1. cryptography developed across the world, 2. the actual schemes were overwhelmingly by European authors 3. standardized by the US 4. other countries standardizations have been substantially similar (e.g. the ongoing Korean one, the German BSI's recommendations. China's CACR [had one with substantially similar schemes](https://www.sdxcentral.com/analysis/china-russia-to-adopt-sl...). Note that this is separate from a "standardization", which sounds like it is starting soon).

In particular, given that China + the US ended up with (essentially the same) underlying math, you'd have to have a very weird hypothetical scenario for the conclusion to not be "these seem secure", and instead "there is a global cabal pushing insecure schemes".

Practically though, there are some downsides. Elliptic curves tend to have smaller ciphertexts/keys/signatures/so are better on bandwidth. If you do everything right with elliptic curves, we're also more confident in the hardness of the underlying problems (cf "generic group lower bounds", and other extensions of this model).

The new algorithms tend to be easier to implement (important, as a big source of practical insecurity is implementation issues. historically much more than the underlying assumption breaking). This isn't uniformly, e.g. I still think that the FN-DSA algorithm will have issues of this type, but ML-DSA and ML-KEM are fine. They're also easier to "specify", meaning it is much harder to accidentally choose a "weak" instance of them (in several senses. the "weak curve" attacks are not really possible. there isn't really a way to hide a NOBUS backdoor like there was for DUAL_EC_DRBG). They also tend to be faster.

1. the main "eye catching" attack was the [attack on SIDH](https://eprint.iacr.org/2022/975.pdf). it was very much a "thought to be entirely secure" to "broken in 5 minutes with a Sage (python variant) implementation" within ~1 week. Degradation from "thought to be (sub-)exp time" to "poly time". very bad.

2. the other main other "big break" was the [RAINBOW attack](https://eprint.iacr.org/2022/214.pdf). this was a big attack, but it did not break all parameter sets, e.g. it didn't suddenly reduce a problem from exp-time to poly-time. instead, it was a (large) speedup for existing attacks.

anyway, someone popular among some people in tech (the cryptographer Dan Bernstein) has been trying (successfully) to slow the PQC transition for ~10 years. His strategy throughout has been complaining that a very particular class of scheme ("structured LWE-based schemes") are suspect. He has had several complaints that have shifted throughout the years (galois automorphism structure for a while, then whatever his "spherical models" stuff was lmao). There have been no appreciable better attacks (nothing like the above) on them since then. But he still complains, saying that instead people should use

1. NTRU, a separate structured lattice scheme (that he coincidentally submitted a scheme for standardization with). Incidentally, it had [a very bad attack](https://eprint.iacr.org/2016/127) ~ 2016. Didn't kill PQC, but killed a broad class of other schemes (NTRU-based fully homomorphic encryption, at least using tensor-based multiplication)

2. McCliece, a scheme from the late 70s (that has horrendously large public keys --- people avoid it for a reason). He also submitted a version of this for standardization. It also had a [greatly improved attack recently](https://eprint.iacr.org/2024/1193).

Of course, none of those are relevant to improved attacks on the math behind ML-KEM (algebraically structured variants on ring LWE). there have been some progress on these, but not really. It's really just "shaving bits", e.g. going from 2^140 to 2^135 type things. The rainbow attack (of the first two, the "mild" one) reduced things by a factor ~2^50, which is clearly unacceptable.

Unfortunately, because adherents of Dan Bernstein will pop up, and start saying a bunch of stuff confidently that is much too annoying to refute, as they have no clue what the actual conversation is. So the conversation becomes

1. people who know things, who tend to not bother saying anything (with rare exceptions), and 2. people who parrot Dan's (very wrong at this point honestly, but they've shifted over time, so it's more of 'wrong' and 'unwilling to admit it was wrong') opinions.

the dynamic is similar to how when discussions of vaccines on the internet occur, many medical professionals may not bother engaging, so you'll get a bunch of insane anti-vax conspiracies spread.