Permutation polynomials EA-equivalent to the inverse function over GF(2(n))
In this paper, a proof is given that there does not exist a linearized polynomial L(x) is an element of F-2n[x] such that x(-1) + L(x) is a permutation on F-2n when n >= 5, which is proposed as a conjecture in Li and Wang (Des Codes Cryptogr 58(3):259-269, 2011). As a consequence of this result, if a permutation is EA-equivalent to the inverse function over F-2n, then it is affine equivalent to the inverse mapping when n >= 5.
permutation polynomial ea-equivalence inverse function s-box kloosterman sums