2 research outputs found
Two infinite classes of rotation symmetric bent functions with simple representation
In the literature, few -variable rotation symmetric bent functions have
been constructed. In this paper, we present two infinite classes of rotation
symmetric bent functions on of the two forms:
{\rm (i)} ,
{\rm (ii)} ,
\noindent where , is any rotation
symmetric polynomial, and is odd. The class (i) of rotation
symmetric bent functions has algebraic degree ranging from 2 to and the
other class (ii) has algebraic degree ranging from 3 to
Affine equivalence for quadratic rotation symmetric Boolean functions
Let denote the algebraic normal form
(polynomial form) of a rotation symmetric (RS) Boolean function of degree
in variables and let denote the Hamming weight of this
function. Let denote the function of degree
in variables generated by the monomial
Such a function is called monomial rotation symmetric (MRS). It was
proved in a paper that for any MRS with the sequence of
weights satisfies a homogeneous linear
recursion with integer coefficients. This result was gradually generalized in
the following years, culminating around with the proof that such
recursions exist for any rotation symmetric function Recursions for
quadratic RS functions were not explicitly considered, since a paper had
already shown that the quadratic weights themselves could be given by an
explicit formula. However, this formula is not easy to compute for a typical
quadratic function. This paper shows that the weight recursions for the
quadratic RS functions have an interesting special form which can be exploited
to solve various problems about these functions, for example, deciding exactly
which quadratic RS functions are balanced.Comment: 27 pages + references; minor typo correction