Experimental Methods for Constructing MDS Matrices of a Special Form
- 3 Downloads
MDS matrices are widely used as a diffusion primitive in the construction of block type encryption algorithms and hash functions (such as AES and GOST 34.12-2015). The matrices with the maximum number of 1s and minimum number of different elements are important for more efficient realizations of the matrix-vector multiplication. The article presents a new method for the MDS testing of matrices over finite fields and shows its application to the (8 × 8)-matrices of a special form with many 1s and few different elements; these matrices were introduced by Junod and Vaudenay. For the proposed method we obtain some theoretical and experimental estimates of effectiveness. Moreover, the article comprises a list of some MDS matrices of the above-indicated type.
KeywordsMDS matrix MDS code
Unable to display preview. Download preview PDF.
- 4.M. Matsui, “On Correlation between the Order of S-Boxes and the Strength of DES,” in Advances in Cryptology — EUROCRYPT’ 94: (Proceedings of the Workshop on Theory and Application of Cryptography Techniques, Perugia, Italy, May 9–12, 1994) (Springer, Heidelberg, 1995), pp. 366–375.CrossRefGoogle Scholar
- 5.D. Augot and M. Finiasz, “Exhaustive Search for Small Dimension Recursive MDS Diffusion Layers for Block Ciphers and Hash Functions,” in Proceedings of 2013 IEEE International Symposium on Information Theory (Istanbul, Turkey, July 7–12, 2013) (IEEE, Piscataway, 2013), pp. 1551–1555.CrossRefGoogle Scholar
- 10.K. C. Gupta and I. G. Ray, “On Constructions of MDS Matrices from Companion Matrices for Lightweight Cryptography,” in Security Engineering and Intelligence Informatics (Proceedings. CD-ARES 2013 Workshops: MoCrySEn SeCIHD, Regensburg, Germany, September 2–6, 2013) (Springer, Heidelberg, 2013), pp. 29–43.Google Scholar
- 12.P. Junod and S. Vaudenay, “Perfect Diffusion Primitives for Block Ciphers: Building Efficient MDS Matrices,” in Selected Areas in Cryptography (Revised Selected Papers. 11th International Conference, Waterloo, Canada, August 9–10, 2004) (Springer, Heidelberg, 2005), pp. 84–99.Google Scholar