Abstract:

Let n be a positive integer, q a power of the prime p, K=F_q the finite field with q elements and F=F_qⁿ the n-th extension of K,β a primitive element of K. It is proved that the primitive elements of F in N^-1_F/K(β) is uniformly distributied. Where N^-1_F/K(β) is the inverse function of the norm function N_F/K(α) of α over K.This result isuseful in the elliptic curves public-key cryptic system.

Key words: elliptic curves public-key cryptic system, primitive elements, norm function