Applied Post-Quantum Cryptography

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1. Part I: Foundations
2. 1The Quantum Threat
3. 2SageMath Basics for Post-Quantum Cryptography
4. 3Linear Algebra Foundations
5. 4Polynomial Rings
6. 5From Convolution to Negacyclic Ring Arithmetic
7. 6Number Theoretic Transform (NTT)
8. Part II: Lattice-Based Cryptography
9. Lattices and Hard Problems
10. 7Lattices
11. 8Gram–Schmidt Orthogonalization and the LLL Algorithm
12. 9Shortest Vector Problem (SVP)
13. Learning With Errors and Its Variants
14. 10Probability and Error Distribution
15. 11Learning With Errors (LWE)
16. 12Ring-LWE (RLWE)
17. 13Module-LWE (MLWE)
18. Building ML-KEM (FIPS 203)
19. 14Introduction to Kyber (ML-KEM)
20. 15Centered Binomial Distribution (CBD) – Why Kyber does not use Gaussian
21. 16Complete Implementation of ML-KEM (FIPS 203)
22. Signatures: ML-DSA and FN-DSA
23. 17Complete Implementation of ML-DSA (FIPS 204)
24. 18FN-DSA (Falcon): Draft-Oriented Walkthrough
25. Part III: Hash-Based Cryptography
26. 19Hash-Based Signatures: One-Time and Few-Time
27. 20Merkle Trees and Stateless Signatures
28. 21SLH-DSA (SPHINCS+, FIPS 205): Algorithm Walkthrough
29. Part IV: Code-Based Cryptography
30. 22Classic McEliece
31. 23HQC
32. Part V: Multivariate and Isogeny-Based Cryptography
33. 24Multivariate Cryptography
34. 25Isogeny-Based Cryptography
35. Part VI: Post-Quantum Cryptography in Practice
36. 26Side-Channel Security
37. 27Deploying Post-Quantum Cryptography
38. 28Post-Quantum Migration of Blockchains
39. Appendix
40. ABinary Goppa Codes