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Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

arxiv.org

121–130 of 146 posts

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#121
post #18

Earlier quoted context omitted.

So, then I am definitely good using 4096 RSA?

Sure, but ridiculously large key sizes like 4096 bit RSA are not really any more resistant to quantum computing than smaller sizes. This is probably a joke, but the suggestion was made that you might be OK with a 1 TB RSA key size: * https://www.schneier.com/blog/archives/2017/05/post-quantum_...

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Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#122

I fear it is my obligation to point out this excellent screed by Scott Lockin: "Quantum computing as a field is obvious bullshit". A beautiful excerpt from the article: When I say Quantum Computing is a bullshit field, I don’t mean everything in the field is bullshit, though to first order, this appears to be approximately true. I don’t have a mathematical proof that Quantum Computing isn’t at least theoretically pos…

except we already use qubits in the real world, and we already use entangled pairs in banking, so it's not really all that bullshit anymore. Quantum computers with a significant number (e.g thousands, but really, millions) of qubits, however, are still quite a ways away. But clearly not in the realm of bullshit anymore.

I would love to learn more, please share any relevant useful links.

Edit: Cursorily googled and did not find a reference for usage but plenty of papers talking about potential applications. Might be wrong though.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#123
post #74

Earlier quoted context omitted.

Imagine that you find Satoshi's private key and start trying to sell his million bitcoins. Approximately one minute after you start this process, someone will figure out that either (1) bitcoins no longer securely belong to anyone or (2) Satoshi thinks selling off all his bitcoin is a good idea. Approximately two minutes after you start this process, the price of bitcoin will plummet. Sorry, you will not be taking ho…

There is a theory that the key to satishi's wallet is hidden somewhere in the beginning of the blockchain. So it might not be too wild if coins started moving

How could it possibly still be secure, then? Also, I've never heard of that theory and it sounds interesting. Source?

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#124
post #49

Earlier quoted context omitted.

Quantum computers exist today, they're just very low power, low gate counts, and extremely expensive. Don't discount it as magic just because of the claims. Scaling up QC would be like bringing mathematics to Mesopotamia. But it isn't "magic", it's physics.

The research in this field proceeds under the umbrella and framework of physics, yes. But it's not clear that it's possible to scale up to the number qubits required do anything nontrivial. It's plausible there are hard engineering limits on error correction which make it asymptotically more difficult with each order of magnitude more qubits involved. It might not look that way because there's a lot of (relatively) m…

Admittedly, it's not a gate-model system, but at D-Wave we've been able to scale up to 5,000+ qubits now, and the future is promising for further advancements in qubit count, noise, and other advanced features.

The gate-model systems have shown that they are pursuing a much more difficult path, one that may indeed be fruitless for years or decades before they can approach our raw qubit count. We also have examples of nontrivial, paying-customer use cases that become more compelling with each new announcement. Factoring integers is indeed an interesting hard problem which would have a massive (negative?) impact on the world if realized, but besides Shor's and Grover's algorithms, it's not like gate-model QPUs have a ton of use cases significantly better than what a quantum annealer can accomplish.

I like to think of it this way: we're basically at the point of an ENIAC scale machine, if you liken quantum computing progress to classical computing. Fills up a room, very specific environmental and power requirements, little or no "memory" to speak of, esoteric and hard for anyone without years of training to master. Only a few decades later, the state of the art machine was thousands of times more capable, far cheaper and smaller, more reliable, more accessible in every way. Imagine describing the Internet as we use it today to an ENIAC operator, or a speculative investor considering IBM, Honeywell, etc. - it would sound like an impossible, Asimovesque dream, not something that children would literally be playing with sixty years later.

The only difference is that so far, we don't really seem to have a real exponential Moore's Law effect in quantum computing. Google et al. still have very low numbers of qubits without any real promise that they'll be able to deliver more of them in any consistent timeframe. At D-Wave we've done better on the scaling front, and we've been trying to keep up to our former founder's "Rose's Law" of qubit scale growth, but fabrication is an incredibly expensive, complicated, competitive endeavour that necessitates incredible quality control in order to produce processors that are up to spec. There are also other factors beyond the raw qubit count; the bigger advantage in our latest Advantage chip may actually be the higher connectivity between qubits on the graph, rather than their raw number.

Of course, we expect that we'll continue to push the envelope in this regard, and given enough time and investment, some of the early applications we're seeing now may well eventually be integrated into large scale products people use every day.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#125

I fear it is my obligation to point out this excellent screed by Scott Lockin: "Quantum computing as a field is obvious bullshit". A beautiful excerpt from the article: When I say Quantum Computing is a bullshit field, I don’t mean everything in the field is bullshit, though to first order, this appears to be approximately true. I don’t have a mathematical proof that Quantum Computing isn’t at least theoretically pos…

except we already use qubits in the real world, and we already use entangled pairs in banking, so it's not really all that bullshit anymore. Quantum computers with a significant number (e.g thousands, but really, millions) of qubits, however, are still quite a ways away. But clearly not in the realm of bullshit anymore.

Is this referencing quantum cryptography being used in banking? Any good sources for more info on this, it sounds really interesting.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#126
post #12

This paper basically explores a hypothetical scenario where scaling quantum memory ends up being cheaper than scaling computational qubits. The title (or abstract) unfortunately does not mention the quantum memory requirements at n=2048 explicitly. For factoring 2048 RSA integers, the technique proposed in the paper would require ~430 million memory qubits (see the table at top of page 16).

So magic computer could be more effective with more magic memory than with more magic processing power, right?

You know that qubit processors already exist, right? This is like going "yeah right, we can factor large primes if we had a 4.2GHz processor. So, magical processing power, right?" in the 386 era.

We may not have 13k qubit systems today, but we do have qubit systems already. Expecting us to get better at them is pretty reasonable.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#127
post #2

Just to be clear such a machine has not yet been built. This is only a theoretical paper at the moment.

Do I understand correctly, that largest quantum computer that exists today contains less than 100 qubits? Also it does not seem that there's an exponential grow in this area: https://www.statista.com/statistics/993634/quantum-computers... . They hit the wall in 2017. We should be safe for now :)

The largest production quantum computer that exists today - as in, the largest you personally can get access to - has 5,436 qubits: the D-Wave Advantage system.

Admittedly, it's not a gate-model machine that can run Shor's Algorithm, but it is a quantum computer, and at more than double the number of qubits plus far higher inter-qubit connectivity than our previous D-Wave 2000Q, it definitely demonstrates tremendous progress.

If you have a moment, you can sign up to use it for free at https://cloud.dwavesys.com - we have an online IDE, Jupyter notebook training material and tons of docs, a community forum, and of course some shiny demos that submit problems to the live QPU if you want to try them out.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#128
post #75

layman here. i understand that if said theoretical computer did exist, encrypted stored data using today's standards is for the most part compromised, outside of further obfuscation, which the popular opinion seems to believe only helps so much. that means the past is compromised, with some amount of implementation afterwards. i've always wondered just how much the future is compromised. i've always thought about enc…

Quantum computers will have civilian access. They already do in fact. And the issue is that they change _the complexity_ for some algorithms so adding rounds isn't going to help.

We'll just migrate to quantum resistant algorithms like we migrated away from MD5.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#129
post #36

Earlier quoted context omitted.

In common practice RSA keys/certificates are used for TLS and similar protocols where it does not allow to decrypt past recorded communications, as those are encrypted with an ephemeral session keys that can not be determined from observing the handshake even if you have the keys. Obtaining a private key would allow you to MITM future sessions and decrypt them, but it would not break confidentiality of past messages.…

That's not how this works. An attacker can record the key exchange. That is not using RSA, today it's usually some variation of elliptic curve diffie hellman. But that is just as vulnerable to quantum attacks as RSA. So you're attacking the key exchange, not the RSA signature. What you're probably alluding to here is the forward secrecy property of TLS. But that is only true under the assumption that the key exchange…

Diffie hellman is on the table to be cracked too by quantum computers, just as much as RSA.

Re: Factoring 2048 RSA integers in 177 days with 13436 qubits and a multimode memory

#130

Earlier quoted context omitted.

So magic computer could be more effective with more magic memory than with more magic processing power, right?

You know that qubit processors already exist, right? This is like going "yeah right, we can factor large primes if we had a 4.2GHz processor. So, magical processing power, right?" in the 386 era. We may not have 13k qubit systems today, but we do have qubit systems already. Expecting us to get better at them is pretty reasonable.

Not sure it is reasonable.

Quantum systems don't scale that way. In order to get the quantum speedup you need to be able to maintain the larger quantum state which gets a lot harder the larger these systems get.

This is like saying we already have 7nm process today for silicon so expecting us to get better, like 1nm, 10 angstrom... or we have a plane that goes 2000 miles per hour, expecting 10kmph, 100kmph, 2000kmph... physics doesn't work like that.

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