Computer Security and Cryptography

8.3 THE ALGEBRA OF POLYNOMIALS OVER

will denote the set of polynomials in the variable z whose coefficients {p_i} are in :

Arithmetic operations on polynomials are the usual, except that the addition and multiplication of coefficients is performed modulo 2. We write deg(p) for the degree of p ∈ The subset of consisting of polynomials with deg(p) ≤ n will be denoted by P_n[z]. We next summarize several basic properties of .

8.3.1 Properties of

1. f ∈ has a factorization, if f(z) = g(z)h(z) with g, h ∈ . If f(z) = g(z)h(z), then g(z) and h(z) are factors of f(z)

   (a)    f(z) = g(z)h(z) is a non-trivial ...