Track: Code-based KEMs

Prereqs: Fundamentals · Bridge
Next: McEliece–Niederreiter equivalence · Gaps

Primary curated path for this lab’s learning curriculum. Goal: take a motivated beginner from fundamentals through TIT code-based papers, then optional ePrint leaves.

How to use

1. Finish the Fundamentals block (or skim if you already know it).
2. Walk the Bridge block (long explainers — do not skip if new to coding theory).
3. Walk Concepts in order (compact vocabulary).
4. Read the TIT paper explainers in order (core path).
5. Optional: ePrint modelling leaf (2025/018).
6. Skim Gaps for open questions.
7. More leaves: docs/PAPERS.md with tag code-based-cryptosystem — prefer papers/tit-pqc/ when adding explainers via research-pqc-learn.

Core path

A. Fundamentals

1. How to read the math
2. Why cryptography?
3. Modular arithmetic
4. Bits, XOR, and randomness
5. Probability (gentle)
6. Hard problems
7. Public-key picture
8. Vectors and matrices
9. Polynomials (gentle) — Part A
   8b. Polynomial wrap-around — Part B
10. Quantum threat

B. Bridge (close the gap)

1. Bridge overview
2. From bits to codes
3. Noisy channel story
4. Generator and parity-check
5. Decoding as a puzzle
6. McEliece in plain words
7. From KEM API to noise
8. Finite fields beyond F₂
9. Security bits and attack work

C. Concepts

1. Error-correcting codes
2. Hamming metric
3. Linear codes
4. Syndrome decoding
5. Information-set decoding
6. Goppa and alternant
7. Niederreiter
8. Quasi-cyclic codes
9. MDPC and QC-MDPC
10. Bit-flipping decoding
11. KEM
12. IND-CPA / IND-CCA
13. DFR
14. Independence heuristics
15. KL divergence

D. Papers — TIT core (beginner explainers)

1. TIT — McEliece ↔ Niederreiter equivalence
2. TIT — Ouroboros KEM family
3. TIT — QC-MDPC reaction attack

E. Papers — optional ePrint leaf

1. ePrint 2025/018 — Independence assumption in QC code-based crypto

F. Frontier / gaps

• gaps.yaml
• Lab WIP (research, not curriculum defaults): ideal blockwise LRPC / SSRS projects under projects/wip/

Optional leaves (no explainer yet)

Prefer new explainers from papers/tit-pqc/ (already digested). Add with research-pqc-learn.

Mindmap (textual)

fundamentals → bridge (codes, G/H, McEliece story, KEM↔noise)
                              ↓
                         concepts (compact)
                              ↓
                      quasi-cyclic + DFR + independence
                              ↓
     TIT: equivalence → Ouroboros → QC-MDPC reaction
                              ↓
              optional: 2025/018 audits independence (KL/TV)
                              ↓
                    open: modern ISD joint-W / CCA+DFR / unstructured ti

Machine-readable edges: edges.yaml.