The Reducibility of a Special Binary Pentanomial. (2nd September 2014) - Kim, Ryul; Kim, Yun Mi
Abstract : Swan's theorem determines the parity of the number of irreducible factors of a binary trinomial. In this work, we study the parity of the number of irreducible factors for a special binary pentanomial with even degree x m + x n 1 + x n 2 + x n 3 + 1, where 0 < n 3 < n 2 < n 1 ≤ m / 2, and exactly one of  n 1, n 2,   and  n 3 is odd. This kind of irreducible pentanomials can be used for a fast implementation of trace and square root computations in finite fields of characteristic 2.