## 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

*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 ...*

Get *Computer Security and Cryptography* now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.