Solving the Shortest Vector Problem in $2^{0.6039n}$ Time via Mid-Point Hessian

Solving the Shortest Vector Problem in $2^{0.6039n}$ Time via Mid-Point Hessian(arxiv.org)

25 points by sbulaev 7 days ago | 6 comments

hyperhello 31 minutes ago |

For those who don’t have math extensions in the browser, if that is 2^0.6039, then why don’t math extensions just detect math syntax and style it directly?

tikhonj 21 minutes ago | |

I mean, in this case, it's 2^{0.6039n}, and the n is pretty important. I can see why trying to automatically detect cases like this would run into a bunch of wrong behaviors (either styling text that was not meant to be math notation, or parsing the implied math notation incorrectly).

hyperhello 10 minutes ago | | |

Okay, I had the problem going the other way. I assumed the n was a symbol on the previous number, like an f suffix in C. But even still, 2^(0.6039n) could have been rendered in a nice way stripping out the parenthesis, leaving the core text mathematically correct.

slwvx 57 minutes ago |

I was very happy to see an "AI use disclosure" right on the title page under the abstract.

It's not clear if this is solely a possible theoretical result or if it has any practical value. I.e. is it only useful on lattices that are so large as to not be of use, or could it be used for cryptanalysis? If one is using AI to generate a theory paper such as this, why not use the AI to also generate code that uses it, put it on GitHub, and show the results, say against fplll and the tool in the paper below?

https://ir.cwi.nl/pub/35237/35237.pdf

GracefullyShot 1 hour ago |

could this be a problem for the security of Falcon (aka FN-DSA) post quantum signature scheme?

mswphd 56 minutes ago | |

not really. The hardness of SVP is relevant, but this is a paper giving improved provable bounds for SVP algorithms. heuristically (which people use to choose parameter sizes etc) people assume SVP is much easier to solve, closer to 2^{.29n + o(n)}.

So it's tangentially related, but does not itself imply an improvement on the (heuristically assumed) SOTA for these problems.

pretzellogician 1 hour ago |

Wow, just yesterday I was thinking this exact problem would be a good candidate for AI. Seems it is!