Kyber

For the fictional crystals, see Lightsaber. For the computing I/O scheduler, see I/O scheduling. For other uses, see Khyber (disambiguation).

Kyber is a key encapsulation mechanism (KEM) designed to be resistant to cryptanalytic attacks with future powerful 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 asymmetric cryptosystem uses a variant of the learning with errors lattice problem as its basic trapdoor function. It won the NIST competition for the first post-quantum cryptography (PQ) standard.^[1]

Properties

The system is based on the module learning with errors (M-LWE) problem, in conjunction with cyclotomic rings.^[2] Recently, there has also been a tight formal mathematical security reduction of the ring-LWE problem to MLWE.^[3][4] 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.^[5] Variants with different security levels have been defined: Kyber512 (NIST security level 1, ≈AES 128), Kyber768 (NIST security level 3, ≈AES 192), and Kyber1024 (NIST security level 5, ≈AES 256).^[6] At a complexity of 161 bits, the secret keys are 2400, the public keys 1184, and the ciphertexts 1088 bytes in size.^[7][8] With an accordingly optimized implementation, 4 kilobytes of memory can be sufficient for the cryptographic operations.^[9] For a chat encryption scenario using liboqs, replacing the extremely efficient, non-quantum-safe ECDH key exchange using Curve25519 was found to increase 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.^[10] 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, 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.^[11] 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 hashing internally. In Kyber's case, variants of Keccak (SHA-3/SHAKE) are used here, to generate pseudorandom numbers, among other things.^[9] In 2017 the method was submitted to the US National Institute of Standards and Technology (NIST) for its public 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.^[3] 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.^[9] 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 attacks (SCA).^[3]

Evolution

During the NIST standardization process, Kyber has undergone changes. In particular, in the submission for round 2 (so called Kyber v2), the following features have been changed:^[12]

• 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 ${\displaystyle \eta =2}$  for faster noise sampling;
• public key representation is changed to NTT domain in order to save the NTT operations.

Submission to round 3 underwent further tweaks:^[13]

• 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.^[14] The program library liboqs of the Open Quantum Safe (OQS) project contains an implementation based^[15] on that.^[10] OQS also maintains a quantum-safe development branch of OpenSSL,^[16] has integrated it into BoringSSL, and its code has also been integrated into WolfSSL.^[17] There are a handful of implementations using various other programming languages from third-party developers, including JavaScript and Java.^[18][19][20] Various (free) optimized hardware implementations exist, including one that is resistant to side-channel attacks.^[21][22] The German Federal Office for Information Security is aiming for implementation in Thunderbird, and in this context also an implementation in the Botan program library and corresponding adjustments to the OpenPGP standard.^[23] In 2023, the encrypted messaging service Signal implemented PQXDH, a Kyber-based post-quantum encryption algorithm, to their Signal Protocol which is used by WhatsApp and others.^[24][25]

References

1. Moody, Dustin (2022). "Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process" (PDF). Gaithersburg, MD: NIST IR 8413. doi:10.6028/nist.ir.8413. S2CID 247903639. {{cite journal}}: Cite journal requires |journal= (help)
2. What was NIST thinking? (PDF-Datei)
3. Status Report on the Second Round of the NIST PQC Standardization Process (PDF-Datei)
4. Chris Peikert, Zachary Pepin (2019), "Algebraically Structured LWE, Revisited" (PDF), Theory of Cryptography, Lecture Notes in Computer Science (in German), Cham: Springer International Publishing, vol. 11891, pp. 1–23, doi:10.1007/978-3-030-36030-6_1, ISBN 978-3-030-36029-0, S2CID 199455447
5. Lattice-based cryptography and SABER – Andrea Basso (PDF; 2,0 MB)
6. Overview of NIST Round 3 Post-Quantum cryptography Candidates (PDF; 157 kB)
7. Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, and Damien Stehlé (2018), "CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM", 2018 IEEE European Symposium on Security and Privacy, EuroS&P 2018., IEEE, pp. 353-367, doi:10.1109/EuroSP.2018.00032, ISBN 978-1-5386-4228-3, S2CID 20449721{{citation}}: CS1 maint: multiple names: authors list (link)
8. https://pq-crystals.org/kyber/data/kyber-specification-round3-20210804.pdf^{[bare URL PDF]}
9. Leon Botros, Matthias J. Kannwischer, Peter Schwabe (2019), "Memory-Efficient High-Speed Implementation of Kyber on Cortex-M4" (PDF), Progress in Cryptology – AFRICACRYPT 2019, Lecture Notes in Computer Science (in German), Cham: Springer International Publishing, vol. 11627, pp. 209–228, doi:10.1007/978-3-030-23696-0_11, ISBN 978-3-030-23696-0, S2CID 174775508{{citation}}: CS1 maint: multiple names: authors list (link)
10. Ines Duits (2019-02-05), University of Twente (ed.), The Post-Quantum Signal Protocol: Secure Chat in a Quantum World (PDF) (in German)
11. https://pq-crystals.org/^{[bare URL]}
12. Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, Damien Stehlé. CRYSTALS–Kyber (Round 2 presentation) August 23, 2019.
13. Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, Damien Stehlé. CRYSTALS–Kyber (Round 3 presentation) June 9, 2021.
14. Kyber/LICENSE at master · pq-crystals/kyber · GitHub
15. . Archived from the original on 2021-04-20. Retrieved 2022-01-13.
16. "Post-Quantum TLS". Microsoft Research.
17. "wolfSSL and libOQS Integration". WolfSSL-Website. 2021-09-01.
18. "CRYSTALS KYBER Java". GitHub. 25 October 2021.
19. "CRYSTALS-KYBER JavaScript". GitHub. 11 December 2021.
20. . Archived from the original on 2021-07-28. Retrieved 2022-01-13. {{cite web}}: External link in |title= (help)
21. B. Dang, Kamyar Mohajerani, K. Gaj (2021), High-Speed Hardware Architectures and Fair FPGA Benchmarking (PDF) (in German){{citation}}: CS1 maint: multiple names: authors list (link)
22. Arpan Jati, Naina Gupta, A. Chattopadhyay, S. Sanadhya (2021), "A Configurable Crystals-Kyber Hardware Implementation with Side-Channel Protection" (PDF), IACR Cryptol. ePrint Arch. (in German){{citation}}: CS1 maint: multiple names: authors list (link)
23. "E-Vergabe, die Vergabeplattform des Bundes".
24. "Add Kyber KEM and implement PQXDH protocol". GitHub.
25. "Signal Messenger Introduces PQXDH Quantum-Resistant Encryption". The Hacker News. Retrieved 2023-09-22.

External links

• Official website
• kyber on GitHub
• original method by Oded Regev (2005), "On lattices, learning with errors, random linear codes, and cryptography", Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC '05) (in German), Baltimore, MD, USA: ACM Press, p. 84, doi:10.1145/1060590.1060603, ISBN 978-1-58113-960-0, S2CID 53223958