轻量级MDS矩阵的构造
The Construction of Lightweight MDS Matrix
DOI: 10.12677/AAM.2018.74054, PDF,  被引量    科研立项经费支持
作者: 周 敏：西华大学数学研究所，四川 成都；顾 执：西南交通大学数学学院，四川 成都
关键词: MDS矩阵；线性扩散层；循环矩阵；Hadamard矩阵；异或数；MDS Matrix； Linear Diffusion Layer； Cyclic Matrix； Hadamard Matrix； Number of XOR
摘要: MDS矩阵在密码学中有重要的应用，可以用来构造分组密码。MDS矩阵的异或数是衡量密码算法的有效性的一个重要指标。本文研究MDS矩阵的性质，考虑循环、矩阵分块和迭代等思想，分别针对几类特殊性质的MDS矩阵构造，包括循环MDS矩阵、Hadar MDS矩阵和迭代MDS矩阵等。在m = 4, 8情况下，使用程序来搜索满足条件的MDS矩阵，给出了具有最小异或数的MDS矩阵的数目和例子，得到m = 4, 8情况下许多具有已知最小异或数的MDS矩阵，得到了m = 4时具有异或数12的循环MDS矩阵，也构造了m = 8时具有异或数10的最佳MDS矩阵。
Abstract: MDS Matrix has important applications in cryptography and it can be used to construct block ciphers. The number of XOR of a MDS Matrix is an important index to measure the validity of cipher algorithm. In this paper, we study the properties of MDS matrix and consider the ideas of cycle, block matrix and so on. The MDS matrix is constructed for several special properties, including cyclic MDS matrix, Hadamard MDS matrix and iterative MDS matrix etc. When the number m = 4, 8, we use the program to search the MDS matrix that satisfies the condition. The number of MDS matrix with the minimum number of XOR and examples are given and we get many MDS matrices with the minimum number of XOR; when m = 4, we have given the circulating MDS Matrix with the number of XOR with 12, when m = 8 we have given the best MDS Matrix with the number of XOR with 10.
文章引用：周敏, 顾执. 轻量级MDS矩阵的构造[J]. 应用数学进展, 2018, 7(4): 429-445. https://doi.org/10.12677/AAM.2018.74054

参考文献

[1] Daemen, J. and Rijmen, V. (2001) The Wide Trail Design Strategy. Proceedings of the 8th IAM international Conference, Springer-Verlag, Berlin, Volume 2260: 222-238.
[2] Daemen, J. and Rijmen, V. (2002) The Design of Rijndael: AES—The Advanced Encryption Standard. Springer Science & Business Media. [Google Scholar] [CrossRef] 
[3] Rijmen, V., Daemen, J., Preneel, B., Bosselaers, A. and De Win, E. (1996) The cIpher SHARK. In: Fast Software Encryption. Vol. 1039 of Lecture Notes in Computer Science. Springer Berlin Heidelberg, 99-111. [Google Scholar] [CrossRef] 
[4] Schneier, B., Kelsey, J., Whiting, D., Wagner, D., Hall, C. and Ferguson, N. (1998) Twofish: A 128-Bitblock Cipher. NIST AES Proposal, 15. http://dblp.uni-trier.de/db/conf/rsfdgrc/index.html
[5] Barreto, P. and Rijmen, V. (2000) The Khazad Legacy-Level Block Cipher. Submission to the Nessie Project, 97. http://dblp.uni-trier.de/db/conf/rsfdgrc/index.html
[6] Guo, J., Peyarin, T. and Poschmann, A. (2011) The PHOTON Family of Lightweight Hash Function. CRYPTO’11, Springer-Verlag, Berlin, Volume 6841: 222-239.
[7] Li, Y. and Wang, M. (2016) On the Construction of Lightweight Circulant Involutory MDS Matrices. FSE 2016. IACR Cryptology ePrint Archive, 2016: 406. http://eprint.iacr.org/
[8] Junod, P. and Vaudenay, S. (2004) Perfect Diffusion Primitives for Block Ciphers Building Efficient MDS Matrices. In: Handschuh, H. and Hasan, M.A., Eds., SAC 2004. LNCS, Volume 3357, 84-99. Springer, Heidelberg.
[9] Wu, S., Wang, M. and Wu, W. (2012) Recursive Diffusion Layers for (Lightweight) Block Ciphers and Hash Functions. In: Knudsen, L.R. and Wu, H., Eds., SAC 2012: Selected Areas in Cryptography, LNCS, Volume 7707, 355-371. [Google Scholar] [CrossRef] 
[10] Guo, J., Peyrin, T., Poschmann, A. and Robshaw, M. (2011) The LED Block Cipher. In: Preneel, B. and Takagi, T., Eds., CHES 2011: Cryptographic Hardware and Embedded Systems, LNCS, Volume 6917, 326-341. Springer, Heidelberg. [Google Scholar] [CrossRef] 

为你推荐