View source for Kyber

{{Short description|Quantum-safe key encapsulation mechanism}}
{{For-multi|the fictional crystals|Lightsaber|the computing I/O scheduler|I/O scheduling|other uses|Khyber (disambiguation)}}
'''Kyber''' is a [[key encapsulation mechanism]] (KEM) designed to be resistant to [[cryptanalysis|cryptanalytic]] attacks with future powerful [[quantum computing|quantum computers]]. It is used to establish a [[shared secret]] between two communicating parties without an ([[IND-CCA2]]) attacker in the transmission system being able to decrypt it. This [[public-key cryptography|asymmetric cryptosystem]] uses a variant of the [[learning with errors]] [[lattice problem]] as its basic [[trapdoor function]]. It won the [[NIST Post-Quantum Cryptography Standardization|NIST competition]] for the first [[post-quantum cryptography]] (PQ) standard.<ref>{{citation |last=Moody |first=Dustin |date=2022 |title=Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process |url=https://nvlpubs.nist.gov/nistpubs/ir/2022/NIST.IR.8413.pdf |location=Gaithersburg, MD |pages=NIST IR 8413 |doi=10.6028/nist.ir.8413|s2cid=247903639 }}</ref> NIST calls its standard '''Module-Lattice-Based Key-Encapsulation Mechanism''' ('''ML-KEM''').<ref>{{cite web |last1=Technology |first1=National Institute of Standards and |title=Module-Lattice-Based Key-Encapsulation Mechanism Standard [FIPS 203]|url=https://csrc.nist.gov/pubs/fips/203/final |publisher=U.S. Department of Commerce |language=en |date=13 August 2024}}</ref>
== Properties ==
The system is based on the module [[learning with errors]] (M-LWE) problem, in conjunction with [[cyclotomic field|cyclotomic]] [[Ring (mathematics)|rings]].<ref name="Moody2019"/> Recently, there has also been a tight formal mathematical security [[reduction (mathematics)|reduction]] of the ring-LWE problem to MLWE.<ref name="NISTIR 8309"/><ref name="Peikert&Pepin"/> Compared to competing PQ methods, it has typical advantages of lattice-based methods, e.g. in regard to runtime as well as the size of the ciphertexts and the key material.<ref name="Basso2021"/>
Variants with different security levels have been defined: Kyber512 ([[NIST]] security level 1, ≈[[Advanced Encryption Standard|AES]] 128), Kyber768 (NIST security level 3, ≈AES 192), and Kyber1024 (NIST security level 5, ≈AES 256).<ref name="PQSecure"/> At the Kyber768 level, the secret keys are 2400 bytes in size, the public keys 1184, and the ciphertexts 1088.<ref name="Bos et al."/><ref name="v3.02"/>
With an accordingly optimized implementation, 4 kilobytes of memory can be sufficient for the cryptographic operations.<ref name="nttm4"/> For a [[online chat|chat]] encryption scenario using liboqs, replacing the extremely efficient, non-quantum-safe [[Elliptic-curve Diffie–Hellman|ECDH]] key exchange using [[Curve25519]] was found to increase [[runtime (program lifecycle phase)|runtime]] by a factor of about 2.3 (1.5–7), an estimated 2.3-fold (1.4–3.1) increase in energy consumption, and have about 70 times (48–92) more data [[overhead (computing)|overhead]].<ref name="Duits19"/> Internal hashing operations account for the majority of the runtime, which would thus potentially benefit greatly from corresponding [[hardware acceleration]].
== Development ==
Kyber is derived from a method published in 2005 by [[Oded Regev (computer scientist)|Oded Regev]], developed by developers from Europe and North America, who are employed by various government universities or research institutions, or by private companies, with funding from the [[European Commission]], Switzerland, the Netherlands, and Germany.<ref name="ack">[https://pq-crystals.org/] {{Bare URL inline|date=August 2022}}</ref> They also developed the related and complementary signature scheme ''Dilithium'', as another component of their "Cryptographic Suite for Algebraic Lattices" (CRYSTALS). Like other PQC-KEM methods, Kyber makes extensive use of [[cryptographic hash function|hashing]] internally. In Kyber's case, variants of Keccak ([[SHA-3]]/SHAKE) are used here, to [[Pseudorandom number generator|generate pseudorandom numbers]], among other things.<ref name="nttm4"/> In 2017 the method was submitted to the US [[National Institute of Standards and Technology]] (NIST) for its public [[NIST Post-Quantum Cryptography Standardization|selection process]] for a first standard for quantum-safe cryptographic primitives (NISTPQC). It is the only key encapsulation mechanism that has been selected for standardization at the end of the third round of the NIST standardization process.<ref name="NISTIR 8309"/> According to a footnote the report announcing the decision, it is conditional on the execution of various [[patent]]-related agreements, with [[NTRU]] being a fallback option. Currently, a fourth round of the standardization process is underway, with the goal of standardizing an additional KEM. In the second phase of the selection process, several parameters of the algorithm were adjusted and the compression of the public keys was dropped.<ref name="nttm4"/> Most recently, NIST paid particular attention to costs in terms of runtime and complexity for implementations that mask runtimes in order to prevent corresponding [[side-channel attack]]s (SCA).<ref name="NISTIR 8309"/>
=== Evolution ===
Kyber underwent changes during the NIST standardization process. In particular, in the submission for round 2 (so called ''Kyber v2''), the following features were changed:<ref name=v2>Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, Damien Stehlé. [https://csrc.nist.gov/CSRC/media/Presentations/crystals-kyber-round-2-presentation/images-media/crystals-kyber-schwabe.pdf CRYSTALS–Kyber] (Round 2 presentation) August 23, 2019.</ref>
* public key compression removed (due to NIST comments on the security proof);
* parameter ''q'' reduced to 3329 (from 7681);
* ciphertext compression parameters changed;
* [[number-theoretic transform]] (NTT) definition changed along the lines of [[NTTRU]] for faster polynomial multiplication;
* noise parameter reduced to {{nowrap|1=''η'' = 2}} for faster noise sampling;
* public key representation changed to NTT domain in order to save the NTT operations.
Submission to round 3 underwent further tweaks:<ref name=r3>Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, Damien Stehlé. [https://csrc.nist.gov/CSRC/media/Presentations/crystals-kyber-round-3-presentation/images-media/session-7-crystals-kyber-schwabe.pdf CRYSTALS–Kyber] (Round 3 presentation) June 9, 2021.</ref>
* the use of [[Fujisaki–Okamoto transformation]] (FO transform) modified;
* noise level increased and ciphertext compression reduced for the level 1 parameter set;
* sampling algorithm improved.
== Usage ==
The developers have released a [[reference implementation]] into the [[public domain]] (or under [[CC0]]), which is written in [[C (programming language)|C]].<ref name="PD"/> The [[library (computing)|program library]] ''liboqs'' of the [[Open Quantum Safe]] (OQS) project contains an implementation based<ref>{{cite web |url=https://openquantumsafe.org/liboqs/algorithms/kem/Kyber |title=Kyber – Open Quantum Safe |access-date=2022-01-13 |archive-date=2021-04-20 |archive-url=https://web.archive.org/web/20210420002308/https://openquantumsafe.org/liboqs/algorithms/kem/kyber |url-status=dead }}</ref> on that.<ref name="Duits19"/> OQS also maintains a quantum-safe Provider module for [[OpenSSL]] 3.x,<ref name="PQ OpenSSL"/> and has integrated its code into [[BoringSSL]] and [[wolfSSL]].<ref name="wolfSSL-liboqs"/> There are a handful of implementations using various other programming languages from third-party developers, including JavaScript and Java.<ref>{{cite web |url=https://github.com/fisherstevenk/kyberJCE |title = CRYSTALS KYBER Java|website = [[GitHub]] |date = 25 October 2021 }}</ref><ref>{{cite web |url=https://github.com/antontutoveanu/crystals-kyber-javascript |title = CRYSTALS-KYBER JavaScript |website = [[GitHub]] |date = 11 December 2021 }}</ref><ref>{{cite web |url=https://git.schwanenlied.me/yawning/kyber |title=Yawning/Kyber |access-date=2022-01-13 |archive-date=2021-07-28 |archive-url=https://web.archive.org/web/20210728002417/https://git.schwanenlied.me/yawning/kyber |url-status=dead }}</ref> Various (free) optimized hardware implementations exist, including one that is resistant to side-channel attacks.<ref name="Dang et al."/><ref name="Jati et al."/> The German [[Federal Office for Information Security]] is aiming for implementation in [[Mozilla Thunderbird|Thunderbird]], and in this context also an implementation in the [[Botan (programming library)|Botan]] program library and corresponding adjustments to the [[OpenPGP]] standard.<ref name="Thunderbird"/>
In 2023, the encrypted messaging service [[Signal (messaging app)|Signal]] implemented [[PQXDH]], a Kyber-based post-quantum encryption algorithm, to their [[Signal Protocol]] which is used by [[WhatsApp]] and others.<ref name="Signal"/><ref>{{cite web |title=Signal Messenger Introduces PQXDH Quantum-Resistant Encryption |url=https://thehackernews.com/2023/09/signal-messenger-introduces-pqxdh.html |access-date=2023-09-22 |website=The Hacker News |language=en}}</ref>
== Implementations ==
* [[wolfSSL]]
* libOQS
== References ==
{{Reflist|refs=
<ref name="Moody2019">[https://www.maths.ox.ac.uk/system/files/attachments/What%20was%20NIST%20thinking.pdf What was NIST thinking?]
(PDF-Datei)</ref>
<ref name="NISTIR 8309">[https://nvlpubs.nist.gov/nistpubs/ir/2022/NIST.IR.8413-upd1.pdf Status Report on the Second Round of the NIST PQC Standardization Process] (PDF-Datei)</ref>
<ref name="Peikert&Pepin">
{{citation
|author1=Chris Peikert, Zachary Pepin
|periodical=Theory of Cryptography
|title=Algebraically Structured LWE, Revisited
|series=Lecture Notes in Computer Science
|volume=11891
|publisher=Springer International Publishing |publication-place=Cham
|pages=1–23
|isbn=978-3-030-36029-0
|date=2019
|language=German
|doi=10.1007/978-3-030-36030-6_1 |s2cid=199455447
|url=http://web.eecs.umich.edu/~cpeikert/pubs/structured-lwe.pdf
}}</ref>
<ref name="Basso2021">[https://www.cs.bham.ac.uk/~axb1471/QCSseminar.pdf Lattice-based cryptography and SABER – Andrea Basso] (PDF; 2,0&nbsp;MB)</ref>
<ref name="PQSecure">[https://www.pqsecurity.com/wp-content/uploads/2020/07/Round-3.pdf Overview of NIST Round 3 Post-Quantum cryptography Candidates] (PDF; 157&nbsp;kB)</ref>
<ref name="Bos et al.">
{{citation
|author=Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, and Damien Stehlé
|title=CRYSTALS – Kyber: A CCA-Secure Module-Lattice-Based KEM
|periodical=2018 IEEE European Symposium on Security and Privacy, EuroS&P 2018.
|publisher=IEEE
|pages=353–367
|date=2018
|url=https://eprint.iacr.org/2017/634
|isbn=978-1-5386-4228-3
|doi=10.1109/EuroSP.2018.00032 |s2cid=20449721
|hdl=2066/195423|hdl-access=free
}}</ref>
<ref name="v3.02">https://pq-crystals.org/kyber/data/kyber-specification-round3-20210804.pdf {{Bare URL PDF|date=March 2022}}</ref>
<ref name="nttm4">
{{citation
|author=Leon Botros, Matthias J. Kannwischer, Peter Schwabe
|periodical=Progress in Cryptology – AFRICACRYPT 2019
|title=Memory-Efficient High-Speed Implementation of Kyber on Cortex-M4
|series=Lecture Notes in Computer Science
|publisher=Springer International Publishing
|publication-place=Cham
|pages=209–228
|isbn=978-3-030-23696-0
|date=2019
|volume=11627
|language=German
|doi=10.1007/978-3-030-23696-0_11 |s2cid=174775508
|url=https://kannwischer.eu/papers/2019_nttm4.pdf
}}</ref>
<ref name="Duits19">
{{citation
|author=Ines Duits
|editor-surname1= University of Twente
|title=The Post-Quantum Signal Protocol: Secure Chat in a Quantum World
|date=2019-02-05
|language=German
|url=https://essay.utwente.nl/77239/1/Duits_MA_EEMCS.pdf
}}</ref>
<ref name="PD">[https://github.com/pq-crystals/kyber/blob/master/LICENSE Kyber/LICENSE at master · pq-crystals/kyber · GitHub]</ref>
<ref name="PQ OpenSSL">
{{cite web |title=OQS Provider for OpenSSL 3.x
|periodical=oqs-provider
|publisher=
|url=https://github.com/open-quantum-safe/oqs-provider
|url-status=
|format=
|access-date=
|archive-url= |archive-date= |last= |date= |year=
|language=en-US
|pages=
}}</ref>
<ref name="wolfSSL-liboqs">
{{cite web
|title=wolfSSL and libOQS Integration
|periodical=WolfSSL-Website
|publisher=
|url=https://www.wolfssl.com/wolfssl-liboqs-integration/
|url-status=
|format=
|access-date=
|archive-url=
|archive-date=
|last=
|date=2021-09-01
|language=en-US
|pages=
}}</ref>
<ref name="Dang et al.">
{{citation
|author=B. Dang, Kamyar Mohajerani, K. Gaj
|title=High-Speed Hardware Architectures and Fair FPGA Benchmarking
|date=2021
|language=German
|url=https://csrc.nist.gov/CSRC/media/Events/third-pqc-standardization-conference/documents/accepted-papers/gaj-high-speed-hardware-gmu-pqc2021.pdf
}}</ref>
<ref name="Jati et al.">
{{citation |surname1=Arpan Jati, Naina Gupta, A. Chattopadhyay, S. Sanadhya
|periodical=IACR Cryptol. ePrint Arch.
|title=A Configurable Crystals-Kyber Hardware Implementation with Side-Channel Protection
|date=2021
|language=German
|url=https://eprint.iacr.org/2021/1189.pdf
}}</ref>
<ref name="Thunderbird">
{{Cite web
|url=https://www.evergabe-online.de/tenderdetails.html?id=397181
|title = E-Vergabe, die Vergabeplattform des Bundes
}}</ref>
<ref name="Signal">
{{cite web
|url=https://github.com/signalapp/libsignal/commit/ff09619432e19e96231ebed913fe4433f26ee0d2
|title = Add Kyber KEM and implement PQXDH protocol
|website = [[GitHub]]
}}</ref>
}}
== External links ==
* {{Official website|https://pq-crystals.org/kyber/}}
* {{GitHub|pq-crystals/kyber}}
* original method by {{citation |surname1=Oded Regev |periodical=Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC '05) |title=On lattices, learning with errors, random linear codes, and cryptography |publication-place=Baltimore, MD, USA |publisher=ACM Press |page=84 |isbn=978-1-58113-960-0 |date=2005 |language=German |doi=10.1145/1060590.1060603 |s2cid=53223958 |url=http://portal.acm.org/citation.cfm?doid=1060590.1060603 |arxiv=2401.03703 }}
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