Thanks for sharing. That's a long and tough read (in his style) but pretty interesting.
This is not his style, for what it's worth, at least not for standalone long-form writing. His most influential cryptography writing is concise and lucid.
In between a bunch of conspiratorial hinting, djb argues that KYBER-512 is weaker than NIST claims.
To make that argument, he points out a fairly egregious math mistake (the whole "2^40+2^40" bit) and then shows that NIST was inconsistent in applying the rules of the contest it refereed.
He also offers an explanation for why NIST would be so inconsistent about it, namely that they were influenced to pick KYBER, even if it wasn't the best candidate.
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My personal takeaway was that he was both being a sore loser but also that KYBER-512 is weaker than it should be, weaker than it is claimed to be and that for some reason NIST still wanted it to win.
Makes me skeptical about KYBER-512 (but not larger sizes) and reinforces my worry that NIST can be influenced to pick less-than-optimal algorithms.
But then, I'm not a cryptographer and in the lucky situation where for any application I encounter, I can just go for KYBER-768 or 1024 or NTRU and just be fine - I don't have to understand this situation perfectly.
Hope you get some value from this outside perspective.
If anything, this reinforces my belief that KYBER is a good design. If this is the best he can come up with to try and discredit it, then it must be pretty solid.
What doesn't seem clear to me, and I'd appreciate if you could tell me why you think differently, is that KYBER-512 isn't as strong as it was targeted to be. I find djb's argument on this narrow point fairly convincing: KYBER-512 isn't as secure as AES-128 (by the methods used to measure "secure" in this competition).
Given that I already generally use AES-256, why shouldn't I treat this the same way as AES-128?
That is, "it's probably fine-ish, but if you have the power, just go one bigger".
But by all means feel free to go one bigger and pick KYBER-768, and I believe lots of people do recommend this. Obviously, there is a performance penalty (as there is when moving from AES 128 to 256), and for PQ schemes there is also more importantly also a big increase in the size of bytes on the wire when public keys have to be exchanged (e.g. in TLS) - in this case a jump from 800 bytes to 1,184 bytes (a 48% increase). (Compare this to ECC public keys which are typically around 32-65 bytes, depending on encoding).
It has also been pointed out to me that djb has been quietly ignoring another metric in which KYBER beats NTRU: implementation complexity.
Even accepting all other arguments about the tradeoffs between NTRU and KYBER (and I do take your point about size of keys being more important than CPU cycles), even then, KYBER is judged to have lower implementation complexity.
Having read about all the crypto libraries who produced broken output because they made a mistake in the implementation, that's something I immediately understand as a big benefit.
Again, thanks for the conversation and helping me understand!
Re: style, this seems longer and more rambling than usual, but other stuff on his blog has been long, and his style with lots of background, asides, references, self-quotes seems pretty distinctive, isn't it?
But I'm sure you paid more attention to this than me.
Kagi Universal Summarizer output for "Summary":
This web page discusses the selection of the Kyber and NTRU cryptosystems as the quantum-resistant digital signature algorithms by the National Institute of Standards and Technology (NIST). It analyzes NIST's claims about the security levels of Kyber-512 compared to AES-128. While NIST argued Kyber-512's security level is boosted enough by memory access costs to meet the AES-128 threshold, the text raises uncertainties around accurately modeling such costs and argues NTRU may have advantages in flexibility and performance. Overall, the page questions whether NIST fully justified selecting Kyber-512 over NTRU given the uncertainties in quantifying the security of lattice-based cryptosystems against future attacks.
Kagi Universal Summarizer output for "Key moments":
- There is debate around whether Kyber-512 provides adequate security compared to the AES-128 benchmark. NIST claims it meets this level factoring in memory access costs, but others argue the analysis is uncertain.
- NIST's analysis added 40 bits of estimated security to Kyber-512's post-quantum security level due to memory costs, bringing it above the AES-128 threshold. Critics question this calculation.
- NTRU provides greater flexibility than Kyber in supporting a wider range of security levels. At some levels it also has better performance and security than Kyber options.
- The security of lattice-based cryptosystems like Kyber and NTRU is not fully understood, and there is a risk of better attacks being discovered in the future.
- Standardizing a system like Kyber-512 that may have limited security margin could be reckless given lattice cryptanalysis uncertainties.
- Critics argue NIST has not clearly explained its security evaluations and claims about Kyber-512's margin above AES-128.
- Memory access costs are important to lattice security but are not fully quantified in their impact on Kyber versus classical attacks on AES.
- Removing Kyber-512 could make NTRU the strongest candidate given its flexibility at multiple security levels.
- One paper argued multi-ciphertext attacks on Kyber may be as difficult as single-ciphertext attacks.
- There are calls for NIST to be transparent about its analysis and decision making regarding Kyber-512.
anyways, it seems i cannot delete the comment, so would be great if a moderator or something could do it, thanks.