1,034 research outputs found
A complete characterization of plateaued Boolean functions in terms of their Cayley graphs
In this paper we find a complete characterization of plateaued Boolean
functions in terms of the associated Cayley graphs. Precisely, we show that a
Boolean function is -plateaued (of weight ) if and only
if the associated Cayley graph is a complete bipartite graph between the
support of and its complement (hence the graph is strongly regular of
parameters ). Moreover, a Boolean function is
-plateaued (of weight ) if and only if the associated
Cayley graph is strongly -walk-regular (and also strongly
-walk-regular, for all odd ) with some explicitly given
parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201
Landscape Boolean Functions
In this paper we define a class of Boolean and generalized Boolean functions
defined on with values in (mostly, we consider
), which we call landscape functions (whose class containing generalized
bent, semibent, and plateaued) and find their complete characterization in
terms of their components. In particular, we show that the previously published
characterizations of generalized bent and plateaued Boolean functions are in
fact particular cases of this more general setting. Furthermore, we provide an
inductive construction of landscape functions, having any number of nonzero
Walsh-Hadamard coefficients. We also completely characterize generalized
plateaued functions in terms of the second derivatives and fourth moments.Comment: 19 page
Effective Construction of a Class of Bent Quadratic Boolean Functions
In this paper, we consider the characterization of the bentness of quadratic
Boolean functions of the form where ,
is even and . For a general , it is difficult to determine
the bentness of these functions. We present the bentness of quadratic Boolean
function for two cases: and , where and are two
distinct primes. Further, we give the enumeration of quadratic bent functions
for the case
Octal Bent Generalized Boolean Functions
In this paper we characterize (octal) bent generalized Boolean functions
defined on \BBZ_2^n with values in \BBZ_8. Moreover, we propose several
constructions of such generalized bent functions for both even and odd
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