import sympy
from random import randint
import hashlib

def genSchnorr(bits = 1024, subbits=256):
    q = sympy.randprime(2**subbits, 2**(subbits+1))
    while True:
        t = randint(2**(bits-subbits), 2**(bits-subbits+1)-1)
        p = t*q + 1
        if sympy.isprime(p): break
    while True:
        h = randint(2**subbits, 2**(subbits+1)-1)
        g = pow(h, t, p)
        if g != 1:
            break
    x = randint(2, 2**subbits-1)
    y = pow(g, x, p)
    return (p, q, g, x, y)

def sha256int(m):
    H = hashlib.sha256(m.encode()).hexdigest()
    return int(H, 16)

def sign(p, q, g, x, m):
    k = randint(1, q-1)
    r = sha256int(m + str(pow(g, k, p)))
    s = (k + x*r) % q
    return r, s

def verify(p, q, g, y, m, r, s):
    w = pow(g, s, p) * pow(y, -r, p) % p
    return sha256int(m + str(w)) == r

def shadysign(p, q, g, x, m):
    k = (sha256int(str(x)) + randint(1, 2**18)) % q
    r = sha256int(m + str(pow(g, k, p)))
    s = (k + x*r) % q
    return r, s
    
def genHW():
    p, q, g, x, y = genSchnorr()
    shadysigs = []
    for m in range(2**10):
        r, s = shadysign(p, q, g, x, str(m))
        shadysigs.append((r,s))
    return

###############################################################################
p, q, g, x, y = genSchnorr()

m = 'Experimental text to sign!'
r, s = sign(p, q, g, x, m)
print(r,s)
print(verify(p, q, g, y, m, r, s))

m = 'Experimental text to sign!'
r, s = shadysign(p, q, g, x, m)
print(r,s)
print(verify(p, q, g, y, m, r, s))