# -*- coding: utf-8 -*-
"""
Created on Sun Mar 19 17:32:56 2023

@author: simon
"""

from Crypto.PublicKey import DSA
import random

DSAkey=DSA.generate(int(1024))
p = DSAkey.p
q = DSAkey.q

print("p = {}".format(hex(p)))
print("q = {}".format(hex(q)))
#p = 59
#q = 29
foundAlpha = True
while not foundAlpha:
    #for alpha in range(2,p-1):
    alpha = random.randint(2,p-1)
    #alpha = DSAkey.y
    if pow(alpha,q,p) == 1:
        # check if smaller integer k exists
        for k in range(1,q):
            if pow(alpha,k,p) == 1:
                if k == q:
                    foundAlpha = True
                    break
                else:
                    break
    if foundAlpha == True:
        break
alpha = DSAkey.y
if foundAlpha:
    print("found alpha={}, where ord(alpha)=q".format(alpha))
else:
    print("unable to find alpha")
    exit(1)
    
d = random.randint(1, q-1)
#d = 7
print("d={}".format(d))
for beta in range(1,p):
    if (beta % p) == pow(alpha,d,p):
        break
print("beta={}".format(beta))

ke = random.randint(1, q-1)
ke = 10

for r in range(1,p-1):
    if pow(pow(alpha,ke,p),1,q) == pow(r,1,q):
        break
print("r={}".format(r))