Classical Crypto Today

Foundations

The math and primitives underneath everything else — modular arithmetic, hashing, randomness, key derivation.

The history and purpose of cryptography: Before the math: what cryptography is actually trying to do, and the 2,500-year arms race between codemakers and codebreakers that got us here.
The math underneath: modular arithmetic & one-way functions: Every public-key algorithm in this catalog leans on the same idea: a calculation that's easy in one direction and effectively impossible to undo in the other.
Hash functions & digital signatures: One-way fingerprints for data, and the mechanism that proves a message is authentic and untampered — without encrypting anything.
Password hashing & key derivation: PBKDF2, bcrypt, scrypt, Argon2: A cryptographic hash is too fast for passwords. KDFs deliberately slow things down — and not all of them do it the same way.
Key sizes & security levels: what the numbers mean: 128-bit AES, 2048-bit RSA, 256-bit ECC — these numbers aren't comparable at face value. Here's how to actually read them.
Random number generation: the primitive everything else depends on: Every key, nonce, and IV in this catalog assumes truly unpredictable randomness. When that assumption breaks, everything built on top breaks with it.
Why quantum computers break this: Shor's algorithm: The bridge module: why everything above is called "classical" cryptography, and exactly what a future quantum computer would do to it.

One shared key encrypts and decrypts. Fast, and doing most of the actual work in any connection.

Symmetric-key cryptography & AES: The same key locks and unlocks the data. Fast, simple in concept, and everywhere — from disk encryption to the bulk of every TLS session.
Stream ciphers & ChaCha20-Poly1305: Not every symmetric cipher works in fixed blocks. ChaCha20 generates a keystream instead — and paired with Poly1305, it's AES-GCM's fastest rival.

Two mathematically linked keys solve the problem symmetric crypto can't: sharing a secret with a stranger.

RSA & public-key cryptography: Two mathematically linked keys — one public, one private — solve the problem symmetric crypto can't: how do you share a secret with someone you've never met?
RSA padding: OAEP, PKCS#1 v1.5, and why raw RSA fails: Textbook RSA is deterministic and malleable. Padding schemes are what actually make RSA encryption and signing safe to use in the real world.
Elliptic Curve Cryptography (ECC / ECDSA): The same public-key guarantees as RSA, with dramatically smaller keys — because the underlying hard problem is different math entirely.

How the primitives above get composed into systems you actually use — HTTPS, SSH, certificates, messaging.

Diffie-Hellman key exchange: Two parties agree on a shared secret over a public channel, without ever transmitting the secret itself — the idea that started public-key cryptography.
X.509 certificates & the PKI trust hierarchy: A certificate is just a signed statement binding a public key to an identity. Here's what's actually inside one, and how revocation works.
JSON Web Tokens & API authentication: JWTs put a signed claim in every request header. They're everywhere in modern APIs — and a few well-known implementation mistakes keep recurring.
SSH: key exchange, host keys, and authentication: The protocol behind every remote login and git push combines the same primitives as TLS, arranged slightly differently.
TLS in practice: how HTTPS puts it all together: Every padlock icon runs a coordinated handshake combining key exchange, certificates, symmetric encryption, and integrity checks — in under a round trip.
End-to-end encrypted messaging: the Signal Protocol: TLS protects data in transit to a server. The Signal Protocol's Double Ratchet goes further — encrypting so not even the server operator can read your messages.

Where cryptography meets the real world — attacks, blockchains, and the risk that's already here.

Side-channel & timing attacks: when the math is fine but the implementation isn't: A cryptographic algorithm can be mathematically unbreakable and still leak its secret key through how long it takes to run.
Cryptography inside blockchains: hashing, Merkle trees, and signatures: Bitcoin and Ethereum don't invent new cryptography — they compose the same primitives in this catalog into a specific, tamper-evident structure.
Harvest now, decrypt later: the risk that's already here: You don't need a working quantum computer today to be at risk today. Anything encrypted now with RSA or ECC can simply be recorded and decrypted later.