42 lines
852 B
Python
42 lines
852 B
Python
#!/usr/bin/env python3
|
|
|
|
from Cryptotools.Groups.cyclic import Cyclic
|
|
from Cryptotools.Numbers.primeNumber import isPrimeNumber
|
|
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)
|
|
order = len(g) # Length of the group
|
|
print(f"len: {order}")
|
|
print(f"prime: {isPrimeNumber(order)}")
|
|
|
|
cyclic.generator()
|
|
|
|
print(f"All generators: {cyclic.getGenerators()}")
|
|
print(f"Is cyclic: {cyclic.isCyclic()}")
|
|
|
|
# Check if the abelian group is respected
|
|
print(f"It is an abelian group: {cyclic.closure()}\n")
|
|
|
|
|
|
e = choice(cyclic.getGenerators())
|
|
z = list()
|
|
for a in range(1, n):
|
|
res = operation(e, a, n)
|
|
z.append(res)
|
|
|
|
print(z)
|
|
if z == g:
|
|
print(f"The group generated with the generator {e} works")
|