Geodesic
Characterization of linear transformations defined by Finite Field Hadamard Matrices and circulant matrices
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 10-11.

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We consider general and cryptographic properties of circulant matrices and Finite Field Hadamard Matrices. We describe invariant subspaces of linear transformations defined by Finite Field Hadamard Matrices and construct a class of invariant subspaces for circulant matrices.
Keywords: invariant subspaces, Finite Field Hadamard Matrices
Mots-clés : circulant matrices. 
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A. V. Volgin; G. V. Kryuchkov. Characterization of linear transformations defined by Finite Field Hadamard Matrices and circulant matrices. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 10-11. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a1/

[1] Barreto P. S. L. M., Rijmen V., The KHAZAD Legacy-Level Block Cipher, Submission to the NESSIE Project, , 2000 https://www.researchgate.net/publication/228924670_The_Khazad_legacy-level_block_cipher

[2] Biryukov A., “Analysis of involutional ciphers: Khazad and Anubis”, Intern. Workshop Fast Software Encryption, Springer, Berlin–Heidelberg, 2003, 45–53 | Zbl

[3] Daemon J., Rijmen V., “The Rijndael block cipher: AES proposal”, First AES Candidate Conf., AES1 (Ventura, California, August 20–22, 1998), 343–348

[4] Barreto P. S. L. M., Rijmen V., “The Whirlpool hashing function”, First open NESSIE Workshop, 13, Leuven, Belgium, 2000, 14

[5] Pogorelov B. A., Pudovkina M. A., “Kombinatornaya kharakterizatsiya XL-sloev”, Matematicheskie voprosy kriptografii, 4:3 (2013), 99–129

[6] Burov D. A., Pogorelov B. A., “An attack on 6 rounds of Khazad”, Matematicheskie voprosy kriptografii, 7:2 (2016), 35–46 | MR

[7] Leander G. et al., “A cryptanalysis of PRINTcipher: the invariant subspace attack”, Ann. Cryptology Conf., Springer, Berlin–Heidelberg, 2011, 206–221 | MR | Zbl

[8] Gupta K. C., Ray I. G., “On constructions of involutory MDS matrices”, Intern. Conf. Cryptology in Africa, Springer, Berlin–Heidelberg, 2013, 43–60 | MR | Zbl

[9] Sakall M. T., Akleylek S., Aslan B., et al., “On the construction of $20\times20$ and $24\times24$ binary matrices with good implementation properties for lightweight block ciphers and hash functions”, Mathematical Problems in Engineering, 2014 (2014), Article ID 540253, 12 pp. | MR | Zbl

[10] Gray M., “Toeplitz and circulant matrices: a review”, Foundations and Trends in Communications and Information Theory, 2:3 (2006), 155–239 | DOI