A more efficient implementation of Shor's algorithm
lwn.net

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83 points

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signa11

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2 days ago

22 comments

smj-edison ・ 4 hours ago

Wait, the article mentions that Shor's algorithm is factoring (which is what I understood), but then it's talking about elliptic curve cryptography? I thought ECC didn't use the same mathematical foundations of RSA, and RSA has been slowly phased out anyways...

  • lima ・ 3 hours ago

    Shor published multiple quantum algorithms, including one for discrete logarithms. The term is sometimes used interchangeably.

    They're closely related, ECC and RSA are both instances of the hidden subgroup problem.

  • bjoli ・ 3 hours ago

    Quite the contrary. Shor's algorithm actually works better for the shorter keys of ECC. The rule of thumb is 2n qbits for RSA keys and 6n qbits for ecc. I believe it has something to do with hownit applies to the hidden subgroup problem of finite abelian groups rather than factorisation, but I am really not a cryptographer not especially mathsy. I just asked the same question you did, and someone in the know pointed me to that.

  • raverbashing ・ 3 hours ago

    > I thought ECC didn't use the same mathematical foundations of RSA

    It kinda does, it just uses them differently

    The basis here is the discrete inverse logarithm in a specific group (elliptic curves over rationals or multiplicative group module n)

Genbox ・ 2 days ago

Publishing a zero knowledge proof rather than the solution is pretty clever.

  • adrian_b ・ an hour ago

    This has been used for centuries. It is not a new invention.

    Hundreds of years ago, it was not unusual to publish an encrypted solution of some mathematical problem, in order to establish priority without disclosing the algorithm that was used.

    Of course, at that time very simple encryption methods were used, for instance an anagram of the solution was published (i.e. encryption by letter transposition).

  • coherentpony ・ 6 hours ago

    Is it? Nobody else can really build on their work.

    • riffraff ・ 6 hours ago

      AIU the intent of this publication is not to further research but to make it clear to anyone that we need to move to post quantum cryptography ASAP.

      • rwmj ・ a minute ago

        But the algorithm still isn't practical on existing quantum computers, or ones that are going to be around any time soon, so there's no reason not to publish in full.

      • QuaternionsBhop ・ 5 hours ago
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        If only AI safety research had a mechanism this clear. "We have proof that building the machine will kill everybody, so get to work making a provably safe version."

        • AnthonyMouse ・ an hour ago
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          "AI safety" is essentially incoherent. It's like trying to build an all-purpose chemistry lab that can't produce explosives.

          • cubefox ・ an hour ago
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            Neat, an ontological argument against AI safety. Similar argument:

            "God doesn't exist" is essentially incoherent. God is the perfect being, and if he didn't exist, he wouldn't be perfect.

            I think the logical mistake is obvious.

            • AnthonyMouse ・ 22 minutes ago

              Except that you have the logic backwards. It's an argument that something ("safe" general purpose AI) can't exist rather than that it has to.

              People want AI to be able to do every good thing but no bad thing, which is impossible twice. First because false positives and false negatives trade against each other, so a general purpose AI which can do anything approximating all the good things is going to have the bias leaning heavily towards being able to do things in general and therefore being able to do many things that are bad. And second because "good" and "bad" aren't things that anybody can agree on and then some people will demand that it must do X while others demand that it not do X (e.g. "help the rebels win the war"), which means someone is inherently going to be unsatisfied and it's not a thing that can be sensibly regarded as everyone working towards a common goal.

      • adastra22 ・ an hour ago

        That may be the intent, but it is very anti-science.

fguerraz ・ 3 hours ago

However, the author managed to squeeze the word "however" eleven times in this article, however.

  • pixelpoet ・ an hour ago

    How did the author squeeze the word "however"?

    I did notice a stray apostrophe here and there, I'm guessing the editor noted out at the wall of quite technical writing.

  • flimflamm ・ 2 hours ago

    However, there was only 57 however's in the paper it self.

cubefox ・ 4 hours ago

> If the paper's authors had chosen to release their circuit, they would certainly have been recognized for the important progress they made in the science of quantum computing. Other researchers would have gone on to build on their work, and the entire scientific community would be richer for it.

... and the world could well have been unsafer. There is pretty strong reason not to release insights which could be used as an attack on public key cryptography. We already know the fix anyway, post quantum cryptography algorithms.

Sometimes scientific curiosity has to step back when it comes to potentially dangerous research. Scott Aaronson recently [1] compared this case to when scientists stopped publishing on nuclear fission research because the possibility of developing an atomic bomb became concrete:

> When I got an early heads-up about these results—especially the Google team’s choice to “publish” via a zero-knowledge proof—I thought of Frisch and Peierls, calculating how much U-235 was needed for a chain reaction in 1940, but not publishing it, even though the latest results on nuclear fission had been openly published just the year prior.

1: https://scottaaronson.blog/?p=9665

  • free_bip ・ 4 hours ago

    Oh please, the government could easily force them to hand over their research. This is not a serious argument.

    • ziofill ・ 3 hours ago

      Would it be really so straightforward for the government to do that?

      • throawayonthe ・ 2 hours ago

        i doubt they don't have access already