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Track: Lattice / LWE

Prereqs: Fundamentals (through vectors + modular arithmetic) · Lattices (gentle)
Next: Noisy linear equations (LWE story) · PQC hardware track · Code-based KEMs track · index

Secondary curated path for lattice-based PQC (ML-KEM / LWE-shaped schemes). Goal: leave the integer-grid picture, meet noisy modular equations, then Module-LWE vocabulary — before optional paper / hardware leaves.

How to use

  1. Finish shared Fundamentals at least through Modular arithmetic, Vectors, Probability, and Hard problems.
  2. Walk this track’s lattice fundamental + LWE bridge + concepts below.
  3. Reuse shared concepts: KEM, IND-CPA / CCA, Security bits.
  4. Optional: TIT paper explainers when added via research-pqc-learn.
  5. Hardware path: after Module-LWE, fork to PQC hardware.
  6. Code-based papers remain the densest TIT explainer path in this lab — use that track in parallel if you want research reading first.

Core path

A. Shared entry

  1. Modular arithmetic
  2. Vectors and matrices
  3. Polynomials (gentle) — Part A · Part B wrap-around — needed before Module-LWE
  4. (Helpful) Finite fields beyond F₂ — modulus / alphabet intuition

B. Lattice fundamental + bridge

  1. Lattices (gentle)
  2. Noisy linear equations (LWE story)

C. Lattice concepts

  1. LWE
  2. Module-LWE
  3. Shared: KEM · IND-CPA / CCA

D. Hardware fork (modules → accelerator)

After Module-LWE feels solid, walk the curated HW path (digital intuition → modmul → poly/NTT → accelerator anatomy):

Paper explainers for TCAS-II circuit digests hang there as optional leaves — not required to finish this theory track.

E. Papers (optional leaves — no explainers required yet)

Prefer digested lattice-tagged rows in docs/PAPERS.md / papers/tit-pqc/ when expanding with research-pqc-learn.

F. Frontier / gaps

  • Research gaps ledger: gaps.yaml
  • Lab hardware WIP under projects/papers/ is implementation, not default curriculum

Mindmap (textual)

shared fundamentals (mod q, vectors, polynomials)
                 ↓
     lattices-gentle (grid, SVP/CVP slogans)
                 ↓
     bridge: noisy linear equations (LWE story)
                 ↓
     concepts: LWE → Module-LWE → shared KEM/CCA
                 ↓
     optional TIT leaves · fork → pqc-hardware track

Return anytime to the code-based KEMs track or the PQC hardware track.