
Mathematicians have found a new way to multiply two numbers together - sahin-boydas
https://www.newscientist.com/article/2198155-mathematicians-have-found-a-new-way-to-multiply-two-numbers-together/
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jeremyjs
What are the security implications? Does this make password cracking more
feasible?

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exabrial
argh... non-paywall anywhere?

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weld
The paper - [https://hal.archives-
ouvertes.fr/hal-02070778/document](https://hal.archives-
ouvertes.fr/hal-02070778/document)

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gota
Is there a humanly readable version?

Just kidding, but although I understand the value and importance of the heavy
formulation, especially under the circumstances of the media of academic
papers where proofs are necessary/desirable, this will be largely useless for
disseminating the knowledge of the algorithm for all but a handful of people.

We need someone to write it down for us with all the simplifications that are
possible given that we 'trust' all the relevant claims (the algorithm is
correct, its complexity is O(n log n), etc.) and we simply don't care for the
heavier side of the proofs

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MrEldritch
The reason it isn't actually important to have a specific algorithmic
implementation is that - like other exotic multiplication algorithms with
better big-O complexity than the usual ones - the _constant factors_ are much,
much bigger, to the point where they would only become noticeably faster for
absurdly huge integers. The theoretical aspect of this _is_ the interesting
part.

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db48x
In fact, in this case the algorithm is only intended for numbers with 2^4096
bits. See section 5 of the paper:

    
    
      In this section we present the main integer multiplication
      algorithm. We actually give a family of algorithms,
      parameterised by a dimension parameter d > 2. Let n_0 :=
      2^(d^12) > 2^4096, and suppose that we wish to multiply
      integers with n bits. For n < n_0, we may use any convenient
      base-case multiplication algorithm, such as the classical
      O(n^2) algorithm.

