708 research outputs found
On a secondary construction of quadratic APN functions
Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known constructions of APN functions are obtained as functions over finite fields F27 and very little is known about combinatorial constructions in F2n. We consider how to obtain a quadratic APN function in n + 1 variables from a given quadratic APN function in n variables using special restrictions on new terms
Metrical properties of the set of bent functions in view of duality
In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered
Some results on -ary bent functions
Kumar et al.(1985) have extended the
notion of classical bent Boolean functions in the generalized setup
on \BBZ_q^n. They have provided an analogue of classical
Maiorana-McFarland type bent functions. In this paper, we study the
crosscorrelation of a subclass of such generalized
Maiorana-McFarland (\mbox{GMMF}) type bent functions. We provide a
construction of quaternary () bent functions on
variables in terms of their subfunctions on -variables. Analogues
of sum-of-squares indicator and absolute indicator of
crosscorrelation of Boolean functions are defined in the generalized
setup. Further, -ary functions are studied in terms of these
indictors and some upper bounds of these indicators are obtained.
Finally, we provide some constructions of balanced quaternary
functions with high nonlinearity under Lee metric
Generalizations of Bent Functions. A Survey
Bent functions (Boolean functions with extreme nonlinearity properties) are actively studied for their numerous applications in cryptography, coding theory, and other fields. New statements of problems lead to a large number of generalizations of the bent functions many of which remain little known to the experts in Boolean functions. In this article, we offer a systematic survey of them
Secondary constructions on generalized bent functions
In this paper, we construct generalized bent Boolean functions in variables from generalized Boolean functions in variables. We also show that the direct sum of two generalized bent Boolean functions is generalized bent. Finally, we identify a set of affine functions in which every function is generalized bent
Связь между кватернарными и компонентными булевыми бент-функциями
Исследуются кватернарные бент-функции. Функция g : Zn Z4 называется кватернарной функцией от n переменных. Доказано, что свойство кватернарной функции g(x + 2y) = a(x,y) + 2b(x, y) быть бент напрямую не зависит от того, являются ли функции b и a ® b булевыми бент-функциями. Получено количество кватернарных бент-функций от одной и двух переменных с описанием свойств булевых функций b и a ® b. Представлены простые конструкции кватернарных бент-функций от любого числа переменных
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