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Post-Quantum Cryptography Standardizationcite-ref-1[1] is a program and competition by NIST to update their standards to include post-quantum cryptography.cite-ref-2[2] It was announced at PQCrypto 2016.cite-ref-3[3] 23 signature schemes and 59 encryption/KEM schemes were submitted by the initial submission deadline at the end of 2017cite-ref-4[4] of which 69 total were deemed complete and proper and participated in the first round. Seven of these, of which 3 are signature schemes, advanced to the third round, which was announced on July 22, 2020.

On August 13, 2024, NIST released final versions of the first three Post Quantum Crypto Standards: FIPS 203, FIPS 204, and FIPS 205.cite-ref-nistrelase2024-5-0[5]

• Background

• Round one

• Round one submissions published attacks

• Round two

• Round three

• Finalists

• Alternate candidates

• Intellectual property concerns

• Round three submissions published attacks

• Adaptations

• Selected Algorithms 2022

• Round four

• Round four submissions published attacks

• Selected Algorithm 2025

• First release

• Additional Digital Signature Schemes

• Round One

• Round one submissions published attacks

• Round Two

• See also

• References

• External links

Academic research on the potential impact of quantum computing dates back to at least 2001.cite-ref-6[6] A NIST published report from April 2016 cites experts that acknowledge the possibility of quantum technology to render the commonly used RSA algorithm insecure by 2030.cite-ref-7[7] As a result, a need to standardize quantum-secure cryptographic primitives was pursued. Since most symmetric primitives are relatively easy to modify in a way that makes them quantum resistant, efforts have focused on public-key cryptography, namely digital signatures and key encapsulation mechanisms. In December 2016 NIST initiated a standardization process by announcing a call for proposals.cite-ref-8[8]

Under consideration were:cite-ref-9[9]

(strikethrough means it had been withdrawn)

| Type | PKE/ KEM | Signature | Signature & PKE/KEM |

|---|---|---|---|

| Lattice | Compact LWE CRYSTALS-Kyber Ding Key Exchange EMBLEM and R.EMBLEM FrodoKEM HILA5 (withdrawn and merged into Round5) KCL (pka OKCN/AKCN/CNKE) KINDI LAC LIMA Lizard LOTUS NewHope NTRUEncrypt [ 10 ] NTRU-HRSS-KEM NTRU Prime Odd Manhattan Round2 (withdrawn and merged into Round5) Round5 (merger of Round2 and Hila5, announced 4 August 2018) [ 11 ] SABER Three Bears Titanium | CRYSTALS-Dilithium DRS FALCON pqNTRUSign [ 10 ] qTESLA [ 12 ] [ 13 ] | |

| Code-based | BIG QUAKE BIKE Classic McEliece + NTS- KEM DAGS Edon-K HQC LAKE (withdrawn and merged into ROLLO) LEDAkem LEDApkc Lepton LOCKER (withdrawn and merged into ROLLO) McNie NTS-KEM ROLLO (merger of Ouroboros-R, LAKE and LOCKER) [ 14 ] Ouroboros-R (withdrawn and merged into ROLLO) QC-MDPC KEM Ramstake RLCE-KEM RQC | pqsigRM RaCoSS RankSign | |

| Hash-based | | Gravity-SPHINCS SPHINCS+ | |

| Multivariate | CFPKM Giophantus | DualModeMS GeMSS Gui HiMQ-3 LUOV MQDSS Rainbow | SRTPI DME |

| Braid group | | WalnutDSA | |

| Supersingular elliptic curve isogeny | SIKE | | |

| Satirical submission | | | pq RSA [ 15 ] [ 16 ] |

| Other | Guess Again HK17 Mersenne-756839 RVB | Picnic | |

• Guess Again by Lorenz Panny cite-ref-17[17]

• RVB by Lorenz Pannycite-ref-18[18]

• RaCoSS by Daniel J. Bernstein, Andreas Hülsing, Tanja Lange and Lorenz Pannycite-ref-19[19]

• HK17 by Daniel J. Bernstein and Tanja Langecite-ref-20[20]

• SRTPI by Bo-Yin Yangcite-ref-21[21]

• WalnutDSA

• by Ward Beullens and Simon R. Blackburncite-ref-22[22]

• by Matvei Kotov, Anton Menshov and Alexander Ushakovcite-ref-23[23]

• DRS by Yang Yu and Léo Ducas cite-ref-24[24]

• DAGS by Elise Barelli and Alain Couvreurcite-ref-25[25]

• Edon-K by Matthieu Lequesne and Jean-Pierre Tillichcite-ref-26[26]

• RLCE by Alain Couvreur, Matthieu Lequesne, and Jean-Pierre Tillichcite-ref-27[27]

• Hila5 by Daniel J. Bernstein, Leon Groot Bruinderink, Tanja Lange and Lorenz Pannycite-ref-28[28]

• Giophantus by Ward Beullens, Wouter Castryck and Frederik Vercauterencite-ref-29[29]

• RankSign by Thomas Debris-Alazard and Jean-Pierre Tillich cite-ref-30[30]

• McNie by Philippe Gaborit;cite-ref-31[31] Terry Shue Chien Lau and Chik How Tan cite-ref-32[32]

Candidates moving on to the second round were announced on January 30, 2019. They are:cite-ref-33[33]

| Type | PKE/KEM | Signature |

|---|---|---|

| Lattice | CRYSTALS-Kyber [ 34 ] FrodoKEM [ 35 ] LAC NewHope [ 36 ] NTRU (merger of NTRUEncrypt and NTRU-HRSS-KEM) [ 10 ] NTRU Prime [ 37 ] Round5 (merger of Round2 and Hila5, announced 4 August 2018) [ 11 ] SABER [ 38 ] Three Bears [ 39 ] | CRYSTALS-Dilithium [ 34 ] FALCON [ 40 ] qTESLA |

| Code-based | BIKE [ 41 ] Classic McEliece HQC [ 42 ] LEDAcrypt (merger of LEDAkem [ 43 ] and LEDApkc [ 44 ] ) NTS-KEM [ 45 ] ROLLO (merger of Ouroboros-R, LAKE and LOCKER) [ 14 ] RQC [ 46 ] | |

| Hash-based | | SPHINCS+ [ 47 ] |

| Multivariate | | GeMSS [ 48 ] LUOV [ 49 ] MQDSS [ 50 ] Rainbow |

| Supersingular elliptic curve isogeny | SIKE [ 51 ] | |

| Zero-knowledge proofs | | Picnic [ 52 ] |

On July 22, 2020, NIST announced seven finalists ("first track"), as well as eight alternate algorithms ("second track"). The first track contains the algorithms which appear to have the most promise, and will be considered for standardization at the end of the third round. Algorithms in the second track could still become part of the standard, after the third round ends.cite-ref-2ndround-53-0[53] NIST expects some of the alternate candidates to be considered in a fourth round. NIST also suggests it may re-open the signature category for new schemes proposals in the future.cite-ref-54[54]

On June 7–9, 2021, NIST conducted the third PQC standardization conference, virtually.cite-ref-55[55] The conference included candidates' updates and discussions on implementations, on performances, and on security issues of the candidates. A small amount of focus was spent on intellectual property concerns.

| Type | PKE/KEM | Signature |

|---|---|---|

| Lattice | CRYSTALS-Kyber NTRU SABER | CRYSTALS-Dilithium FALCON |

| Code-based | Classic McEliece | |

| Multivariate | | Rainbow |

| Type | PKE/KEM | Signature |

|---|---|---|

| Lattice | FrodoKEM NTRU Prime | |

| Code-based | BIKE HQC | |

| Hash-based | | SPHINCS+ |

| Multivariate | | GeMSS |

| Supersingular elliptic curve isogeny | SIKE | |

| Zero-knowledge proofs | | Picnic |

After NIST's announcement regarding the finalists and the alternate candidates, various intellectual property concerns were voiced, notably surrounding lattice-based schemes such as Kyber and NewHope. NIST holds signed statements from submitting groups clearing any legal claims, but there is still a concern that third parties could raise claims. NIST claims that they will take such considerations into account while picking the winning algorithms.cite-ref-56[56]

• Rainbow: by Ward Beullens on a classical computercite-ref-57[57]

During this round, some candidates have shown to be vulnerable to some attack vectors. It forces these candidates to adapt accordingly:

may change the nested hashes used in their proposals in order for their security claims to hold.cite-ref-58[58]

side channel attack using electromagnetic measurements to extract the secret signing keys. A masking may be added in order to resist the attack. This adaptation affects performance and should be considered whilst standardizing.cite-ref-59[59]

On July 5, 2022, NIST announced the first group of winners from its six-year competition.cite-ref-60[60]cite-ref-61[61]

| Type | PKE/KEM | Signature |

|---|---|---|

| Lattice | CRYSTALS-Kyber | CRYSTALS-Dilithium FALCON |

| Hash-based | | SPHINCS+ |

On July 5, 2022, NIST announced four candidates for PQC Standardization Round 4.cite-ref-62[62]

| Type | PKE/KEM |

|---|---|

| Code-based | BIKE Classic McEliece HQC |

| Supersingular elliptic curve isogeny | SIKE (Broken August 5, 2022) [ 63 ] |

• SIKE: by Wouter Castryck and Thomas Decru on a classical computercite-ref-64[64]cite-ref-65[65]

On March 11, 2025, NIST announced the selection of a backup algorithm for KEM.cite-ref-nist250311-66-0[66]

| Type | PKE/KEM |

|---|---|

| Code-based | HQC |

On August 13, 2024, NIST released final versions of its first three Post Quantum Crypto Standards.cite-ref-nistrelase2024-5-1[5] According to the release announcement:

While there have been no substantive changes made to the standards since the draft versions, NIST has changed the algorithms’ names to specify the versions that appear in the three finalized standards, which are: Federal Information Processing Standard (FIPS) 203, intended as the primary standard for general encryption. Among its advantages are comparatively small encryption keys that two parties can exchange easily, as well as its speed of operation. The standard is based on the CRYSTALS-Kyber algorithm, which has been renamed ML-KEM, short for Module-Lattice-Based Key-Encapsulation Mechanism. FIPS 204, intended as the primary standard for protecting digital signatures. The standard uses the CRYSTALS-Dilithium algorithm, which has been renamed ML-DSA, short for Module-Lattice-Based Digital Signature Algorithm. FIPS 205, also designed for digital signatures. The standard employs the SPHINCS+ algorithm, which has been renamed SLH-DSA, short for Stateless Hash-Based Digital Signature Algorithm. The standard is based on a different math approach than ML-DSA, and it is intended as a backup method in case ML-DSA proves vulnerable. Similarly, when the draft FIPS 206 standard built around FALCON is released, the algorithm will be dubbed FN-DSA, short for FFT (fast-Fourier transform) over NTRU-Lattice-Based Digital Signature Algorithm.

On March 11, 2025 NIST released Hamming Quasi-Cyclic (HQC) as the fifth algorithm for post-quantum asymmetric encryption as used for key encapsulation / exchange.cite-ref-nist250311-66-1[66] The new algorithm is as a backup for ML-KEM, the main algorithm for general encryption. HQC is a code-based scheme using different math than ML-KEM, thus mitigating possible weaknesses should any be found in the lattice-based ML-KEM.cite-ref-67[67] The draft standard incorporating the HQC algorithm is expected in early 2026 with the final in 2027.

NIST received 50 submissions and deemed 40 to be complete and proper according to the submission requirements.cite-ref-68[68] Under consideration are:cite-ref-69[69]

(strikethrough means it has been withdrawn)

| Type | Signature |

|---|---|

| Lattice | EagleSign EHTv3 and EHTv4 HAETAE [ 70 ] HAWK [ 71 ] HuFu [ 72 ] Raccoon [ 73 ] [ 74 ] SQUIRRELS [ 75 ] |

| Code-based | CROSS [ 76 ] Enhanced pqsigRM FuLeeca [ 77 ] LESS [ 78 ] MEDS [ 79 ] Wave [ 80 ] |

| MPC-in-the-Head | MIRA [ 81 ] MiRitH [ 82 ] MQOM [ 83 ] PERK [ 84 ] RYDE [ 85 ] SDitH [ 86 ] |

| Multivariate | 3WISE ("the submitter agrees that the scheme is insecure, but prefers to not withdraw in the hope that studying the scheme will advance cryptanalysis" [ 87 ] ) Biscuit [ 88 ] DME-Sign ("Our first impression is that the attack works and we are checking the details of the attack .We are implementing a variant of the DME that may resist the attack but we have to verify it." [ 89 ] ) HPPC MAYO [ 90 ] PROV [ 91 ] QR-UOV [ 92 ] SNOVA [ 93 ] TUOV [ 94 ] UOV [ 95 ] VOX [ 96 ] |

| Supersingular elliptic curve isogeny | SQIsign [ 97 ] |

| Symmetric-based | AIMer [ 98 ] Ascon-Sign FAEST [ 99 ] SPHINCS-alpha |

| Other | ALTEQ [ 100 ] eMLE-Sig 2.0 KAZ-SIGN Preon Xifrat1-Sign.I |

• 3WISE by Daniel Smith-Tonecite-ref-0-87-1[87]

• EagleSign by Mehdi Tibouchicite-ref-101[101]

• KAZ-SIGN by Daniel J. Bernstein;cite-ref-102[102] Scott Fluhrercite-ref-103[103]

• Xifrat1-Sign.I by Lorenz Pannycite-ref-104[104]

• eMLE-Sig 2.0 by Mehdi Tibouchicite-ref-105[105] (implementation by Lorenz Pannycite-ref-106[106])

• HPPC by Ward Beullens;cite-ref-107[107] Pierre Briaud, Maxime Bros, and Ray Perlnercite-ref-108[108]

• ALTEQ by Markku-Juhani O. Saarinencite-ref-109[109] (implementation only?)

• Biscuit by Charles Bouillaguetcite-ref-110[110]

• MEDS by Markku-Juhani O. Saarinen and Ward Beullenscite-ref-111[111] (implementation only)

• FuLeeca by Felicitas Hörmann and Wessel van Woerdencite-ref-112[112]

• LESS by the LESS team (implementation only)cite-ref-113[113]

• DME-Sign by Markku-Juhani O. Saarinencite-ref-114[114] (implementation only?); Pierre Briaud, Maxime Bros, Ray Perlner, and Daniel Smith-Tonecite-ref-115[115]

• EHTv3 by Eamonn Postlethwaite and Wessel van Woerden;cite-ref-116[116] Keegan Ryan and Adam Suhlcite-ref-117[117]

• Enhanced pqsigRM by Thomas Debris-Alazard, Pierre Loisel and Valentin Vasseur;cite-ref-118[118] Pierre Briaud, Maxime Bros, Ray Perlner and Daniel Smith-Tonecite-ref-119[119]

• HAETAE by Markku-Juhani O. Saarinencite-ref-120[120] (implementation only?)

• HuFu by Markku-Juhani O. Saarinencite-ref-121[121]

• SDitH by Kevin Carrier and Jean-Pierre Tillich;cite-ref-122[122] Kevin Carrier, Valérian Hatey, and Jean-Pierre Tillichcite-ref-123[123]

• VOX by Hiroki Furue and Yasuhiko Ikematsucite-ref-124[124]

• AIMer by Fukang Liu, Mohammad Mahzoun, Morten Øygarden, Willi Meiercite-ref-125[125]

• SNOVA by Yasuhiko Ikematsu and Rika Akiyamacite-ref-126[126]

• PROV by Ludovic Perret, and River Moreira Ferreiracite-ref-127[127] (implementation only)

NIST deemed 14 submissions to pass to the second round.cite-ref-128[128]

| Type | Signature | Technique(s) Used | Hard Problem |

|---|---|---|---|

| Lattice | HAWK [ 129 ] | Hash-and-sign | lattice problems |

| Code-based | CROSS [ 130 ] | Fiat–Shamir heuristic | Syndrome Decoding Problem |

| Code-based | LESS [ 131 ] | Fiat–Shamir heuristic | Linear Equivalence Problem |

| MPC-in-the-Head | Mirath [ 132 ] (merge of MIRA and MiRitH) | "in the head", Fiat–Shamir heuristic | MinRank (matrix-based) |

| MPC-in-the-Head | MQOM [ 133 ] | "in the head", Fiat–Shamir heuristic | Multivariable Quadratic Problem |

| MPC-in-the-Head | PERK [ 134 ] | "in the head", Fiat–Shamir heuristic | Permuted Kernel Problem (matrix-based) |

| MPC-in-the-Head | RYDE [ 135 ] | "in the head", Fiat–Shamir heuristic | Rank Syndrome Decoding Problem (code-based) |

| MPC-in-the-Head | SDitH [ 136 ] | "in the head", Fiat–Shamir heuristic | Syndrome Decoding Problem (code-based) |

| Multivariate | MAYO [ 137 ] | Unbalanced Oil and Vinegar | Multivariable Quadratic Problem |

| Multivariate | QR-UOV [ 138 ] | Unbalanced Oil and Vinegar | Multivariable Quadratic Problem |

| Multivariate | SNOVA [ 139 ] | Unbalanced Oil and Vinegar | Multivariable Quadratic Problem |

| Multivariate | UOV [ 140 ] | Unbalanced Oil and Vinegar | Multivariable Quadratic Problem |

| Supersingular elliptic curve isogeny | SQIsign [ 141 ] | Fiat–Shamir heuristic | Endomorphism Ring Problem |

| Symmetric-based | FAEST [ 142 ] | "in the head", Fiat–Shamir heuristic | breaking AES |

• Advanced Encryption Standard process

• CAESAR Competition – Competition to design authenticated encryption schemes

• Lattice-based cryptography

• NIST hash function competition

cite-note-11. ↑ "Post-Quantum Cryptography PQC". 3 January 2017.

cite-note-22. ↑ "Post-Quantum Cryptography Standardization – Post-Quantum Cryptography". Csrc.nist.gov. 3 January 2017. Retrieved 31 January 2019.

cite-note-33. ↑ citerefmoody2020Moody, Dustin (24 November 2020). "The Future Is Now: Spreading the Word About Post-Quantum Cryptography". NIST.

cite-note-44. ↑ "Final Submission received". Archived from the original on 29 December 2017. Retrieved 29 December 2017.

cite-note-nistrelase2024-55. ↑ NIST Releases First 3 Finalized Post-Quantum Encryption Standards, NIST, August 13, 2024

cite-note-66. ↑ citerefhong2001Hong, Zhu (2001). "Survey of Computational Assumptions Used in Cryptography Broken or Not by Shor's Algorithm" (PDF).

cite-note-77. ↑ "NIST Released NISTIR 8105, Report on Post-Quantum Cryptography". 21 December 2016. Retrieved 5 November 2019.

cite-note-88. ↑ "NIST Asks Public to Help Future-Proof Electronic Information". NIST. 20 December 2016. Retrieved 5 November 2019.

cite-note-99. ↑ citerefcomputer-security-division2017Computer Security Division, Information Technology Laboratory (3 January 2017). "Round 1 Submissions – Post-Quantum Cryptography – CSRC". Csrc.nist.gov. Retrieved 31 January 2019.

cite-note-onboardsecurity-101. "NIST Post Quantum Crypto Submission". Archived from the original on 29 December 2017. Retrieved 29 December 2017.

cite-note-google-com-112. "Google Groups". Groups.google.com. Retrieved 31 January 2019.

cite-note-123. citerefqtesla-teamqTESLA team. "Efficient and post-quantum secure lattice-based signature scheme". qTESLA.org. Archived from the original on 9 December 2023. Retrieved 4 March 2024.

cite-note-134. "qTESLA". Microsoft Research. Archived from the original on 31 December 2022. Retrieved 4 March 2024.

cite-note-pqc-rollo-org-145. "ROLLO". Pqc-rollo.org. Retrieved 31 January 2019.

cite-note-156. RSA using 231 4096-bit primes for a total key size of 1 TiB. "Key almost fits on a hard drive" citerefbernstein2010Bernstein, Daniel (28 May 2010). "McBits and Post-Quantum RSA" (PDF). Retrieved 10 December 2019.

cite-note-167. citerefbernsteinheninger2017Bernstein, Daniel; Heninger, Nadia (19 April 2017). "Post-quantum RSA" (PDF). Retrieved 10 December 2019.

cite-note-1717. ↑ "Dear all, the following Python script quickly recovers the message from a given "Guess Again" ciphertext without knowledge of the private key" (PDF). Csrc.nist.gov. Retrieved 30 January 2019.

cite-note-1818. ↑ citerefpanny2017Panny, Lorenz (25 December 2017). "Fast key recovery attack against the "RVB" submission to #NISTPQC: t .... Computes private from public key". Twitter. Retrieved 31 January 2019.

cite-note-1919. ↑ "Comments on RaCoSS". Archived from the original on 26 December 2017. Retrieved 4 January 2018.

cite-note-2020. ↑ "Comments on HK17". Archived from the original on 5 January 2018. Retrieved 4 January 2018.

cite-note-2121. ↑ "Dear all, We have broken SRTPI under CPA and TPSig under KMA" (PDF). Csrc.nist.gov. Retrieved 30 January 2019.

cite-note-2222. ↑ citerefbeullensblackburn2018Beullens, Ward; Blackburn, Simon R. (2018). "Practical attacks against the Walnut digital signature scheme". Cryptology ePrint Archive.

cite-note-2323. ↑ citerefkotovmenshovushakov2018Kotov, Matvei; Menshov, Anton; Ushakov, Alexander (2018). "An attack on the walnut digital signature algorithm". Cryptology ePrint Archive.

cite-note-2424. ↑ citerefyuducas2018Yu, Yang; Ducas, Léo (2018). "Learning strikes again: the case of the DRS signature scheme". Cryptology ePrint Archive.

cite-note-2525. ↑ citerefbarellicouvreur2018Barelli, Elise; Couvreur, Alain (2018). "An efficient structural attack on NIST submission DAGS". arXiv:1805.05429 [cs.CR].

cite-note-2626. ↑ citereflequesnetillich2018Lequesne, Matthieu; Tillich, Jean-Pierre (2018). "Attack on the Edon-K Key Encapsulation Mechanism". arXiv:1802.06157 [cs.CR].

cite-note-2727. ↑ citerefcouvreurlequesnetillich2018Couvreur, Alain; Lequesne, Matthieu; Tillich, Jean-Pierre (2018). "Recovering short secret keys of RLCE in polynomial time". arXiv:1805.11489 [cs.CR].

cite-note-2828. ↑ citerefbernsteingroot-bruinderinklangelange2017Bernstein, Daniel J.; Groot Bruinderink, Leon; Lange, Tanja; Lange, Lorenz (2017). "Hila5 Pindakaas: On the CCA security of lattice-based encryption with error correction". Cryptology ePrint Archive.

cite-note-2929. ↑ "Official Comments" (PDF). Csrc.nist.gov. 13 September 2018.

cite-note-3030. ↑ citerefdebris-alazardtillich2018Debris-Alazard, Thomas; Tillich, Jean-Pierre (2018). "Two attacks on rank metric code-based schemes: RankSign and an Identity-Based-Encryption scheme". arXiv:1804.02556 [cs.CR].

cite-note-3131. ↑ "I am afraid the parameters in this proposal have at most 4 to 6-bits security under the Information Set Decoding (ISD) attack" (PDF). Csrc.nist.gov. Retrieved 30 January 2019.

cite-note-3232. ↑ citereflautan2019Lau, Terry Shue Chien; Tan, Chik How (31 January 2019). "Key Recovery Attack on McNie Based on Low Rank Parity Check Codes and Its Reparation". In Inomata, Atsuo; Yasuda, Kan (eds.). Advances in Information and Computer Security. Lecture Notes in Computer Science. Vol. 11049. Springer International Publishing. pp. 19–34. doi:10.1007/978-3-319-97916-8_2. ISBN 978-3-319-97915-1.

cite-note-3333. ↑ citerefcomputer-security-division2017Computer Security Division, Information Technology Laboratory (3 January 2017). "Round 2 Submissions – Post-Quantum Cryptography – CSRC". Csrc.nist.gov. Archived from the original on 14 November 2019. Retrieved 31 January 2019.

cite-note-auto-348. citerefschwabeSchwabe, Peter. "CRYSTALS". Pq-crystals.org. Retrieved 31 January 2019.

cite-note-359. "FrodoKEM". Frodokem.org. Retrieved 31 January 2019.

cite-note-3610. citerefschwabeSchwabe, Peter. "NewHope". Newhopecrypto.org. Retrieved 31 January 2019.

cite-note-3711. "NTRU Prime: Intro". Archived from the original on 1 September 2019. Retrieved 30 January 2019.

cite-note-3812. "SABER". Retrieved 17 June 2019.

cite-note-3913. "ThreeBears". SourceForge.net. Retrieved 31 January 2019.

cite-note-4014. "Falcon". Falcon. Retrieved 26 June 2019.

cite-note-4115. "BIKE – Bit Flipping Key Encapsulation". Bikesuite.org. Retrieved 31 January 2019.

cite-note-4216. "HQC". Pqc-hqc.org. Retrieved 31 January 2019.

cite-note-4317. "LEDAkem Key Encapsulation Module". Ledacrypt.org. Retrieved 31 January 2019.

cite-note-4418. "LEDApkc Public Key Cryptosystem". Ledacrypt.org. Retrieved 31 January 2019.

cite-note-4519. "NTS-Kem". Archived from the original on 29 December 2017. Retrieved 29 December 2017.

cite-note-4620. "RQC". Pqc-rqc.org. Retrieved 31 January 2019.

cite-note-4721. "Sphincs". Sphincs.org. Retrieved 19 June 2023.

cite-note-4822. "GeMSS". Archived from the original on 31 January 2019. Retrieved 30 January 2019.

cite-note-4923. "LUOV -- An MQ signature scheme". Retrieved 22 January 2020.

cite-note-5024. "MQDSS post-quantum signature". Mqdss.org. Retrieved 31 January 2019.

cite-note-5125. "SIKE – Supersingular Isogeny Key Encapsulation". Sike.org. Retrieved 31 January 2019.

cite-note-5226. "Picnic. A Family of Post-Quantum Secure Digital Signature Algorithms". microsoft.github.io. Retrieved 26 February 2019.

cite-note-2ndround-5353. ↑ citerefmoodyalagicaponcooper2020Moody, Dustin; Alagic, Gorjan; Apon, Daniel C.; Cooper, David A.; Dang, Quynh H.; Kelsey, John M.; Liu, Yi-Kai; Miller, Carl A.; Peralta, Rene C.; Perlner, Ray A.; Robinson, Angela Y.; Smith-Tone, Daniel C.; Alperin-Sheriff, Jacob (2020). "Status Report on the Second Round of the NIST Post-Quantum Cryptography Standardization Process". doi:10.6028/NIST.IR.8309. S2CID 243755462. Retrieved 23 July 2020.

cite-note-5454. ↑ Third PQC Standardization Conference - Session I Welcome/Candidate Updates, 10 June 2021, retrieved 6 July 2021

cite-note-5555. ↑ citerefcomputer-security-division2021Computer Security Division, Information Technology Laboratory (10 February 2021). "Third PQC Standardization Conference | CSRC". CSRC | NIST. Retrieved 6 July 2021.

cite-note-5656. ↑ "Submission Requirements and Evaluation Criteria" (PDF).

cite-note-5757. ↑ citerefbeullens2022Beullens, Ward (2022). "Breaking Rainbow Takes a Weekend on a Laptop" (PDF). Eprint.iacr.org.

cite-note-5858. ↑ citerefgrubbsmarampaterson2021Grubbs, Paul; Maram, Varun; Paterson, Kenneth G. (2021). "Anonymous, Robust Post-Quantum Public Key Encryption". Cryptology ePrint Archive.

cite-note-5959. ↑ citerefkarabulutaysu2021Karabulut, Emre; Aysu, Aydin (2021). "Falcon Down: Breaking Falcon Post-Quantum Signature Scheme through Side-Channel Attacks". Cryptology ePrint Archive.

cite-note-6060. ↑ "NIST Announces First Four Quantum-Resistant Cryptographic Algorithms". NIST. 5 July 2022. Retrieved 9 July 2022.

cite-note-6161. ↑ "Selected Algorithms 2022". CSRC | NIST. 5 July 2022. Retrieved 9 July 2022.

cite-note-6262. ↑ "Round 4 Submissions". CSRC | NIST. 5 July 2022. Retrieved 9 July 2022.

cite-note-6327. "SIKE Team - Foreword and postscript" (PDF).

cite-note-6464. ↑ citerefgoodin2022Goodin, Dan (2 August 2022). "Post-quantum encryption contender is taken out by single-core PC and 1 hour". Ars Technica. Retrieved 6 August 2022.

cite-note-6565. ↑ https://nvlpubs.nist.gov/nistpubs/ir/2025/NIST.IR.8545.pdf

cite-note-nist250311-6666. ↑ "NIST Selects HQC as Fifth Algorithm for Post-Quantum Encryption". NIST. 11 March 2025. Retrieved 20 May 2025.

cite-note-6767. ↑ https://nvlpubs.nist.gov/nistpubs/ir/2025/NIST.IR.8545.pdf

cite-note-6868. ↑ citerefmoody2023Moody, Dustin (17 July 2023). "Onramp submissions are posted!".

cite-note-6969. ↑ "Digital Signature Schemes". csrc.nist.gov. 29 August 2022. Retrieved 17 July 2023.

cite-note-7028. "SMAUG & HAETAE - HAETAE".

cite-note-7129. "Hawk".

cite-note-7230. "Hufu".

cite-note-7331. "RACCOON – Not just a signature, a whole family of it !".

cite-note-7432. "masksign/raccoon: Raccoon Signature Scheme -- Reference Code". GitHub.

cite-note-7533. "Squirrels - Introduction".

cite-note-7634. "CROSS crypto".

cite-note-7735. "FuLeeca: A Lee-based Signature Scheme - Lehrstuhl für Nachrichtentechnik".

cite-note-7836. "LESS project".

cite-note-7937. "MEDS".

cite-note-8038. "WAVE".

cite-note-8139. "MIRA".

cite-note-8240. "MiRitH".

cite-note-8341. "MQOM".

cite-note-8442. "PERK".

cite-note-8543. "RYDE".

cite-note-8644. "SD-in-the-Head".

cite-note-0-8787. citerefsmith-tone2023Smith-Tone, Daniel (17 July 2023). "OFFICIAL COMMENT: 3WISE".

cite-note-8845. "Home".

cite-note-8946. "OFFICIAL COMMENT: DME Key Recovery Attack". groups.google.com. Retrieved 10 September 2023.

cite-note-9047. "MAYO".

cite-note-9148. "PROV".

cite-note-9249. "QR-UOV".

cite-note-9350. "SNOVA". snova.pqclab.org. Retrieved 23 September 2023.

cite-note-9451. "TUOV".

cite-note-9552. "UOV".

cite-note-9653. "VOX".

cite-note-9754. "SQIsign".

cite-note-9855. "AIMer Signature".

cite-note-9956. "Come and join the FAEST | FAEST Signature Algorithm".

cite-note-10057. "ALTEQ".

cite-note-101101. ↑ citereftibouchi2023Tibouchi, Mehdi (17 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: EagleSign".

cite-note-102102. ↑ citerefbernstein2023Bernstein, D.J. (17 July 2023). "OFFICIAL COMMENT: KAZ-SIGN".

cite-note-103103. ↑ citereffluhrer2023Fluhrer, Scott (17 July 2023). "KAZ-SIGN".

cite-note-104104. ↑ citerefpanny2023Panny, Lorenz (17 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: Xifrat1-Sign.I".

cite-note-105105. ↑ citereftibouchi2023Tibouchi, Mehdi (18 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: EagleSign".

cite-note-106106. ↑ citerefpannyPanny, Lorenz. "Round 1 (Additional Signatures) OFFICIAL COMMENT: EagleSign". groups.google.com. Retrieved 13 May 2025.

cite-note-107107. ↑ citerefbeullens2023Beullens, Ward (18 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: HPPC".

cite-note-108108. ↑ citerefperlner2023Perlner, Ray (21 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: HPPC".

cite-note-109109. ↑ citerefsaarinen2023Saarinen, Markku-Juhani O. (18 July 2023). "OFFICIAL COMMENT: ALTEQ".

cite-note-110110. ↑ citerefbouillaguet2023Bouillaguet, Charles (19 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: Biscuit".

cite-note-111111. ↑ citerefniederhagen2023Niederhagen, Ruben (19 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: MEDS".

cite-note-112112. ↑ citerefvan-woerden2023van Woerden, Wessel (20 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: FuLeeca".

cite-note-113113. ↑ citerefpersichetti2023Persichetti, Edoardo (21 July 2023). "OFFICIAL COMMENT: LESS".

cite-note-114114. ↑ citerefsaarinenSaarinen, Markku-Juhani O. "Round 1 (Additional Signatures) OFFICIAL COMMENT: DME-Sign".

cite-note-115115. ↑ "OFFICIAL COMMENT: DME Key Recovery Attack". groups.google.com. Retrieved 10 September 2023.

cite-note-116116. ↑ citerefvan-woerden2023van Woerden, Wessel (25 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: EHTv3".

cite-note-117117. ↑ citerefsuhl2023Suhl, Adam (29 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: EHT".

cite-note-118118. ↑ citerefvasseur2023VASSEUR, Valentin (29 July 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: Enhanced pqsigRM".

cite-note-119119. ↑ "Round 1 (Additional Signatures) OFFICIAL COMMENT: Enhanced pqsigRM". groups.google.com. Retrieved 30 September 2023.

cite-note-120120. ↑ citerefsaarinen2023Saarinen, Markku-Juhani O. (27 July 2023). "Buffer overflows in HAETAE / On crypto vs implementation errors".

cite-note-121121. ↑ citerefsaarinen2023Saarinen, Markku-Juhani O. (29 July 2023). "HuFu: Big-flipping forgeries and buffer overflows".

cite-note-122122. ↑ citerefcarrier2023Carrier, Kevin (3 August 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: SDitH".

cite-note-123123. ↑ citerefcarrierhateytillich2023Carrier, Kevin; Hatey, Valérian; Tillich, Jean-Pierre (5 December 2023). "Projective Space Stern Decoding and Application to SDitH". arXiv:2312.02607 [cs.IT].

cite-note-124124. ↑ citereffurue2023Furue, Hiroki (28 August 2023). "Round 1 (Additional Signatures) OFFICIAL COMMENT: VOX".

cite-note-125125. ↑ citerefliumahzoun-ygardenmeier2023Liu, Fukang; Mahzoun, Mohammad; Øygarden, Morten; Meier, Willi (10 November 2023). "Algebraic Attacks on RAIN and AIM Using Equivalent Representations". IACR ePrint (2023/1133).

cite-note-126126. ↑ citerefikematsuakiyama2024Ikematsu, Yasuhiko; Akiyama, Rika (2024), Revisiting the security analysis of SNOVA, retrieved 28 January 2024

cite-note-127127. ↑ citerefferreiraperret2024Ferreira, River Moreira; Perret, Ludovic (2024), Polynomial-Time Key-Recovery Attack on the ${\tt NIST}$ Specification of ${\tt PROV}$, retrieved 4 April 2024

cite-note-128128. ↑ citerefmoody2024Moody, Dustin (24 October 2024). "Status Report on the First Round of the Additional Digital Signature Schemes for the NIST Post-Quantum Cryptography Standardization Process".

cite-note-12958. "Hawk".

cite-note-13059. "CROSS crypto".

cite-note-13160. "LESS project".

cite-note-13261. "Mirath".

cite-note-13362. "MQOM".

cite-note-13463. "PERK".

cite-note-13564. "RYDE".

cite-note-13665. "SD-in-the-Head".

cite-note-13766. "MAYO".

cite-note-13867. "QR-UOV".

cite-note-13968. "SNOVA". snova.pqclab.org. Retrieved 23 September 2023.

cite-note-14069. "UOV".

cite-note-14170. "SQIsign".

cite-note-14271. "Come and join the FAEST | FAEST Signature Algorithm".

• NIST's official Website on the standardization process

• Post-quantum cryptography website by djb