Applied Post-Quantum Cryptography

A LaTeX book that builds post-quantum cryptography from the ground up, by Stephen Duan and Wei Li.

• Repository: https://github.com/AppliedPQC/AppliedPQC
• Live PDF: https://appliedpqc.io/apqc.pdf

About the book

The book develops the subject as a single arc, from first principles to deployment. It starts with the quantum threat (why Shor breaks today's public-key cryptography while Grover only weakens symmetric primitives) and the mathematical foundations (finite fields, linear algebra, polynomial rings). It then builds the lattice world -- lattices and hard problems, the Learning-With-Errors family, and the machinery (NTT, CBD, seed expansion) that leads to the ML-KEM standard (FIPS 203). From there it treats digital signatures grouped by their hard problem: lattice-based (ML-DSA / FIPS 204 and FN-DSA / FIPS 206) and hash-based (built up from one-time and Merkle-tree signatures to SLH-DSA / FIPS 205). It closes with code-based cryptography (Classic McEliece, HQC), implementation and side-channel security, and a final part on deploying post-quantum cryptography in real systems (hybrid TLS 1.3, certificates, and on-chain verification).

Every chapter follows the same style: worked SageMath experiments, TikZ figures, formal definitions and algorithm blocks, and a reference list. The four standards chapters are backed by complete, test-vector-verified SageMath implementations in sage/ (see below). The full table of contents lives in the compiled PDF.

Build the PDF

The simplest way is the provided Makefile:

make          # compiles apqc.tex into apqc.pdf
make clean    # remove generated files

The Makefile runs pdflatex twice, which is enough to resolve the cross-references and the (manual) bibliography -- no BibTeX pass is needed.

Manual build

pdflatex -interaction=nonstopmode -halt-on-error apqc.tex
pdflatex -interaction=nonstopmode -halt-on-error apqc.tex

The document uses TikZ, pgfplots, and the algorithm packages, so a fairly complete TeX Live is required (the CI installs texlive-latex-base, -recommended, -extra, -fonts-recommended, -pictures, and -science).

GitHub Pages

Every push to main triggers .github/workflows/deploy-pages.yml, which builds the PDF and publishes it via GitHub Actions. The site is served at:

https://appliedpqc.io/          # landing page
https://appliedpqc.io/apqc.pdf  # the book

Pages must be enabled once, with its source set to "GitHub Actions", in the repository settings. The site is served from the custom domain appliedpqc.io, with HTTPS enforced; the old appliedpqc.github.io/AppliedPQC/ address redirects to it.

SageMath implementations of FIPS 203-206

Alongside the chapters, sage/ holds complete, byte-exact SageMath implementations of all four NIST post-quantum standards. Every numbered algorithm of each standard appears as its own function, named after the standard and annotated with its algorithm number.

FIPS 203, 204 and 205 are checked against NIST's ACVP test vectors and reproduce them byte for byte. FIPS 206 is still in development at NIST -- no public draft, no vectors -- so FN-DSA follows the round-3 Falcon submission and is validated against Falcon's own known-answer tests instead. See sage/README.md for the details.

make kat        # download the test vectors and run the quick check
make kat-full   # every available test vector

make kat needs sage on your PATH; override it with make kat SAGE=/path/to/sage. These are teaching implementations: readable and standards-exact, but not constant-time and not for production use.