Resources

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Curated learning materials for understanding post-quantum cryptography. From official NIST standards to beginner-friendly explanations.

NIST Standards

FIPS 203 — ML-KEM

Module-Lattice-Based Key-Encapsulation Mechanism Standard

FIPS 204 — ML-DSA

Module-Lattice-Based Digital Signature Standard

FIPS 205 — SLH-DSA

Stateless Hash-Based Digital Signature Standard

Learning Materials

Getting Started

NIST Post-Quantum Cryptography Project

Official NIST page with background, timeline, and all standardization documents.

Post-Quantum Cryptography for Engineers

A practical introduction from the Cloud Security Alliance aimed at developers and engineers.

PQC Migration Handbook (ANSSI & BSI)

Joint guidance from French and German cybersecurity agencies on migrating to post-quantum algorithms.

Lattice Cryptography

The Learning With Errors Problem

Oded Regev's original 2005 paper that launched lattice-based cryptography. Technical but foundational.

A Decade of Lattice Cryptography (Chris Peikert)

A comprehensive survey covering the evolution of lattice-based schemes from theory to practice.

Hash-Based Signatures

Hash-Based Signatures: An Illustrated Primer

Accessible introduction to Merkle trees, WOTS, and SPHINCS+ with clear diagrams.

SPHINCS+ Specification

The original SPHINCS+ submission to NIST that became SLH-DSA.

Quantum Computing Background

Shor's Algorithm Explained

Why quantum computers break RSA and ECC — Shor's algorithm for factoring and discrete logarithms.

Grover's Algorithm and Symmetric Key Search

Understanding the quadratic speedup that affects hash functions and symmetric ciphers.

Implementation & Libraries

liboqs — Open Quantum Safe

Open-source C library implementing post-quantum algorithms with language bindings for Python, Go, Java, and more.

PQClean

Clean, portable C implementations of post-quantum schemes. Useful as a reference for understanding algorithm internals.

NIST PQC Reference Implementations

Official reference implementations submitted as part of the NIST standardization process.

Glossary

KEM
Key Encapsulation Mechanism — a method for two parties to establish a shared secret key.
LWE
Learning With Errors — a hard mathematical problem involving noisy linear equations over lattices.
MLWE
Module Learning With Errors — a structured variant of LWE using polynomial modules for efficiency.
Polynomial Ring
An algebraic structure R_q = Z_q[X]/(X^n + 1) where computations happen on polynomials modulo X^n + 1.
Lattice
A regular grid of points in high-dimensional space. Finding short vectors in large lattices is believed to be hard even for quantum computers.
Merkle Tree
A binary tree of hash values where each parent is the hash of its children. The root acts as a fingerprint for all leaves.
WOTS+
Winternitz One-Time Signature Plus — a hash-based signature scheme that can only be used once safely.
Rejection Sampling
A technique where the signer discards outputs that would leak information about the secret key.
Fiat-Shamir Transform
A technique to convert an interactive proof into a non-interactive signature by replacing the verifier with a hash function.
Grover's Algorithm
A quantum algorithm that searches unsorted data in O(sqrt(N)) time — provides a quadratic (not exponential) speedup.
Shor's Algorithm
A quantum algorithm that breaks RSA and ECC by efficiently factoring large numbers and computing discrete logarithms.
Authentication Path
The set of sibling hashes needed to recompute a Merkle tree root from a single leaf — proof of membership.

Ready to see these concepts in action?

ML-KEMML-DSASLH-DSA