ExploitRS.py

import random

# Elliptic Curve Parameters (secp256k1 - Bitcoin Standard)
p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F  # Prime field
a = 0  # Curve parameter a
b = 7  # Curve parameter b
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240  # Generator x
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337424483  # Generator y
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141  # Order of the group

# Elliptic curve point addition
def point_addition(P, Q):
    if P == (0, 0):
        return Q
    if Q == (0, 0):
        return P

    if P == Q:
        lam = (3 * P[0] ** 2 + a) * pow(2 * P[1], -1, p) % p
    else:
        lam = (Q[1] - P[1]) * pow(Q[0] - P[0], -1, p) % p

    x = (lam ** 2 - P[0] - Q[0]) % p
    y = (lam * (P[0] - x) - P[1]) % p

    return x, y


def scalar_multiplication(k, P):
    result = (0, 0)
    temp = P

    while k:
        if k & 1:
            result = point_addition(result, temp)
        temp = point_addition(temp, temp)
        k >>= 1

    return result


# Generate private key (x), public key (P = xG)
def generate_keys():
    x = random.randint(1, n - 1)  # Private key
    P = scalar_multiplication(x, (Gx, Gy))  # Public key
    return x, P


# Sign a message
def sign_message(x, m, k):
    t = scalar_multiplication(k, (Gx, Gy))  # t = Gk
    r = t[0] % n  # X coordinate of t
    s = (m + x * r) * pow(k, -1, n) % n  # s = (m + x * r) / k
    return r, s


# Verify signature
def verify_signature(P, m, r, s):
    w = pow(s, -1, n)  # w = 1 / s
    u1 = (m * w) % n
    u2 = (r * w) % n
    t = point_addition(scalar_multiplication(u1, (Gx, Gy)), scalar_multiplication(u2, P))
    return t[0] % n == r


# Main function
if __name__ == "__main__":
    print("=== Simplified Bitcoin-like ECDSA Implementation ===")

    # Step 1: Generate or Input Keys
    print("\nChoose an option:")
    print("1. Generate new keys")
    print("2. Input your own private key")
    choice = input("Enter your choice (1 or 2): ")

    if choice == "1":
        private_key, public_key = generate_keys()
        print("\nGenerated Keys:")
        print(f"Private Key (x): {private_key}")
        print(f"Public Key (P = xG): {public_key}")
    elif choice == "2":
        private_key = int(input("Enter your private key (x): "))
        public_key = scalar_multiplication(private_key, (Gx, Gy))
        print("\nDerived Public Key:")
        print(f"Public Key (P = xG): {public_key}")
    else:
        print("Invalid choice! Exiting.")
        exit()

    # Step 2: Input Message
    message = int(input("\nEnter your message (as an integer): "))

    # Step 3: Input or Generate Nonce (k)
    print("\nChoose an option for nonce:")
    print("1. Generate random nonce (k)")
    print("2. Input your own nonce (k)")
    k_choice = input("Enter your choice (1 or 2): ")

    if k_choice == "1":
        k = random.randint(1, n - 1)
        print(f"\nGenerated Nonce (k): {k}")
    elif k_choice == "2":
        k = int(input("Enter your nonce (k): "))
    else:
        print("Invalid choice! Exiting.")
        exit()

    # Step 4: Generate Signature
    r, s = sign_message(private_key, message, k)
    print(f"\nGenerated Signature:")
    print(f"r = {r}")
    print(f"s = {s}")

    # Step 5: Verify the Signature
    print("\nVerifying the signature...")
    is_valid = verify_signature(public_key, message, r, s)
    print(f"Signature valid: {is_valid}")