Cryptographic Mathematics

Number theory that protects the internet. Modular arithmetic, the Euclidean algorithm, inverses, Fermat/Euler theorems and the Chinese Remainder Theorem, then RSA, Diffie–Hellman and elliptic-curve cryptography with key-size and post-quantum considerations.

• Number Theory & Modular Arithmetic — Modular arithmetic — 'clock arithmetic' — is the foundation of cryptography, hashing, checksums and error-detecting codes. Learn divisibility, primes, gcd and the Euclidean algorithm, Bézout's identity, congruences, modular inverses, fast modular exponentiation, Fermat's and Euler's theorems, and the Chinese Remainder Theorem.
• Public-Key Cryptography: RSA & Elliptic Curves — Public-key cryptography lets strangers communicate securely. Learn RSA key generation, encryption, decryption and signatures from Euler's theorem; Diffie–Hellman key exchange; elliptic-curve group law, scalar multiplication and ECDH; key sizes and security levels; and why hashing, padding and quantum threats matter — with toy RSA and ECC in Python.