Geodesic
Construction methods for MDS matrices using companion and permutation matrices for lightweight cryptography
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 211-216.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, we propose a new construction method of MDS-matrices of dimension $k = 4, 6$ by means of summation of a power $r$ of the companion matrix of a certain polynomial and a fixed permutation matrix over the finite field $\mathrm{GF}(2^8) $. The method is represented by the expression $S_f^r + P$ for a polynomial $f(x)=x^k+f_{k-1}x^{k-1}+\ldots+f_1x+f_0$, where $S_f$ is the companion matrix of the polynomial $f(x)$, $P$ is a permutation matrix, $r={3k}/{2}$, and the coefficients $f_i\in\{0,1,\alpha,\alpha^{-1},\alpha^2,\alpha^3\}$. For its effective implementation, it is proposed to apply $S_f$ as a linear feedback shift register with characteristic polynomial $f(x)$ and $P$ as a Feistel network with $k$ entrances. The XOR-count metric is used to show the effectiveness of the proposed method in algorithms that require low implementation cost.
Mots-clés : MDS-matrices, permutation matrices, LFSR
Keywords: companion matrices, finite field, lightweight cryptography, XOR-count. 
@article{PDMA_2019_12_a58,
     author = {O. Coy Puente},
     title = {Construction methods for {MDS} matrices using companion and permutation matrices for lightweight cryptography},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {211--216},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a58/}
}
TY  - JOUR
AU  - O. Coy Puente
TI  - Construction methods for MDS matrices using companion and permutation matrices for lightweight cryptography
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2019
SP  - 211
EP  - 216
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2019_12_a58/
LA  - ru
ID  - PDMA_2019_12_a58
ER  - 
%0 Journal Article
%A O. Coy Puente
%T Construction methods for MDS matrices using companion and permutation matrices for lightweight cryptography
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2019
%P 211-216
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2019_12_a58/
%G ru
%F PDMA_2019_12_a58
O. Coy Puente. Construction methods for MDS matrices using companion and permutation matrices for lightweight cryptography. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 211-216. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a58/

[1] Augot D., Finiasz M., “Direct construction of recursive MDS diffusion layers using shortened BCH codes”, LNCS, 8540, 2014, 3–17

[2] Guo J., Peyrin T., Poschmann A., “The PHOTON family of lightweight hash functions”, LNCS, 6841, 2011, 222–239 | Zbl

[3] Sarkar S., Sim S. M., “A deeper understanding of the XOR count distribution in the context of lightweight cryptography”, LNCS, 9646, 2016, 167–182 | MR | Zbl

[4] Toh D., Teo J., Khoo K., Sim S. M., “Lightweight MDS serial-type matrices with minimal fixed XOR count”, LNCS, 10831, 2018, 51–71 | MR | Zbl

[5] Gupta K. C., Ray I. G., “On constructions of MDS matrices from companion matrices for lightweight cryptography”, LNCS, 8128, 2013, 29–43 | MR