For purposes of implementing field arithmetic in F2n efficiently, it is desirable to have an irreducible polynomial f(x) ∈ F2[x] of degree n with as few terms as possible. The number of terms must be odd, as otherwise x+1 would be a factor. Often a trinomial x+x+1 can be found, or at least a pentanomial, x+x1 +x2 +x3 +1, where n > m1 > m2 > m3 > 0. If α is a root of f , then {1, α, α, . . . , α...