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by eterm 1406 days ago
I look forward to this being in the next set of cryptopals.
1 comments

It's a little unlikely. It's a code-able exploit with a big payoff, which is right in the wheelhouse, but then there's this that Steven Galbraith had to say about how the exploit works:

    *What is this magic ingredient?*
    It is a theorem by Ernst Kani about reducible subgroups of abelian surfaces.

    *Is there a simple way to explain the magic ingredient?*
    Nope. Go learn about Richelot isogenies and abelian surfaces.
As I understand it, even by number-theoretic cryptographic standards, the math here is abstruse. The challenges I think have done pretty well sticking to things where writing the exploit pays off with good intuitions. I guess "don't reveal auxiliary torsion points when exchanging details of an isogeny graph walk" is a useful intuition, maybe.
Even before being broken, the abstruse mathematics is one of the reasons to not go with SIKE or Rainbow. It’s not surprising they are broken.

NTRU is the easiest of the NIST PQC finalists to understand, and will probably beat Kyber because even a relatively new-to-cryptography programmer will be able to understand it and implement it.

You can see why people love it, though; the nuts and bolts of SIDH are extremely elegant. Like, it's a neat trick. I don't understand Richelot isogenies and abelian surfaces and can't speak to the elegance of the break; it's the break that exceeds the threshold for "abstruse" (of course, the abstruse mathematics of things that break cryptosystems do make the underlying cryptosystem abstruse! you have to grok them to use it!)
Ease of understanding isn’t the same as good though. For example RSA is much easier to explain and implement than ECC, but it is much worse.