#!/usr/bin/env python3

from Cryptotools.Groups.cyclic import Cyclic
from math import log, ceil

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

n = 7919
group = list()
for x in range(1, n):
    group.append(x)

cyclic = Cyclic(group, n, ope)
g = cyclic.getPrimitiveRoot()

print(f"g: {g}")

secretKey = 4057

publicKey = ope(g, secretKey, n)
print(f"Public key: {publicKey}")

# Now, we need to find the secret key based on the DLP
for x in range(1, n):
    l = log(x, g)
    h = ceil(g ** l)
    if ope(g, h, n) == publicKey:
        print(f"Secret key found: {h}")
        break