chinese Academy of Sciences, Beijing, 100101, China

    Ruoxin Zhao

Authors
  1. Ruoxin Zhao
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  2. Rui Zhang
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  3. Yongqiang Li
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  4. Baofeng Wu
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Corresponding authors

Correspondence to Ruoxin Zhao, Rui Zhang, Yongqiang Li or Baofeng Wu.

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The authors declare that they have no conflict of interest.

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Zhao, R., Zhang, R., Li, Y. et al. Construction of MDS block diffusion matrices for block ciphers and hash functions. Sci. China Inf. Sci. 59, 99101 (2016). https://doi.org/10.1007/s11432-015-0363-7

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  • DOI: https://doi.org/10.1007/s11432-015-0363-7

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