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14. O nekaterih konstrukcijah kriptografsko pomembnih Boolovih funkcij : doktorska disertacijaSamed Bajrić, 2014, doktorska disertacija Ključne besede: Boolean functions, vectorial (generalized) bent functions, binomial trace functions, symetric polynomials, linenarized polynomials, planar mappings, disjoint spectra, plateaued functions, semi-bent functions, cross-correlation, sum-of-squares indicator
Objavljeno v RUP: 22.11.2017; Ogledov: 2713; Prenosov: 53
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16. Karakterizacija posplošnih zlomljenih funkcij in nekatere druge kriptografske teme : doktorska disertacijaSamir Hodžić, 2017, doktorska disertacija Ključne besede: generalized bent functions, Zq-bent functions, Gray maps, (relative) difference sets, (generalized) Marioana-McFarland class, stream ciphers, filtering generator, guess and determine cryptanalysis, tap positions, (fast) algebraic attacks, algebraic immunity, derivatives, linear structures, planar mappings
Objavljeno v RUP: 09.11.2017; Ogledov: 2526; Prenosov: 57
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17. Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, izvirni znanstveni članek Opis: A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.
Ključne besede: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Objavljeno v RUP: 03.04.2017; Ogledov: 2529; Prenosov: 87
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18. Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, Bojan Kuzma, Marko Orel, 2013, objavljeni znanstveni prispevek na konferenci Opis: Let ▫$\mathbb{F}$▫ be a finite field of characteristic different from 2. We study the cardinality of sets of matrices with a given determinant or a given permanent for the set of Hermitian matrices ▫$\mathcal{H}_n(\mathbb{F})$▫ and for the whole matrix space ▫$M_n(\mathbb{F})$▫. It is known that for ▫$n = 2$▫, there are bijective linear maps ▫$\Phi$▫ on ▫$\mathcal{H}_n(\mathbb{F})$▫ and ▫$M_n(\mathbb{F})$▫ satisfying the condition per ▫$A = \det \Phi(A)$▫. As an application of the obtained results, we show that if ▫$n \ge 3$▫, then the situation is completely different and already for ▫$n = 3$▫, there is no pair ofmaps ▫$(\Phi, \phi)$▫, where ▫$\Phi$▫ is an arbitrary bijective map on matrices and ▫$\phi \colon \mathbb{F} \to \mathbb{F}$▫ is an arbitrary map such that per ▫$A = \phi(\det \Phi(A))$▫ for all matrices ▫$A$▫ from the spaces ▫$\mathcal{H}_n(\mathbb{F})$▫ and ▫$M_n(\mathbb{F})$▫, respectively. Moreover, for the space ▫$M_n(\mathbb{F})$▫, we show that such a pair of transformations does not exist also for an arbitrary ▫$n > 3$▫ if the field ▫$\mathbb{F}$▫ contains sufficiently many elements (depending on ▫$n$▫). Our results are illustrated by a number of examples.
Ključne besede: mathematics, linear algebra, matrix theory, permanent, determinant
Objavljeno v RUP: 03.04.2017; Ogledov: 2119; Prenosov: 125
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20. Verjetnost za nematematike. Pregled teorije in izbrane rešene naloge : drugo učno gradivoMarko Orel, 2015, drugo učno gradivo Ključne besede: elementarna verjetnost, diskretne slučajne spremenljivke, zvezne slučajne spremenljivke, porazdelitvena funkcija, kvantili, večrazsežna porazdelitev, robna porazdelitev, pričakovana vrednost, varianca, centralni limitni izrek
Objavljeno v RUP: 15.10.2015; Ogledov: 2866; Prenosov: 135
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