MDS MATRIX APPLIED IN CRYPTOGRAPHY
Abstract
The security of information is one of the most important aspects in communications, which always demands to improve the existing cryptosystems, and design new ones with high security and performance in real-time applications due to enhancing the danger of hacking efforts. Since MDS matrix a are formal models of computing devices, cryptosystems based on them can be efficiently implemented at software and hardware levels. Today, MDS matrices occupy a special place and are important components in designing the linear diffusion layers of many block ciphers and hash functions. Recently, a lot of work has been done on the construction of lightweight MDS matrices, most of which are based on special types of matrices over finite fields. This article provides an analytical overview of the use of MDS matrices for cryptographic algorithms. The use of the MDS matrix for diffusion is considered, as well as their comparison with other algorithms.
Keywords
About the Authors
T. K. ZhukabaevaKazakhstan
E. M. Mardenov
Kazakhstan
References
1. B. W. Koo, H. S. Jang, J. H. Song. Constructing and Cryptanalysis of a 16x16 Binary Matrix as a Diffusion Layer, Proceedings of Information Security Applications: 4th International Workshop (W ISA2003), Lecture Notes in Computer Science, Vol. 2908, pp. 489-503, Springer-Verlag, 2003.
2. Duval S., Leurent G. MDS matrices with lightweight circuits //IACR Transactions on Symmetric Cryptology. - 2018.
3. Andreeva, E., Bilgin, B., Bogdanov, A., Luykx, A., Mendel, F., Mennink, B., Mouha, N., Wang, Q., Yasuda, K.: PRIMATEs v1. Submission to the CAESAR Competition (2014)
4. Christof Beierle, Thorsten Kranz, and Gregor Leander. Lightweight multiplication in GF(2n) with applications to M DS matrices. In Matthew Robshaw and Jonathan Katz, editors, CRYPTO 2016, Part I, volume 9814 of LNCS, pages 625-653. Springer, Heidelberg, August 201
5. E. Biham and A. Shamir, Differential cryptanalysis of DES-like cryptosystems, Proceedings of CRYPTO’90, Lecture Notes in Computer Science, Vol. 537, pp. 2-21, Springer-Verlag, 1991
6. M. Matsui, Linear cryptanalysis method for DES cipher, Proceedings of EUROCRYPT 93, Lecture Notes in Computer Science, Vol. 765, pp. 386-397, Springer-Verlag, 1994.
7. Jian Guo, Thomas Peyrin, Axel Poschmann, and Matthew J. B. Robshaw. The LED Block Cipher. In CHES, pages 326-341, 2011.
8. J. Nakahara Jr., E. Abrahao, A new Involutory MDS Matrix for the AES, International Journal of Network Security, Vol. 9, n. 2, pp. 109-116, 2009.
9. Guo, J., Peyrin, T., Poschmann, A.: The PHOTON family of lightweight hash functions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 222-239. Springer, Heidelberg (2011).
10. Andreeva, E., Bilgin, B., Bogdanov, A., Luykx, A., Mendel, F., Mennink, B., Mouha, N., Wang, Q., Yasuda, K.: PRIMATEs v1. Submission to the CAESAR Competition (2014)
11. Augot, D., Finiasz, M.: Direct construction of recursive M DS diffusion layers using shortened BCH codes. In: Cid, C., Rechberger, C. (eds.) FSE 2014. LNCS, vol. 8540, pp. 3-17. Springer, Heidelberg (2015)
12. Augot, D., Finiasz, M.: Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash functions. In: ISIT, pp. 1551-1555 (2013)
13. Kishan Chand Gupta and Indranil Ghosh Ray. On Constructions of Involutory MDS Matrices. In AFRICACRYPT, pages 43-60, 2013.
14. K. Khoo, T. Peyrin, A. Poschmann, and H. Yap. FOAM: Searching for Hardware- Optimal SPN Structures and Components with a Fair Comparison. In Crypto- graphic Hardware and Embedded Systems CHES 2014, volume 8731 of Lecture Notes in Computer Science, pages 433-450. Springer Berlin Heidelberg, 2014
15. M. I Sajadieh, M. Dakhilalian, H. Mala, and B. Omoomi. On construction of in- volutory MDS matrices from Vandermonde Matrices in GF(2 q ). Des. Codes Cryptography, 64 (3) : 287-308, 2012.
16. Joan Daemen and Vincent Rijmen. The Design of Rijndael: AES - The Advanced Encryption Standard. Springer, 2002.
17. Pascal Junod and Serge Vaudenay. Perfect Diffusion Primitives for Block Ciphers. In Helena Handschuh and M. Anwar Hasan, editors, Selected Areas in Cryptogra- phy, volume 3357 of LNCS, pages 84-99. Springer, 2004.
18. Kishan Chand Gupta and Indranil Ghosh Ray. On Constructions of Circulant MDS Matrices for Lightweight Cryptography. In ISPEC, pages 564-576, 2014
19. M. I. Sajadieh, M. Dakhilalian, H. Mala, and B. Omoomi. On construction of in- volutory MDS matrices from Vandermonde Matrices in GF(2 q ). Des. Codes Cryptography, 64 (3) : 287-308, 2012.
20. Kishan Chand Gupta and Indranil Ghosh Ray. On Constructions of Involutory MDS Matrices. In AFRICACRYPT, pages 43-60, 2013.
21. Sim S. M. et al. Lightweight MDS involution matrices //International Workshop on Fast Software Encryption. - Springer, Berlin, Heidelberg, 2015. - С. 471-493
22. Augot, D., Finiasz, M.: Direct construction of recursive MDS diffusion layers using shortened BCH codes. In: Cid, C., Rechberger, C. (eds.) FSE 2014. LNCS, vol. 8540, pp. 3-17. Springer, Heidelberg (2015).
23. Qiuping Li, Baofeng Wu, Liu Zhuojun Liu. Lightweight Recursive MDS Matrices with Generalized Feistel Network: 13th International Workshop on Security, IWSEC 2018, Sendai, Japan, September 3-5, 2018, Proceedings Advances in Information and Computer Security
Review
For citations:
Zhukabaeva T.K., Mardenov E.M. MDS MATRIX APPLIED IN CRYPTOGRAPHY. Herald of the Kazakh-British technical university. 2019;16(4):117-121. (In Russ.)