Applied Cryptography

Implement RFC 4648 base64 encoding from scratch: the alphabet, 3-byte to 4-char encoding, padding, decoding with error handling, and the URL-safe variant used in JWT. Used in email, data URIs, HTTP Basic auth, and PEM-encoded keys.

Implement a cryptographic random number generator. Learn why Math.random() and rand() are insecure, how the OS gathers entropy, and implement HMAC-DRBG (NIST SP 800-90A) and Fortuna. The foundation underneath every TLS handshake, every AES IV, every session token.

Implement secure password hashing: salts, PBKDF2-style iteration, bcrypt, argon2id, constant-time comparison, and rehash-on-login. Why SHA/MD5 for passwords is dangerous and what to use instead.

Implement SHA-256 from raw bit operations. You'll build ROTR/Σ/σ/Ch/Maj, the message schedule, the 64-round compression function, padding, and the full Merkle-Damgård construction. Then add HMAC for message authentication. By the end you'll deeply understand the hash function used in Bitcoin, Git, TLS, and JWT.

Implement the AES block cipher from raw bit operations: state matrix, GF(2^8) arithmetic, the S-box, ShiftRows, MixColumns, key schedule, and full 10-round encryption. Then add modes of operation (ECB, CBC, CTR, GCM). The cipher behind TLS, WPA2, and disk encryption.

Implement RSA from number theory primitives: modular exponentiation, prime generation via Miller-Rabin, modular inverse via extended Euclidean, key generation, encrypt/decrypt, signatures, padding (PKCS#1, OAEP, PSS). Then learn the historical attacks. The asymmetric crypto algorithm behind TLS, PGP, SSH, and Bitcoin until 2024.

Build elliptic-curve signatures from scratch: modular arithmetic, finite fields, point addition on secp256k1, scalar multiplication, ECDSA sign/verify. Foundation of Bitcoin, Ethereum, TLS. Includes the famous nonce-reuse attack that broke the PS3.

Build a working CA: parse X.509 / ASN.1 DER, accept CSRs, validate domain ownership, issue certificates with proper extensions, publish to Certificate Transparency logs, manage revocation via CRL/OCSP, and protect signing keys in HSMs. The infrastructure underlying every HTTPS connection.

Build TLS 1.3 from scratch: AEAD ciphers, HKDF key schedule, ephemeral X25519 key exchange, the 1-RTT handshake, encrypted record layer, session resumption with PSK, and 0-RTT data. The protocol securing every HTTPS request on the modern internet.

Build end-to-end encryption like Signal/WhatsApp: X3DH for asynchronous key agreement, the Double Ratchet for forward secrecy + break-in recovery, sender keys for group chat, and metadata-privacy techniques. The protocol behind 2 billion encrypted conversations daily.