Challenge 6: Digital Signature Forgery

Level: Advanced

Description: Provide a digital signature scheme with a weakness (e.g., using a small prime number). Forge a digital signature for a new message.

Challenge Text:

Signature scheme: RSA with n = 391, e = 3, d = 107
Signed message: ("HELLO", signature = 220)
Challenge: Forge a signature for the message "WORLD"

Instructions: 1. Understand the weakness in the provided RSA signature scheme. 2. Forge a signature for the new message. 3. Validate the forged signature.

Answer: For the message "WORLD," a forged signature could be 115.

Code:

n = 391
e = 3
message = "WORLD"

# Compute numeric representation of message
message_numeric = sum([ord(c) * (256 ** i) for i, c in enumerate(message[::-1])])

# Compute forged signature
forged_signature = message_numeric ** e % n

print("Forged signature:", forged_signature)