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Post-Quantum Cryptography Algorithms

A directory of quantum-safe algorithms — NIST-standardised and selected schemes, hash-based and alternative key-encapsulation schemes, NIST additional signature candidates, and tools and references. Links go to the official project or standard page.

38 topics•6 categories•Updated October 2026

NIST-Standardised & Selected Algorithms

9 entries

The algorithms NIST has standardised or selected for standardisation.

01ML-KEM (FIPS 203)Lattice-based key-encapsulation mechanism derived from CRYSTALS-Kyber; the main standard for key establishment. 02ML-DSA (FIPS 204)Lattice-based digital signature standard derived from CRYSTALS-Dilithium. 03SLH-DSA (FIPS 205)Stateless hash-based signature standard derived from SPHINCS+. 04Falcon (FN-DSA)Compact lattice-based signatures selected for standardisation as FN-DSA. 05HQCCode-based key-encapsulation mechanism selected by NIST in 2025 as a backup to ML-KEM. 06CRYSTALS-KyberDesign team site for the scheme that became ML-KEM. 07CRYSTALS-DilithiumDesign team site for the scheme that became ML-DSA. 08NIST Selects HQC (2025)NIST announcement of HQC as a fifth algorithm. 09NIST First 3 Finalised Standards (2024)NIST announcement of FIPS 203, 204 and 205.

Hash-Based Signatures

4 entries

Signature schemes whose security rests only on hash functions.

10SPHINCS+Stateless hash-based signature scheme, standardised as SLH-DSA. 11NIST SP 800-208NIST recommendation for stateful hash-based signatures (LMS and XMSS). 12LMS – RFC 8554Leighton-Micali hash-based signatures, a stateful scheme. 13XMSS – RFC 8391eXtended Merkle Signature Scheme, a stateful hash-based scheme.

Alternative Key-Encapsulation Schemes

2 entries

Conservative KEMs with different security assumptions.

14FrodoKEMConservative unstructured-lattice KEM recommended by several European agencies. 15Classic McElieceCode-based KEM with decades of cryptanalysis and very large public keys.

NIST Additional Signature Candidates

11 entries

Schemes in NIST's additional digital signature project, aiming at shorter signatures and different assumptions.

16NIST Additional Digital SignaturesNIST project evaluating further signature schemes. 17Round 2 CandidatesNIST page listing the Round 2 candidates and submissions. 18UOVUnbalanced Oil and Vinegar: a long-studied multivariate signature scheme with short signatures. 19MAYOOil-and-vinegar based multivariate signature with small keys and signatures. 20SNOVAUOV variant with a shorter public key. 21QR-UOVUOV variant using a polynomial quotient ring for compact keys. 22MQOMMQ-on-my-Mind: signature based on the hardness of unstructured multivariate quadratic equations. 23SDitHSyndrome-Decoding-in-the-Head: code-based signature. 24HAWKLattice-based signature designed for fast verification. 25FAESTSignature scheme built from AES and zero-knowledge proofs (symmetric-based). 26SQIsignIsogeny-based signature with very compact keys and signatures.

Tools, Standards & Further Reading

10 entries

Libraries, protocol standards and curated lists.

27NIST Post-Quantum Cryptography ProjectThe central NIST page for PQC standards and selected algorithms. 28NIST PQC Signature ZooCommunity-maintained overview of the NIST signature candidates. 29liboqsC library of quantum-safe algorithms from Open Quantum Safe. 30Open Quantum SafeOpen-source project for prototyping quantum-resistant cryptography. 31mlkem-nativeHigh-assurance ML-KEM implementation from the PQ Code Package. 32Post-Quantum Cryptography AllianceLinux Foundation alliance for open-source PQC software. 33IETF – ML-KEM in TLSIETF work on using ML-KEM in TLS. 34pqcrypto.orgIntroductory site on post-quantum cryptography families. 35IACR ePrint ArchivePreprint archive where new PQC cryptanalysis and designs appear. 36PQC Providers directoryDirectory of PQC vendors on this site.

Related Pages

2 entries

Related directories on this site.

37Number Theory for AIModular arithmetic, lattice and homomorphic cryptography, and AI for mathematics. 38EncryptionEncryption resources.

Frequently Asked Questions

Which PQC algorithms are standardised?

NIST has standardised ML-KEM (FIPS 203) for key encapsulation and ML-DSA (FIPS 204) and SLH-DSA (FIPS 205) for signatures, with Falcon (FN-DSA) and HQC selected for further standardisation.

What are the main PQC families?

Lattice-based (ML-KEM, ML-DSA, Falcon, FrodoKEM), hash-based (SLH-DSA, LMS, XMSS), code-based (HQC, Classic McEliece), multivariate (UOV, MAYO, SNOVA) and isogeny-based (SQIsign) schemes.

Why does NIST have an additional signature project?

To find signatures with smaller sizes or different security assumptions than the lattice and hash-based standards, increasing diversity in case one family is broken.

What happened to older candidates such as Picnic and qTESLA?

They were not selected by NIST, so they are not listed here as current options.

Should I use these algorithms alone?

Many deployments combine a classical algorithm with a PQC algorithm in a hybrid, so security holds if either is broken. Use standardised algorithms through vetted libraries.