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- W2470991461 abstract "Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over finite fields. First, by using the compositional inverses of certain binomial and trinomial permutations, we present several classes of negabent functions of the form $f(x)=Tr_1^n(lambda x^{2^k+1})+Tr_1^n(ux)Tr_1^n(vx)$, where $lambdain F_{2^n}$, $2leq kleq n-1$, $(u,v)in F^*_{2^n}times F^*_{2^n}$, and $Tr_1^n(cdot)$ is the trace function from $F_{2^n}$ to $F_{2}$. Second, by using Kloosterman sum, we prove that the condition for the cubic monomials given by Zhou and Qu (Cryptogr. Commun., to appear, DOI 10.1007/s12095-015-0167-0.) to be negabent is also necessary. In addition, a conjecture on negabent monomials whose exponents are of Niho type is given." @default.
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- W2470991461 date "2016-06-29" @default.
- W2470991461 modified "2023-09-23" @default.
- W2470991461 title "Several Classes of Negabent Functions over Finite Fields" @default.
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- W2470991461 doi "https://doi.org/10.48550/arxiv.1606.08952" @default.
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