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Typo in complexity for Delfs Galbraith? #32

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GiacomoPope opened this issue Sep 2, 2022 · 2 comments
Open

Typo in complexity for Delfs Galbraith? #32

GiacomoPope opened this issue Sep 2, 2022 · 2 comments

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@GiacomoPope
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GiacomoPope commented Sep 2, 2022

delfs-galbraith:
  name:
    short: DG
    long: Delfs-Galbraith
  complexity: exp(1/2)
  references:
    DG13: "https://arxiv.org/abs/1310.7789"
  comment: >-
    $\exp(1/4)$ reduction of the supersingular isogeny path problem to
    the vectorization problem for supsersingular curves over
    $\mathbb{F}_p$.

Pretty sure complexity: exp(1/2) should be complexity: exp(1/4)? (from the paper's abstract) but wanted to double check before editing it, as I wasn't sure if this was the specific attack for curves over F_p, or the full attack which first looks for curves over F_p then performs the e^1/4 attack which i think still has complexity e^1/2?

@GiacomoPope GiacomoPope changed the title Typo in complexity for Delfs Galbraith Typo in complexity for Delfs Galbraith? Sep 3, 2022
@defeo
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defeo commented Sep 27, 2022

Sorry for sitting on this for so long. In my opinion the error is in the comment, not the complexity field.

This entry is referring to the attack that starts from a curve over GF(p²) and randomly walks until it hits a curve over GF(p). The average complexity is O(√p).

But we have a general problem of it not being clear in terms of what the complexity is expressed. Are these complexities in log(p)? Or something else? I think we need a separate issue and brainstorming for this.

@GiacomoPope
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Yeah, agreeing with the above. Also, a Twitter user mentioned that maybe a "101 in complexities" might be useful for those not used to our notation, Maybe this could be included either at the bottom of the page as an appendix, or in the "about / FAQ" which is (somewhat) finished in a branch i was working on a few weeks ago.

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