International Association for Cryptologic Research (IACR)
Abstract
We present a construction of bent function fa,S with n=2m variables for any nonzero vector a∈F2m and subset S of F2m satisfying a+S=S. We give the simple expression of the dual bent function of fa,S. We prove that
fa,S has optimal algebraic degree m if and only if ∣S∣≡2(mod4). This construction provides series of bent functions with optimal algebraic degree and large symmetric group if a and S are chosen properly