Cryptography from first principles

Zero-dependency number theory and a 512-bit RSA engine in Julia, including Håstad’s attack.

Open curriculum implementing CRT, extended Euclidean algorithm, optimized modular exponentiation, and a full 512-bit RSA generate/encrypt/decrypt path, including a simulation of Håstad’s broadcast attack against unpadded public exponents.

Highlights

• First-principles CRT and modular inverse frameworks
• O(log k) binary-decomposition modular exponentiation
• End-to-end RSA plus broadcast-attack demonstration