Post-Quantum Cryptography — Learning Path

Prereqs: none (curriculum entry)
Next: Motivation · or Orientation hub

A guided path from orientation (why / history / problems / challenges) through fundamentals, bridge pages, and concept cards into curated tracks. Written so newcomers can follow with patience — no prior crypto course assumed.

Lookup: Glossary (plain English) — jump here whenever a word feels fuzzy.
Paper map: Browse indexed papers — search / filter / sort; titles link to publisher URLs.

Who this is for

You are…	Start at
Brand new — want the story before math	Orientation (Motivation → History → Problems → Challenges)
New to cryptography or the math notation	Fundamentals (start with reading math if symbols feel scary)
Finished fundamentals but concepts feel sudden	Bridge
Comfortable with coding intuition	Concepts
Ready for a guided path	Tracks
Curious about chips / accelerators	PQC hardware track

1. Orientation (start here)

Share the why before the how. Four short pages, then Fundamentals.

Hub: orientation/README.md

1. Motivation — why change cryptography; store-now-decrypt-later
2. History — classical PKC → quantum threat → NIST PQC
3. Problems — easy forward, hard backward; family slogans
4. Challenges — size, DFR, SCA, hybrids, moving cryptanalysis

2. Fundamentals

Build mathematical and crypto intuition slowly. No rush. More pages and more wording are intentional.

1. How to read the math — start here if symbols feel scary
2. Why cryptography? — deeper toys after Orientation Motivation
3. Modular arithmetic
4. Bits, XOR, and randomness
5. Probability (gentle)
6. What is a hard problem? — deepen Orientation Problems
7. Public-key crypto in one picture
8. Vectors and matrices (gentle)
9. Polynomials (gentle) — Part A — add/multiply only; do the paper lab
   8b. Polynomial wrap-around — Part B — before QC / HQC-shaped pages
10. Why quantum computers change crypto — deepen Orientation Motivation / History
11. Lattices (gentle) — for the lattice / LWE track

3. Bridge (close the gap)

Longer, story-first pages between fundamentals and compact PQC concepts. Do not skip if concepts feel sudden. More wording is intentional so newcomers can follow with patience.

Start here: bridge/README.md

1. From bits to codes
2. Noisy channel story
3. Generator and parity-check matrices
4. Decoding as a puzzle
5. McEliece in plain words
6. From KEM API to noise
7. Finite fields beyond F₂
8. Security bits and attack work
9. From Hamming to rank — for the rank-metric track
10. Noisy linear equations (LWE story) — for the lattice / LWE track
11. Clocks, registers, and latency — for the PQC hardware track
12. Area, time, power honesty — reading HW comparison tables

4. Concepts

PQC vocabulary cards. Best after the matching bridge pages. Prefer clarity over compression.

Code-based / shared

• Error-correcting codes (intuition)
• Hamming metric
• Linear codes over finite fields
• Syndrome decoding
• Information-set decoding (ISD)
• Goppa and alternant codes
• Niederreiter cryptosystem
• MDPC and QC-MDPC codes
• Bit-flipping decoding
• Quasi-cyclic codes
• Key encapsulation (KEM)
• IND-CPA and IND-CCA
• Decryption failure rate (DFR)
• Independence heuristics
• KL divergence (gentle)

Rank metric

• Rank metric
• LRPC codes
• Rank syndrome decoding

Lattice / LWE

• Learning With Errors (LWE)
• Module-LWE (gentle)

PQC hardware (modules → accelerator)

• Modular multiplier
• Polynomial multiply engines
• NTT butterfly (gentle)
• NTT parallel memory
• KEM accelerator anatomy

5. Tracks

• Code-based KEMs — primary curated path (McEliece intuition → HQC/BIKE-shaped ideas → modelling & cryptanalysis)
• Lattice / LWE — grids → LWE story → Module-LWE
• Rank metric — Hamming→rank bridge + LRPC / rank-SD concepts
• PQC hardware — digital intuition → modmul → poly/NTT → KEM accelerator anatomy

Maintained by skill: research-pqc-learn.