5 research outputs found
Balanced Symmetric Functions over
Under mild conditions on , we give a lower bound on the number of
-variable balanced symmetric polynomials over finite fields , where
is a prime number. The existence of nonlinear balanced symmetric
polynomials is an immediate corollary of this bound. Furthermore, we conjecture
that are the only nonlinear balanced elementary symmetric
polynomials over GF(2), where , and we prove various results in support of this conjecture.Comment: 21 page
Enumeration of Balanced Symmetric Functions over GF(p)
It is proved that the construction and enumeration of the number of balanced symmetric functions over GF(p) are equivalent to solving an equation system and enumerating the solutions. Furthermore, we give an lower bound on number of balanced symmetric functions over GF(p), and the lower bound provides best known results
Improved lower bound on the number of balanced symmetric functions over GF(p)
The lower bound on the number of n-variable balanced symmetric
functions over finite fields GF(p) presented in
{\cite{Cusick}} is improved in this paper
Strict Avalanche Criterion Over Finite Fields
Boolean functions on which satisfy the Strict Avalanche
Criterion () play an important
role in the art of information security. In this paper, we extend the conception
to finite fields . A necessary and sufficient condition is given by
using spectral analysis. Also, based on an interesting permutation
polynomial theorem, we prove various facts about ()-th order functions on
. We also construct many such functions