#!/usr/bin/env python3

from Cryptotools.Groups.cyclic import Cyclic
from random import choice


def operation(a, b, n):
    return (a ** b) % n

n = 19
g = list()
for i in range(1, n):
    g.append(i)
   
print(f"n = {n}")
print(f"G = {g}")

cyclic = Cyclic(g, n, operation)
    
cyclic.generator()
generators = cyclic.getGenerators()
print(f"All generators: {generators}")

e = choice(generators)
z = list()
for a in range(1, n):
    res = operation(e, a, n)
    z.append(res)

z = sorted(z)
if z == g:
    print(f"Working with the generator {e}")