Cryptography¶
Job: secure communication and computation under computational hardness — encryption, signatures, zero-knowledge, multiparty computation, and post-quantum primitives.
Core¶
| Layer | Content |
|---|---|
| Security models | asymptotic / concrete; IND-CPA/CCA; EUF-CMA; ROM |
| Classical | RSA, DH, ElGamal, Schnorr, ECDSA |
| Post-quantum | LWE, lattice, FHE, Kyber/Dilithium, SPHINCS+ |
| ZK & MPC | Σ-protocols, Fiat–Shamir, BGW/GMW, Shamir, Yao |
| Protocols | TLS 1.3, AKE, KEM/DEM, QKD |
Reading map¶
| Page | Focus |
|---|---|
| Foundations | asymptotic security, hardness assumptions, RSA/DH, OTP, reductions |
| Lattice & Post-Quantum | LWE Regev, SVP/CVP, FHE Gentry, Kyber/Dilithium |
| ZK & MPC | Σ-protocol, Fiat–Shamir, BGW/GMW, Shamir, Yao |
| Hash & Signatures | collision-resistant, Merkle–Damgård, EUF-CMA, ECDSA, SPHINCS+ |
| Protocols & TLS | TLS 1.3, KEM, AKE/SIGMA, commitment, QKD BB84 |
Dependency order¶
- Number theory / Abstract algebra (groups, fields, modular)
- Foundations — security models, classical schemes
- Information theory — entropy, secrecy, perfect vs computational
- Post-quantum / ZK / protocols as applied layers
Where it appears¶
- Number theory: RSA, DL, factoring, elliptic curves
- Information theory: Shannon secrecy, entropy bounds, correlation
- Abstract algebra: groups, rings, lattices
- Probability: random oracles, negligible functions
Next¶
Foundations · Lattice & Post-Quantum · ZK & MPC · Hash & Signatures · Protocols & TLS · Number theory · Information theory