{"title":"On the Construction of Lightweight Circulant Maximum Distance Separable Matrices","authors":"Qinyi Mei, Li-Ping Wang","volume":126,"journal":"International Journal of Computer and Systems Engineering","pagesStart":222,"pagesEnd":227,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10007428","abstract":"MDS matrices are of great significance in the design
\r\nof block ciphers and hash functions. In the present paper, we
\r\ninvestigate the problem of constructing MDS matrices which are
\r\nboth lightweight and low-latency. We propose a new method of
\r\nconstructing lightweight MDS matrices using circulant matrices
\r\nwhich can be implemented efficiently in hardware. Furthermore, we
\r\nprovide circulant MDS matrices with as few bit XOR operations as
\r\npossible for the classical dimensions 4 × 4, 8 × 8 over the space of
\r\nlinear transformations over finite field F42
\r\n. In contrast to previous
\r\nconstructions of MDS matrices, our constructions have achieved
\r\nfewer XORs.","references":"[1] Augot, D., Finiasz, M.: Direct construction of recursive MDS diffusion\r\nlayers using shortened BCH codes. In: Cid, C., Rechberger, C. (eds.) FSE\r\n2014. LNCS 8540, pp. 3-17, 2015.\r\n[2] Augot, D., Finiasz, M.: Exhaustive search for small dimension recursive\r\nMDS diffusion layers for block ciphers and hash functions. In Information\r\nTheory Proceedings (ISIT), 2013 IEEE International Symposium on,\r\npages 1551-1555. IEEE, 2013.\r\n[3] Barreto, P., Rijmen, V.: The Anubis Block Cipher. Submission to the\r\nNESSIE Project, 2000.\r\n[4] Berger, T. P.: Construction of Recursive MDS Diffusion Layers from\r\nGabidulin Codes. In INDOCRYPT, LNCS 8250, pages 274-285. 2013.\r\n[5] Blaum, M., Roth, R. M.: On Lowest Density MDS Codes. IEEE\r\nTransactions on Information Theory 45(1), 46-59 (1999).\r\n[6] Daemen, J., Knudsen, L. R., Rijmen, V.: The Block Cipher SQUARE.\r\nIn Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149-165. Springer,\r\nHeidelberg (1997).\r\n[7] Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced\r\nEncryption Standard. Springer, 2002.\r\n[8] Guo, J., Peyrin, T., Poschmann, A.: The PHOTON Family of Lightweight\r\nHash Functions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841,\r\npp. 222-239. Springer, Heidelberg (2011).\r\n[9] Guo, J., Peyrin, T., Poschmann, A., Robshaw, M.: The LED Block Cipher.\r\nIn: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp.\r\n326-341. Springer, Heidelberg (2011).\r\n[10] Gupta, K. C., Ray, I. G.: On Constructions of Involutory MDS Matrices.\r\nIn AFRICACRYPT, pages 43-60, 2013.\r\n[11] Gupta, K. C., Ray, I. G.: On constructions of MDS matrices from\r\ncompanion matrices for lightweight cryptography. In: Cuzzocrea, A.,\r\nKittl, C., Simos, D. E., Weippl, E., Xu, L. (eds.) CD-ARES Workshops\r\n2013. LNCS, vol. 8128, pp. 29-43. Springer, Heidelberg (2013).\r\n[12] Junod, P., Vaudenay, S.: Perfect Diffusion Primitives for Block Ciphers\r\nBuilding Effcient MDS Matrices. In: Handschuh, H., Hasan, M. A. (eds.)\r\nSAC 2004. LNCS, vol. 3357, pp. 84-99. Springer, Heidelberg (2004).\r\n[13] Khoo, K., Peyrin, T., Poschmann, A., Yap, H.: FOAM: Searching\r\nfor Hardware Optimal SPN Structures and Components with a Fair\r\nComparison. In Cryptographic Hardware and Embedded Systems CHES\r\n2014, volume 8731 of Lecture Notes in Computer Science, pages\r\n433-450. Springer Berlin Heidelberg, 2014.\r\n[14] Li, Y., Wang, M.: On the construction of lightweight circulant involutory\r\nMDS matrices. In: Thomas, P. (ed.): FSE 2016, LNCS 9783, pp. 121-139.\r\nSpringer, Heidelberg (2016).\r\n[15] MacWilliams, F. J., Sloane, N. J. A.: The Theory of Error-Correcting\r\nCodes. North-Holland Publishing Company, 2nd edition (1986).\r\n[16] Sajadieh, M., Dakhilalian, M., Mala, H., Sepehrdad, P.: Recursive\r\nDiffusion Layers for Block Ciphers and Hash Functions. In: Canteaut,\r\nA. (ed.) FSE 2012. LNCS, vol. 7549, pp. 385-401. Springer, Heidelberg\r\n(2012).\r\n[17] Shirai, T., Shibutani, K., Akishita, T., Moriai, S., Iwata, T.: The 128-Bit\r\nBlockcipher CLEFIA (Extended Abstract). In: Biryukov, A. (ed.) FSE\r\n2007. LNCS, vol. 4593, pp. 181195. Springer, Heidelberg (2007).\r\n[18] Sim, S.M., Khoo, K., Oggier, F., Peyrin, T.: Lightweight MDS Involution\r\nMatrices. In: Leander, G., Demirci, H. (eds.) FSE 2015. LNCS, Springer\r\n(2015).\r\n[19] Wu, S.,Wang, M.,Wu,W.: Recursive Diffusion Layers for (Lightweight)\r\nBlock Ciphers and Hash Functions. In: L.R. Knudsen and H. Wu (eds.):\r\nSAC 2012, LNCS 7707, pp. 355-371, 2013.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 126, 2017"}