A

primitive polynomial is a polynomial that generates all elements of an extension field.

Here, the adversary should be able to firstly specify the degree of the calculated generator polynomial between an equipment and a base station, and then find the

primitive polynomial per session.

(i) Choose the

primitive polynomial G(Y) of degree 4 as

The algorithm used for both [S.sub.1] and [S.sub.2] is the same but the

primitive polynomial selected to generate the Galois field is different, which really contributes to the outputs.

For each

primitive polynomial, take p positive odd as initial value [m.sub.1], [m.sub.2], ..., [m.sub.p], where [m.sub.i] < [2.sup.i], the top p values of [v.sub.j] can also obtain by type (2) at the same time.

The positive integer m is the degree of a

primitive polynomial (we discuss this below) used to generate the elements of the finite field.

Using this analogy we identify the

primitive polynomial in the SRG as the object to parameterize.

The author chose p(x) to be a

primitive polynomial of degree 19 drawn from Peterson [1961]:

this test requires only the calculation of a binary matrix whose size is about p x p, where p is the degree of the

primitive polynomial.

Mathematically, an m-sequence derived from a

primitive polynomial is usually implemented by a number of shift-registers with different orders [18], say r.

The multipliers of the feedbacks are given by coefficients [q.sub.1],[q.sub.2],...,[q.sub.L],[q.sub.L][member of][0,1,...,p-1] of the

primitive polynomial in GF([p.sup.L]).