A more efficient implementation of Shor's algorithm

https://lwn.net/Articles/1066156/

by signa11 • 3 months ago

125 43 3 months ago

lwn.net

Genbox• 3 months ago

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

coherentpony• 3 months ago

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

riffraff• 3 months 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.

pseudohadamard3• 3 months ago

That's the whole point. And it's not "build on their work", it's "question their work", because so far every time someone's announced some magic quantum thing it's been followed up shortly afterwards by people poking holes on it, a famous recent example being the "quantum computer" that was replaced by /dev/random and it produced the same results. So the magic here isn't the quantum, it's coming up with a way to publish a claim in a way that it can't be refuted.

adrian_b• 3 months 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).

blamestross• 3 months ago

Seems like a wonderful use case for a one time pad! Every time you offer up the encryption key, it shows you were right!

cubefox4• 3 months 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• 3 months ago

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

ziofill• 3 months ago

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

xtracto• 3 months ago

They are not doing Science, they are just bragging.

smj-edison• 3 months 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...

bjoli• 3 months 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.

lima• 3 months 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.

raverbashing• 3 months 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)

pseudohadamard3• 3 months ago

It doesn't, but it's much harder to cheat with the DLP than it is with the IFP, which is what RSA is, which is why everyone announces records for RSA and ignores the fact that the actual problem to solve is the DLP. An example of how to cheat with the IFP is the "compiled Shor's algorithm" which produces the answer by non-quantum means and then throws in a quantum of quantum to make it look like magic happened.

fguerraz• 3 months ago

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

flimflamm• 3 months ago

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

paulnpace• 3 months ago

A new paper provides a major step in that direction, however.

It may have gone unnoticed if used only used once in the article, however.

dahart• 3 months ago

Never twice in one sentence like you did, and there are 13 “but”s. Is something wrong with using ‘however’? If so, what exactly?

loglog2• 3 months ago

How is it possible to provide a zero knowledge proof that their circuit works for large problem instances if there is no efficient way to run or simulate the circuit with the required instance size?

Strilanc• 3 months ago

The dominant cost in Shor's algorithm is the elliptic curve point addition subroutine. That subroutine can be implemented using reversible classical gates. For that kind of implementation, approximate correctness can be verified by fuzz testing classical trajectories through the subroutine.

Note you could ask the same question about Shor's original paper: how did he show the algorithm works without running it? Running X just isn't the only way to analyze X.

loglog2• 2 months ago

For that kind of implementation, ...

This is the key point, what is the meaning of "zero knowledge" here? It seems that you need to know something about the implementation, even if it is not the full implementation. Compare this to a zero knowledge proof that you have, say, a factorization gadget, which works by you running the gadget on adversarial input, thus convincing the adversary that you can factor any of their integers. That discloses no implementation details of your factorization gadget, which can be an efficient classical algorithm, a quantum computer, or a phone line to God.

quuxplusone• 3 months ago

Top comment on LWN is a very interesting read (although neither the commenter nor myself claim any such trickery was involved in this case).

Trail of Bits were able to craft an input that beats Google's circuit and prove it... by virtue of a bug in the verifier: https://blog.trailofbits.com/2026/04/17/we-beat-googles-zero... Google patched the vuln and the original proof still stands, but this is a pretty strange path we seem to be walking down [...]

sigmar• 3 months ago

We contend that the amount of time remaining before the arrival of CRQCs still exceeds the amount of time needed to migrate public blockchains to PQC, though the margin for error is increasingly narrow. Therefore, we have offered updated resource estimates for quantum attacks on blockchain cryptography together with an analysis of vulnerabilities and mitigations in order to urge all vulnerable cryptocurrency communities to begin PQC transition immediately while its timely completion is still the likely prospect.

they really couldn't be shouting "mitigate now or never" any louder. I'm curious how they arrived at the efficiency improvements, but perhaps any mention of that would be similar to releasing the circuit.

upofadown• 3 months ago

Checking the required hardware noise performance:

On superconducting architectures with 10−3 physical error rates...

So still 1-2 orders of magnitude better than what we can achieve.

This is against a 256 bit elliptic curve. For some reason most people are stating the difficulty of using Shor's against 2048 bit RSA. Elliptic curves are easier to break with Shor's. I wonder how much of the optimization came from that fact alone...

pseudohadamard3• 3 months ago

That's because it's easier to cheat with the IFP (the underlying problem that RSA is built on) than the DLP, so everyone generates RSA "records" and ignores the actual problem that needs to be solved.

A more efficient implementation of Shor's algorithm

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