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2016 | OriginalPaper | Buchkapitel

On the Construction of Lightweight Circulant Involutory MDS Matrices

verfasst von : Yongqiang Li, Mingsheng Wang

Erschienen in: Fast Software Encryption

Verlag: Springer Berlin Heidelberg

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Abstract

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.

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Vorheriges Kapitel Lightweight MDS Generalized Circulant Matrices

Nächstes Kapitel Optimizing S-Box Implementations for Several Criteria Using SAT Solvers

More examples of circulant involutory MDS matrices with \(\#A+\#B+\#C=m+1\) are given in the appendix of the extended version of the paper [14].

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)

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)

Barreto, P., Rijmen, V.: The anubis block cipher. Submission to the NESSIE Project (2000)

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

Blaum, M., Roth, R.M.: On lowest density MDS codes. IEEE Trans. Inf. Theory 45(1), 46–59 (1999)MathSciNetCrossRefMATH

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

Cui, T., Jin, C.I., Kong, Z.: On compact Cauchy matrices for substitution permutation networks. IEEE Trans. Comput. 99, 1 (2014). PreprintMathSciNet

Daemen, J., Rijmen, V.: The Design of Rijndael: AES - The Advanced Encryption Standard. Springer, Heidelberg (2002)CrossRefMATH

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)MathSciNetCrossRefMATH

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

Titel: On the Construction of Lightweight Circulant Involutory MDS Matrices
verfasst von: Yongqiang Li
Mingsheng Wang
Verlag: Springer Berlin Heidelberg
Buch: Fast Software Encryption
Print ISBN: 978-3-662-52992-8

Electronic ISBN: 978-3-662-52993-5

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-662-52993-5_7

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