Adding Features of getting a primitive element in GF(q).

Motivation

This library was created to apply Finite Field to cryptography and coding theory, Especially in cryptography, there are many situations where we want to get a primitive element in GF(q). So we implemented a function to get a primitive element for all GF(q).

Usage

It can be retrieved by executing random_primitive_elm() function of the GFp or GFpn class.

gf_11 = GFp(11)
# Getting a random primitive element in GF(11)
gf_11.random_primitive_elm() # 8 (mod 11)

gf_5_4 = GFpn(5, [1, 0, 0, 0, 2])
# Getting a random primitive element in GF(5^4)
gf_5_4.random_primitive_elm() # 1x^3 + 2x^2 + 4x + 3

Be careful when using a finite field with large orders because the computational complexity is very large.