On the Construction of Lightweight Circulant Involutory MDS Matrices

详细信息    查看全文

• 关键词：MDS matrix ; Circulant involutory matrix ; Hadamard matrix ; Lightweight
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9783
• 期：1
• 页码：121-139
• 全文大小：265 KB
• 参考文献：1.Augot, D., Finiasz, M.: 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 (ISIT), pp. 1551–1555. IEEE (2013)
  2.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)
  3.Barreto, P., Rijmen, V.: The anubis block cipher. Submission to the NESSIE Project (2000)
  4.Berger, T.P.: Construction of recursive MDS diffusion layers from Gabidulin codes. In: Paul, G., Vaudenay, S. (eds.) INDOCRYPT 2013. LNCS, vol. 8250, pp. 274–285. Springer, Heidelberg (2013)CrossRef
  5.Blaum, M., Roth, R.M.: On lowest density MDS codes. IEEE Trans. Inf. Theory 45(1), 46–59 (1999)MathSciNet CrossRef MATH
  6.Choy, J., Yap, H., Khoo, K., Guo, J., Peyrin, T., Poschmann, A., Tan, C.H.: SPN-Hash: improving the provable resistance against differential collision attacks. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 270–286. Springer, Heidelberg (2012)CrossRef
  7.Cui, T., Jin, C.I., Kong, Z.: On compact Cauchy matrices for substitution permutation networks. IEEE Trans. Comput. 99, 1 (2014). PreprintMathSciNet
  8.Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Springer, Heidelberg (2002)CrossRef MATH
  9.Guo, J., Peyrin, T., Poschmann, A., Robshaw, M.: The LED block cipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 326–341. Springer, Heidelberg (2011)CrossRef
  10.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)CrossRef
  11.Chand Gupta, K., Ghosh Ray, I.: On constructions of involutory MDS matrices. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 2013. LNCS, vol. 7918, pp. 43–60. Springer, Heidelberg (2013)CrossRef
  12.Gupta, K.C., Ray, I.G.: On constructions of MDS matrices from companion matrices for lightweight cryptography. In: Cuzzocrea, A., Kittl, C., Simos, D.E., Weippl, E., Xu, L. (eds.) CD-ARES Workshops 2013. LNCS, vol. 8128, pp. 29–43. Springer, Heidelberg (2013)CrossRef
  13.Gupta, K.C., Ray, I.G.: Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications. Crypt. Commun. 7, 257–287 (2015)MathSciNet CrossRef MATH
  14.Li, Y., Wang, M.: On the construction of lightweight circulant involutory MDS matrices (Extend version). In: FSE 2016. http://​eprint.​iacr.​org/​2016/​406
  15.Jean, J., Nikolić, I., Peyrin, T.: Joltik v1.1. Submission to the CAESAR competition (2014). http://​www1.​spms.​ntu.​edu.​sg/​~syllab/​Joltik
  16.Nakahara Jr., J., Abraho, I.: A new involutory MDS matrix for the AES. Int. J. Netw. Secur. 9(2), 109–116 (2009)
  17.Junod, P., Vaudenay, S.: Perfect diffusion primitives for block ciphers. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 84–99. Springer, Heidelberg (2004)CrossRef
  18.Kavun, E.B., Lauridsen, M.M., Leander, G., Rechberger, C., Schwabe, P., Yalc, T.: Prøstv1.1. Submission to the CAESAR competition (2014). http://​competitions.​cr.​yp.​to/​round1/​proestv11.​pdf
  19.Khoo, K., Peyrin, T., Poschmann, A.Y., Yap, H.: FOAM: searching for hardware-optimal SPN structures and components with a fair comparison. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 433–450. Springer, Heidelberg (2014)
  20.Sajadieh, M., Dakhilalian, M., Mala, H., Sepehrdad, P.: Recursive diffusion layers for block ciphers and hash functions. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 385–401. Springer, Heidelberg (2012)CrossRef
  21.Sim, S.M., Khoo, K., Oggier, F., Peyrin, T.: Lightweight MDS involution matrices. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 471–493. Springer, Heidelberg (2015)CrossRef
  22.Vaudenay, S.: On the need for multipermutations: cryptanalysis of MD4 and SAFER. In: Preneel, Bart (ed.) FSE 1994. LNCS, vol. 1008, pp. 286–297. Springer, Heidelberg (1994)CrossRef
  23.Wu, S., Wang, M., Wu, W.: Recursive diffusion layers for (lightweight) block ciphers and hash functions. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 355–371. Springer, Heidelberg (2013)CrossRef
  
• 作者单位：Yongqiang Li (14) (15)
  Mingsheng Wang (14)
  
  14. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China
  15. Science and Technology on Communication Security Laboratory, Chengdu, China
  
• 丛书名：Fast Software Encryption
• ISBN：978-3-662-52993-5
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9783

文摘

In the present paper, we investigate the problem of constructing MDS matrices with as few bit XOR operations as possible. The key contribution of the present paper is constructing MDS matrices with entries in the set of \(m\times m\) non-singular matrices over \(\mathbb {F}_2\) directly, and the linear transformations we used to construct MDS matrices are not assumed pairwise commutative. With this method, it is shown that circulant involutory MDS matrices, which have been proved do not exist over the finite field \(\mathbb {F}_{2^m}\), can be constructed by using non-commutative entries. Some constructions of \(4\times 4\) and \(5\times 5\) circulant involutory MDS matrices are given when \(m=4,8\). To the best of our knowledge, it is the first time that circulant involutory MDS matrices have been constructed. Furthermore, some lower bounds on XORs that required to evaluate one row of circulant and Hadamard MDS matrices of order 4 are given when \(m=4,8\). Some constructions achieving the bound are also given, which have fewer XORs than previous constructions.