Geodesic
Complete description of a class of MDS-matrices over finite field of characteristic~2
Matematičeskie voprosy kriptografii, Tome 8 (2017), pp. 5-28.

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

We give complete description of the set of $n\times n$ MDS-matrices, $n>3$, over $GF(2^t)$, $t > 1$, with elements from the set $\{e,\alpha,\alpha^2\}$, where $e$ is an identity element, $\alpha\ne0$, $e$. It is proved that there are no such matrices if $n\geqslant6$. For $n = 4, 5$ the necessary and sufficient conditions of existence of MDS-matrices consisting of elements $e,\alpha,\alpha^2$ are given. 
@article{MVK_2017_8_a0,
     author = {A. V. Anashkin},
     title = {Complete description of a class of {MDS-matrices} over finite field of characteristic~2},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {5--28},
     publisher = {mathdoc},
     volume = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2017_8_a0/}
}
TY  - JOUR
AU  - A. V. Anashkin
TI  - Complete description of a class of MDS-matrices over finite field of characteristic~2
JO  - Matematičeskie voprosy kriptografii
PY  - 2017
SP  - 5
EP  - 28
VL  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2017_8_a0/
LA  - ru
ID  - MVK_2017_8_a0
ER  - 
%0 Journal Article
%A A. V. Anashkin
%T Complete description of a class of MDS-matrices over finite field of characteristic~2
%J Matematičeskie voprosy kriptografii
%D 2017
%P 5-28
%V 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2017_8_a0/
%G ru
%F MVK_2017_8_a0
A. V. Anashkin. Complete description of a class of MDS-matrices over finite field of characteristic~2. Matematičeskie voprosy kriptografii, Tome 8 (2017), pp. 5-28. http://geodesic.mathdoc.fr/item/MVK_2017_8_a0/

[1] Dehnavi S. M., Mahmoodi R. A., Shamsabad M. R., Characterization of MDS mappings, 2015/002, http://eprint.iacr.org

[2] Mak-Vilyams F. Dzh., Sloen N. Dzh. A., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979, 744 pp.

[3] Malyshev F. M., “Dvoistvennost raznostnogo i lineinogo metodov v kriptografii”, Matematicheskie voprosy kriptografii, 5:3 (2014), 35–47

[4] Malyshev F. M., Trifonov D. I., “Rasseivayuschie svoistva XSLP-shifrov”, Matematicheskie voprosy kriptografii, 7:3 (2016), 47–60

[5] Daemen J., Rijmen V., The Rijndael block cipher (AES proposal), , 1999 https://csrc.nist.gov/csrc/media/projects/cryptographic-standards-and-guidelines/documents/aes-development/rijndael-ammended.pdf

[6] Schnorr S., Vaudenay S., “Black box cryptoanalysis of hash networks based on multipermutations”, Lect. Notes Comput. Sci., 950, 1994, 47–57 | DOI | MR

[7] Vaudenay S., “On the need for multipermutations: cryptanalysis of MD4 and SAFER”, Lect. Notes Comput. Sci., 1008, 1994, 286–297 | DOI

[8] Biham E., Shamir A., “Differential cryptanalysis of DES-like cryptosystem”, Lect. Notes Comput. Sci., 537, 1991, 2–21 | DOI | MR | Zbl

[9] Matsui M., “Linear cryptanalysis method for DES”, Lect. Notes Comput. Sci., 765, 1993, 386–397 | DOI

[10] Daemen J., Cipher and hash function design strategies based on linear and differential cryptanalysis, Ph.D. thesis, Elektrotechniek Katholieke Univ., Leuven, Belgium, 1995

[11] Sajadieh M., Dakhilalian M., Mala H., Sepehrdad P., “Recursive diffusion layers for block ciphers and hash functions”, Lect. Notes Comput. Sci., 7549, 2012, 385–401 | DOI | Zbl

[12] Guo J., Peyrin T., Poschmann A., “The PHOTON family of lightweight hash functions”, Lect. Notes Comput. Sci., 6841, 2011, 222–239 | DOI | Zbl

[13] Guo J., Peyrin T., Poschmann A., Robshaw M., “The LED block cipher”, Lect. Notes Comput. Sci., 6917, 2011, 326–341 | DOI | Zbl

[14] Zeng G., He K., Han W., “A trinomial type of $\sigma$-LFSR oriented toward software implementation”, Science in China, Ser. F: Inf. Sci., 50 (2007), 359–372 | MR | Zbl

[15] Gupta K. C., Ray I. G., “On constructions of involutory MDS matrices”, Lect. Notes Comput. Sci., 7918, 2013, 43–60 | DOI | MR | Zbl

[16] Gupta K. C., Ray I. G., “On constructions of MDS matrices from companion matrices for lightweight cryptography”, Lect. Notes Comput. Sci., 8128, 2013, 29–43 | DOI | MR