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Breaking RSA Security with a Low Noise D-Wave 2000Q Quantum Annealer
- 1cvmask 6y agoRSA took money from the NSA to sell intentionally flawed encryption: https://www.cnet.com/news/security-firm-rsa-took-millions-from-nsa-report/ https://www.cnet.com/news/security-firm-rsa-took-millions-fr... Defense contractor Lockheed Martin was breached (supposedly by the Chinese) because they used flawed RSA: https://www.scmagazine.com/home/security-news/rsa-confirms-lockheed-hack-linked-to-securid-breach/ https://www.scmagazine.com/home/security-news/rsa-confirms-l... Companies still buy RSA today. Maybe it is like the Streisand effect. Bad news, instead of backfiring, leads to more business.
- jessriedel 6y agoThis comment isn't relevant to the article.
- deleted 6y ago[deleted]
- archgoon 6y agoWell, for those looking at the comments first: No; they do not actually factor any 1024 or 2048 bit numbers. The largest is 17 bits. Although they point out that representing the problem can be done in a quadratic size of the input, the datapoints in the paper don't give any reason to believe that the time to finding the factors won't just be exponential in the input. Also, no, this is not a record for Quantum Computing; as this is a DWave Quantum Annealing machine which needs to be evaluated by a different standard. This seems to be more interesting if you look at it from the perspective "How can I treat prime factorization as a optimization problem" rather than "Does it look like Quantum Annealing Machines can factor RSA in the near term".
- ohvirginia 6y agoQuadratic in size of input is just the multiplication table of the radix units in some base (in their case binary). It's interesting and I think promising approach to factoring is to use annealing over such a multiplication table trying to resolve the intermediate radix unit products and carries. It's a good way to map the problem to a solution space that is obviously a solution landscape that can be explored. It's true that the number of variables they end up with is still exponential in the bits of input, but then again, that's not really a problem for true quantum computers. It definitely seems factorization is closer to being publicly broken.
- metalrain 6y agoWhat is record for PF on quantum computer? I only found some really old results from 2014 and current records must be higher.
- tialaramex 6y agoThe record for Shor's algorithm is still 21 = 7 x 3 You can instead do "big" numbers like in this article with machines that can't run Shor's algorithm, but there is no good reason to imagine these would ever be competitive with a conventional computer like your laptop or phone. Shor's algorithm (and similar algorithms) are definitively faster, if you can make a quantum computer to run them. That's the hard part, and as you observe the result is no clear progress in almost a decade.
- osamagirl69 6y agoThis is pretty impressive, they were able to factor a 17 bit number (103459 = 337 * 307) using 1635 physical qubits (arranged as 73 logical qubits) using QUBO. In this configuration they were able to achieve an average time to solution of just under 100ms. That said, they did pick an 'easy' number to factor, just like most other quantum factorization results. This number could easily be factored using Fermat's factorization method (only the first step is required). It would have been very interesting to see a list of all primes and the time required to factor them (since they claim it only takes 100ms to factor the 17 bit one, such an experiment should be able to run in a day...). For an extreeme case of this class of 'cheating' compare to the largest number factored on a quantum computer (1,099,551,473,989 =1,048,589 * 1,048,601) which only actually takes 3 qubits to calculate [1] They also estimate that in order to factor a 2048bit number it would require just under a million logical qubits using QUBO, but didn't present a physical implementation. Worse yet, this is still not a general algorithm and is generally predicated on picking an easy number to factor in the first place! [1]https://quantumcomputing.stackexchange.com/questions/9204/the-algorithm-of-the-new-quantum-factoring-record-1-099-551-473-989 https://quantumcomputing.stackexchange.com/questions/9204/th...
- scottlocklin 6y agoq: 103459 evaluates in 4 microseconds in a 12 year old intel chip running a single thread in J
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- dvdkhlng 6y agoGlancing at the paper, I do not find anything that is impressive. AFAICS the algorithm they implement is of asymptotic exponential complexity, even when run on a quantum computer. I cannot imagine how this work would have any effect on the field of asymmetric encryption algorithm research. To me it looks like they took the factorization problem, which has a lot of well-known (relatively) low-complexity algorithms and imlemented it by mapping it onto circuit-SAT [1] (the multiplication table corresponds to a multiplier circuit which they try to solve in reverse). Circuit-SAT is a proven NP-complete problem. There is currently no known quantum-algorithm that solves NP-complete problems in sub-exponential time. Note that in the complexity hierarchy NP-complete problems are "harder" than the factoring problem. These are generally bad problems, were not even a quantum-computer helps (and I know of no asymmetric encryption algorithm that is NP-complete when trying to break it, but maybe the quantum-resistant encryption algorithms are better in that regard). And that's even before we start talking about the limitations of quantum-annealers and the kind of speedups they can gain over classical computers. For a discussion of that, maybe one should start reading Scott Aaronson's blog [2]. [1] https://en.wikipedia.org/wiki/Circuit_satisfiability_problem https://en.wikipedia.org/wiki/Circuit_satisfiability_problem [2] https://www.scottaaronson.com/blog/?p=2555 https://www.scottaaronson.com/blog/?p=2555
- da-x 6y agoIt's 2020, and I'm still waiting to see an impressive proof of work out out of a quantum computer that I can easily verify on my traditional computer (two different files with identical SHA-512, for example?). Maybe a few years from now?
- united893 6y agoIt's been demonstrated already using a random circuit. Two random strings that match SHA, are practically speaking just toy examples using random useless information. There's no meaning to the numbers except that when you apply an operation to them the have the same output. Now, instead of the random string, you have a random circuit. And the output is the goal. The random circuit is as useful to you as the random string. But using a quantum computer you can compute its state when operating. With a traditional computer it is very hard. https://www.nature.com/articles/s41586-019-1666-5 https://www.nature.com/articles/s41586-019-1666-5 https://www.scottaaronson.com/blog/?p=4317 https://www.scottaaronson.com/blog/?p=4317
- adrianN 6y agoThe keywords to google for when looking for such things are "quantum supremacy"
- Yizahi 6y ago"Quantum supremacy", aside from dumb naming, as far as I understood from news is an attempt to find a possible problem to the solution they have invented (quantum device itself), to prove that their quantum device can do at least something which cannot be replicated with the same magnitude of speed (or at all) on "normal" computers. And it was contested even in such limited scope. OP asks for next step - do some useful computation. Reverse order - have the problem at start (preferably "real" problem) and compute solution to it.
- takeda 6y agoMaybe the proof exists in a different reality? :)
- bawolff 6y ago
- ganzuul 6y agoAt what bit lenght is this approach faster than https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%... ?
- NoKnowledge 6y agoThat is apples to oranges, you're citing a lattice reduction algorithm? Maybe you meant the number field sieve https://en.wikipedia.org/wiki/General_number_field_sieve https://en.wikipedia.org/wiki/General_number_field_sieve? In that case the answer is: never. We've tried to generously interpret earlier factoring annealing results (there is nothing new in the top-posted paper) and had to conclude that the overall method just doesn't scale well: https://arxiv.org/abs/1902.01448 https://arxiv.org/abs/1902.01448
- deleted 6y ago[deleted]
- hutzlibu 6y agoLayman question: assuming one day RSA gets actually broken and a quantum computer or a new algorithm can factorize prime numbers fast: would there be any alternatives avaiable for public/private key encryption? Or would the solution be, to use just a lot bigger prime numbers calculated also with a quantum computer? That sounds not too promising.
- dekz 6y agohttps://en.wikipedia.org/wiki/Post-quantum_cryptography https://en.wikipedia.org/wiki/Post-quantum_cryptography
- hutzlibu 6y agoOh thanks. So the answer seems: maybe.
- jessriedel 6y agoMy impression from talking to post-quantum cryptographers is that the answer is "probably" or "it would be pretty surprising, though not radically shocking, if it turns out that any public-key protocol is necessarily quantum-vulnerable".
- deleted 6y ago[deleted]
- thesz 6y agohttps://cr.yp.to/papers/pqrsa-20170419.pdf https://cr.yp.to/papers/pqrsa-20170419.pdf You may need to have 1TB of key storage (and signature) for post quantum RSA.
- rmrfstar 6y agoAn RSA break only breaks key distribution. If you can securely get someone an AES key, you are all set. That is why asset managers are experimenting with quantum communications channels [1]. [1] https://www.bloomberg.com/news/articles/2019-01-14/the-super-secure-quantum-cable-hiding-in-the-holland-tunnel https://www.bloomberg.com/news/articles/2019-01-14/the-super...
- rwmj 6y agoIBM and Google both claim to have 53 qubit computers, which I thought was the edge of the technology at the moment. This machine has 1635 "physical qubits". I'm guessing these are not the same thing. Can anyone comment on what the difference is?
- fsh 6y agoD-Wave is building "Quantum Annealers" which are not universal quantum computers. They cannot run quantum algorithms such as Shor's algorithm and there is serious doubt whether they can achieve any significant speed-up over classical computers, even in principle.
- cwillu 6y agoD-wave has a history. They've been mostly behaving better recently, but https://www.scottaaronson.com/blog/?p=1400 https://www.scottaaronson.com/blog/?p=1400 is a good summary, which emphasizes the differences you're asking about.
- McTossOut 6y agoThis association is likely some variation of Solovay-Kitaev, where imprecise, linearly independent gates can be combined to produce more precise gates, with polynomial resource utilization. The paper isn't formulated with respect to universal quantum computing which frustrates confirming such a claim, but here's a link, anyways... https://en.m.wikipedia.org/wiki/Solovay%E2%80%93Kitaev_theorem https://en.m.wikipedia.org/wiki/Solovay%E2%80%93Kitaev_theor...
- IncRnd 6y agoA single logical qubit is composed of multiple physical qubits in order to achieve some level of error correction and fault tolerance. Scaling the number of qubits is one of the hard problems with true quantum computers.
- dmos62 6y agoI see a slight irony in how I perceive crypto conversations as very cryptic. It's pleasant to wander into a thread like this where you can't really tell up from down (as a relative layperson).
- plopilop 6y agoThe authors give the following factorization with their algorithm: 231037 = 499 * 363. Not only is the product not equal to 231037, but 363 is also clearly not a prime as it is divisible by 3. There is no discussion whatsoever about this failure, except for "The low noise D-Wave 2000Q factored correctly all integers N up to L_N= 17"
- vlovich123 6y agoSeems like it's probably just a typographical error & should be 463*499.
- thesz 6y agoIt is clearly a typo. 231037=499*463.
- osamagirl69 6y agoThey also were not able to actually factor that one, the biggest number which produced the correct answer was 103459 = 337 * 307. Clearly they wrote the paper using the output of their annealer...
- NoKnowledge 6y agoThis study considers seven semi-primes (without justification why these seven) and reports an average(?) runtime of factoring each with D-Wave. No conclusions should be drawn on so few data-points. The proposed "Block Multiplication Table Method" will only affect the constants and thus has no effect on the asymptotics. The embedding from logical to physical qubits appears to have an exponential gap (but again, we shouldn't draw conclusions from so few data-points). However, if this is indeed true then even a polynomial runtime for annealing would still result in an exponential runtime for factoring. All in all, it eludes me why authors conclude that the obtained results are promising.
- TheUndead96 6y agooh boy