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Computer Security and Cryptography by Alan G. Konheim

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8.3 THE ALGEBRA OF POLYNOMIALS OVER image

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

image

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 image The subset of image consisting of polynomials with deg(p) ≤ n will be denoted by Pn[z]. We next summarize several basic properties of image.

8.3.1 Properties of image

  1. f image 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 ...

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