Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FPM_2020_23_2_a3,
author = {A. V. Galatenko and V. A. Nosov and A. E. Pankratiev},
title = {Generation of multivariate quadratic quasigroups by proper families of {Boolean} functions},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {57--73},
publisher = {mathdoc},
volume = {23},
number = {2},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a3/}
}
TY - JOUR AU - A. V. Galatenko AU - V. A. Nosov AU - A. E. Pankratiev TI - Generation of multivariate quadratic quasigroups by proper families of Boolean functions JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2020 SP - 57 EP - 73 VL - 23 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a3/ LA - ru ID - FPM_2020_23_2_a3 ER -
%0 Journal Article %A A. V. Galatenko %A V. A. Nosov %A A. E. Pankratiev %T Generation of multivariate quadratic quasigroups by proper families of Boolean functions %J Fundamentalʹnaâ i prikladnaâ matematika %D 2020 %P 57-73 %V 23 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a3/ %G ru %F FPM_2020_23_2_a3
A. V. Galatenko; V. A. Nosov; A. E. Pankratiev. Generation of multivariate quadratic quasigroups by proper families of Boolean functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 2, pp. 57-73. http://geodesic.mathdoc.fr/item/FPM_2020_23_2_a3/
[1] Nosov V. A., “Kriterii regulyarnosti bulevskogo neavtonomnogo avtomata s razdelennym vkhodom”, Intellekt. sist., 3:3–4 (1998), 269–280
[2] Nosov V. A., “Postroenie klassov latinskikh kvadratov v bulevoi baze dannykh”, Intellekt. sist., 4:3–4 (1999), 307–320
[3] Nosov V. A., “Postroenie parametricheskogo semeistva latinskikh kvadratov v vektornoi baze dannykh”, Intellekt. sist., 8:1–4 (2004), 517–529
[4] Ahlawat R., Gupta K., Pal S. K., “Fast generation of multivariate quadratic quasigroups for cryptographic applications”, Proceeding of Mathematics in Defence, 2009
[5] Alagic G., Alperin-Sheriff J., Apron D., Cooper D., Dang Q., Liu Y.-K., Miller C., Moody D., Peralta R., Perlner R., Robinson A., Smith-Tone D., Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process, National Inst. of Standards and Technology, Dep. of Commerce, 2019
[6] Chen Y., Gligoroski D., Knapskog S., “On a special class of multivariate quadratic quasigroups (MQQs)”, J. Math. Cryptology, 7:8 (2013), 111–141 | MR | Zbl
[7] Chen Y., Knapskog S. J., Gligoroski D., “Multivariate quadratic quasigroups (MQQs): Construction, bounds and complexity”, Inscrypt, ser. 6th Int. Conf. on Information Security and Cryptology, Sci. Press of China, 2010, 20–34
[8] Ding J., Petzoldt A., “Current state of multivariate cryptography”, IEEE Security Privacy, 15:4 (2017), 28–36 | DOI
[9] Faugère J.-C., Ødeg{å}rd R., Perret L., Gligoroski D., “Analysis of the MQQ public key cryptosystem”, Int. Conf. on Cryptology and Network Security CANS 2010: Cryptology and Network Security, Lect. Notes Comput. Sci., 6467, Springer, Berlin, 2010, 169–183 | DOI | Zbl
[10] Garey M. R., Johnson D. S., Computers and Intractability. A Guide to the Theory of NP-Completeness, Freeman, New York, 1979 | MR | Zbl
[11] Gligoroski D., Markovski S., Knapskog J., “Multivariate quadratic trapdoor functions based on multivariate quadratic quasigroups”, Proc. of the American Conference on Applied Mathematics, MATH'08, WSEAS Press, 2008, 44–49
[12] Gligoroski D., Markovski S., Knapskog J., Public key block cipher based on multivariate quadratic quasigroups, Cryptology ePrint Archive, Report 2008/320, , 2008 http://eprint.iacr.org/2008/320 | Zbl
[13] Gligoroski D., Ødeg{å}rd R., Jensen R., Perret L., Faugère J.-C., Knapskog S., Markovski S., “MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme”, INTRUST'11: Proc. of the Third Int. Conf. on Trusted Systems, 2011, 184–203
[14] Klimov A., Shamir A., “A new class of invertible mappings”, Int. Workshop on Cryptographic Hardware and Embedded Systems CHES 2002, Lect. Notes Comput. Sci., 2523, Springer, Berlin, 2002, 470–483 | DOI | Zbl
[15] Lau D., Function Algebras on Finite Sets: A Basic Course on Many-Valued Logic and Clone Theory, Springer, Berlin, 2006 | MR | Zbl
[16] Mohamed M., Ding J., Buchmann J., Werner F., “Algebraic attack on the (MQQ) public key cryptosystem”, Proc. of the 8th Int. Conf. on Cryptology and Network Security, CANS '09, Springer, Berlin, 2009, 392–401 | DOI | Zbl
[17] Nosov V. A., “Constructing families of Latin squares over Boolean domains”, Boolean Functions in Cryptology and Information Security, IOS Press, 2008, 200–207 | MR | Zbl
[18] Nosov V. A., Pankratiev A. E., “Latin squares over Abelian groups”, J. Math. Sci., 149:3 (2008), 1230–1234 | DOI | MR | Zbl
[19] Samardjiska S., Chen Y., Gligoroski D., “Construction of multivariate quadratic quasigroups (MQQs) in arbitrary Galois fields”, 2011 7th Int. Conf. on Information Assurance and Security (IAS), 2011, 314–319
[20] Samardjiska S., Markovski S., Gligoroski D., “Multivariate quasigroups defined by t-functions”, Proc. of SCC 2010, The 2nd Int. Conf. on Symbolic Computation and Cryptography, 2010, 117–127
[21] Wolf C., Preneel B., Taxonomy of public key schemes based on the problem of multivariate quadratic equations, Cryptology ePrint Archive, Report 2005/077, , 2005 https://eprint.iacr.org/2005/077
[22] Zhang Y., Zhang H., “An algorithm for judging and generating bilinear multivariate quadratic quasigroups”, Appl. Math. Inform. Sci., 7:9 (2013), 2071–2076 | DOI | MR
[23] Zhang Y., Zhang H., “An algorithm for judging and generating multivariate quadratic quasigroups over Galois fields”, Springerplus, 5:1 (2016), 1845 | DOI