Cubiod

Prerequisites & Requirements

• Basic familiarity with RSA (public/private keys, modulus N, exponent e) and converting between bytes and integers.
• Comfortable with Python (reading scripts, running small one-off scripts).
• Ability to use/install simple Python packages (e.g., sympy, pycryptodome or gmpy2).

What will you learn?

• Why textbook RSA with a very small public exponent (e.g., e = 3) is dangerous for short messages.
• How to reason about m^e vs N and when modular reduction does not occur.
• Practical technique: recover a plaintext by computing an integer root and converting it back to bytes.

Tools

• Python 3 (interpreter).
• sympy (for integer_nthroot) or gmpy2 (for iroot) for integer roots.
• pycryptodome (Crypto.Util.number) for byte/int conversions if needed.