WeakRSA - Google CTF 2025 Writeup

RSA cryptosystem configured with a small public exponent (e=3). Perform a cube root attack on the ciphertext to decrypt the message without factoring N.

🚩 Challenge Overview

  • Platform/Event: Google CTF 2025
  • Difficulty: Easy
  • Points: 100
  • Solves: 610
  • Category: Crypto
  • Tags: RSA, Symmetric Crypto, Small Exponent, Cube Root

📝 Description

RSA cryptosystem configured with a small public exponent (e=3). Perform a cube root attack on the ciphertext to decrypt the message without factoring N.

💡 Solution / Approach

  1. Identify weak parameters: Public exponent e = 3 and ciphertext c is smaller than modulo N (meaning m^3 < N).

  2. The modulo arithmetic doesn’t wrap around, so c = m^3 mod N simplifies to c = m^3.

  3. Calculate the exact integer cube root of c in Python to get m directly:

import gmpy2
from crypto.util.number import long_to_bytes

c = 12345... # ciphertext
m = gmpy2.iroot(c, 3)[0]
print(long_to_bytes(int(m)))