Ah, that actually wasn't the debacle I had in mind; I'm not too familiar with the details of the Rainbow concerns unfortunately. With respect to the shortest v

Ah, that actually wasn't the debacle I had in mind; I'm not too familiar with the details of the Rainbow concerns unfortunately. With respect to the shortest vector problem (SVP) being a point of contention among NIST PQC participants, two of the round 3 finalists are based on lattice cryptography, with NTRU directly relying on the hardness of SVP. The two concerns are: 1. The risks of lattice-based cryptography are poorly understood [1], [2] 2. Research progress into attacks on lattice-based cryptography have been fruitful during the NIST PQC process [1], [3]. From what I've gathered as a layperson, much of these concerns have been voiced by Daniel J. Bernstein. Bernstein contributed to the NTRU Prime software [4], which was used in OpenSSH 9 (I'll circle back to this point). As a consequence of these two concerns, the main argument seems to be that NIST should at least provide warnings [6] on the risks of lattice cryptography, particularly with regard to the use of cyclotomics by one of the finalists [5]. A common thread amongst these criticisms seems to be a distrust of NIST guidelines (a point that is also echoed by this ML backdoor paper). This has evidently stirred some bad blood between NIST workers and Bernstein [7], [8]. I'm sure to there's more to the story (especially since Bernstein's NTRU prime was a NIST PQC candidate), but I suppose NIST isn't free from passive-aggressiveness? Within the context of this bad-blood, it's amusing that OpenSSH 9 uses Bernstein's NTRU Prime (doesn't use cyclotomics iirc), as opposed to one of NIST PQC's finalists. (DISCLAIMER: I'm a layperson, and I encourage people to read the sources themselves to make an informed opinion. People are welcome to correct. ) [1] - See the link to the "Risks of lattice KEMs" PDF at the top: https://ntruprime.cr.yp.to/warnings.html https://ntruprime.cr.yp.to/warnings.html [2] - https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/Fm4cDfsx65s/m/0dBVXOcSCAAJ https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/Fm4c... [3] - https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/4iaf9O-UjSo/m/c9xzBm8iBwAJ https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/4iaf... [4] - https://ntruprime.cr.yp.to/index.html https://ntruprime.cr.yp.to/index.html [5] - https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/7WhvubvoCVs/m/X2zhcNbaAQAJ https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/7Whv... [6] - https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/KFgw5_qCXiI/m/uVM4O6WpAwAJ https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/KFgw... [7] - https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/Fm4cDfsx65s/m/FRkvMfFpCAAJ https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/Fm4c... [8] - [PDF] - https://csrc.nist.gov/csrc/media/Projects/post-quantum-cryptography/documents/round-3/official-comments/NTRU-Prime-round3-official-comment.pdf https://csrc.nist.gov/csrc/media/Projects/post-quantum-crypt...