TABLE OF CONTENTS In Table 3.5, we list specific primitive polynomials over GF(2) of every degree up to 32. (These were taken from Menezes, van Corschot, and Vanstone (1996).) In the second column of Table 3.5, we represent a primitive polynomial f( x) = x n + c n ?1 x n ? 1 + + c 1 x + c 0 as a vector ( c 0, c 1, , c n ?1). For example, for n = 4, the primitive polynomial is f( x) = x 4 + x + 1. Table 3.6 contains primitive polynomials over GF( p) of degree n where p is a prime with 2 < p ? 127 and p n < 2 32. (These were computed by Amr Youssef.) The primitive polynomials over GF(2 m) of degree n where m ? {2, 3,..., 8 } and n = ml ? 32 are listed in Table 3.7. (These were computed using Theorem 3.14.) The data listed in Table 3.7 were taken from the course projects of the graduate course Sequence Design and Cryptography, Spring 2002, University of Waterloo. The notation used in Table 3.7 is as follows:
f( x) is a primitive polynomial over GF(2) of degree n, taken from Table 3.5, and ? is a root of f( x
