Create valid signatures using genesis block.

Genesis_Signer.py

import math
import ecdsa
import ecdsa.ellipticcurve as EC

#
# Compute the inverse mod p using the extend 
# euclidian algorithm. 
# See O. Forster, Algorithmische Zahlentheorie
#
def inv_mod_p(x, p):
    if 1 != math.gcd(x, p):
        raise ValueError("Arguments not prime")
    q11 = 1
    q22 = 1
    q12 = 0
    q21 = 0
    while p != 0:
        temp = p
        q = x // p
        p = x % p
        x = temp
        t21 = q21
        t22 = q22
        q21 = q11 - q*q21
        q22 = q12 - q*q22
        q11 = t21
        q12 = t22
    return q11

# secp256k1 Curve
curve = ecdsa.SECP256k1
G = curve.generator
n = G.order()

# Genesis Block Key
x = int('678afdb0fe5548271967f1a67130b7105cd6a828e03909a67962e0ea1f61deb6', 16)
y = int('49f6bc3f4cef38c4f35504e51ec112de5c384df7ba0b8d578a4c702b6bf11d5f', 16)
Q = EC.Point(curve.curve, x, y)
pubkey = ecdsa.VerifyingKey.from_public_point(Q, curve)

# Generate Random Values
a = ecdsa.util.randrange(n-1)
b = ecdsa.util.randrange(n-1)
b_inv = inv_mod_p(b, n)

# Calculate 'r'
K = (a*G) + (b*Q)
r = K.x() % n

# Calculate 's'
s = r * b_inv % n

# Calculate "message"
m = (((a * r) % n) * b_inv) % n

print("message: " + str(m))
print("r: " + str(r))
print("s: " + str(s))

sig = ecdsa.ecdsa.Signature(r, s)
if pubkey.pubkey.verifies(m, sig):
    print("SIGNATURE VERIFIED")
else:
    print("FAILED TO VERIFY")

What is the purpose to sign a random message? I mean this is absolutely useless from practical prospective. Yes, signature is valid, but you do not control the message content as it's calculated.

@abhamai this was created in response to Faketoshi sharing a "valid" signature for Satoshi's key, where he only included the message hash, not the message. This code proves that what he shared was meaningless.