On multiple output bent functions
In this article we investigate the possibilities of obtaining multiple output bent functions from certain power polynomials over finite fields. So far multiple output bent functions F : GF(2)(n) -> GF(2)(m) (where is is even and m   GF(2)(m), is a multiple output bent function. We consider all the main cases of monomial trace bent functions and specify the restrictions on lambda and m that yield multiple output bent functions F (x) = Tr-n(m) (lambda x(d)). Interestingly enough, in one particular case when n = 4r, d = (2(r) + 1)(2), a multiple bent function F (x) = Tr-2r(n)(ax(d)) could not be obtained by considering a collection of 2r Boolean bent functions of the form fi(x) = Tr-1(n)(lambda(i)x(d)) for some suitable coefficients lambda(i) epsilon GF(2(n)). (c) 2012 Elsevier B.V. All rights reserved.
multiple output bent functions cryptography boolean functions monomial trace functions