Cryptography is about designing crypto algorithms; cryptanalysis is about breaking them.

Both fall under the umbrella of cryptology, which is the overarching science.

The word "cryptography" comes from the Greek words kryptos (hidden) and graphein (to write) — literally "secret writing."

Tip: Think of it like offense vs. defense — cryptography builds the lock, cryptanalysis tries to pick it.

Go deeper:

• Cryptanalysis - the code-breaking counterpart to cryptography; the two halves of the cryptology umbrella.

Cryptography divides into symmetric, asymmetric, and protocols — based on how keys are shared and used.

* Cryptography by key usage: symmetric, asymmetric, and protocols. *

The taxonomy:

Cryptography
├── Symmetric (shared secret key)
│   ├── Block ciphers (e.g., AES)
│   └── Stream ciphers
├── Asymmetric (public/private key pair)
│   ├── Based on factoring (e.g., RSA)
│   ├── Based on discrete log (e.g., Diffie-Hellman, Schnorr, DSA)
│   └── Based on elliptic curves (also a form of discrete log)
└── Protocols

Protocols here means cryptographic protocols — multi-step interactions that combine the primitives above to reach a goal no single cipher achieves on its own. Examples: key exchange (Diffie-Hellman), the TLS handshake, authentication schemes, and zero-knowledge proofs.

For RSA, the factoring problem is more precisely described as: "if you can factor $N$ into primes, then you can compute the $e$-th root $\bmod N$" — but the reverse has not been proven.

Go deeper:

• Public Key Cryptography - Computerphile - why asymmetric keys exist and how they differ from a shared secret.
• Public-key cryptography - the asymmetric branch of the taxonomy.
• Symmetric-key algorithm - the same-key branch (block and stream ciphers).