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On the maximum number of bent components of vectorial functionsPott, Alexander ...In this paper, we show that the maximum number of bent component functions of a vectorial function ▫$F:GF(2)^{n}\to GF(2)^{n}$▫ is ▫$2^{n}-2^{n/2}$▫. We also show that it is very easy to construct ... such functions. However, it is a much more challenging task to find such functions in polynomial form ▫$F\in GF(2^{n})[x]$▫, where ▫$F$▫ has only a few terms. The only known power functions having such a large number of bent components are ▫$x^d$▫, where ▫$d=2^{n/2}+1$▫. In this paper, we show that the binomials ▫$F^{i}(x) = x^{2^{i}}(x+x^{2^{n/2}})$▫ also have such a large number of bent components, and these binomials are inequivalent to the monomials ▫$x^{2^{n/2}+1}$▫ if ▫$0<i<n/2$▫. In addition, the functions ▫$F^i$▫ have differential properties much better than ▫$x^{2^{n/2}+1}$▫. We also determine the complete Walsh spectrum of our functions when ▫$n/2$▫ is odd and ▫$\mathrm{gcd} (i, n/2)=1$▫.Vir: IEEE transactions on information theory. - ISSN 0018-9448 (Vol. 64, no. 1, Jan. 2018, str. 403-411)Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasleLeto - 2018Jezik - angleškiCOBISS.SI-ID - 31065383
Avtor
Pott, Alexander |
Pašalić, Enes |
Muratović-Ribić, Amela |
Bajrić, Samed
Teme
kriptografija |
Boolove funkcije |
ukrivljene funkcije |
vektorske ukrivljene funkcije |
sledi |
ekvivalenca funkcij |
cryptography |
Boolean functions |
bent functions |
vectorial bent functions |
trace functions |
equivalence of functions
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vir: IEEE transactions on information theory. - ISSN 0018-9448 (Vol. 64, no. 1, Jan. 2018, str. 403-411)
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Pott, Alexander | ![]() |
Pašalić, Enes | 27777 |
Muratović-Ribić, Amela | ![]() |
Bajrić, Samed | 33363 |
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