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...
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.
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."
> 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.
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...
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.
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.
> 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)
However, the author managed to squeeze the word "however" eleven times in this article, however.
Publishing a zero knowledge proof rather than the solution is pretty clever.
Is it? Nobody else can really build on their work.
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.
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."
> 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
Oh please, the government could easily force them to hand over their research. This is not a serious argument.
Would it be really so straightforward for the government to do that?
i doubt they don't have access already