Entries Tagged "quantum computing"

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NIST Draft Document on Post-Quantum Cryptography Guidance

NIST has released a draft of Special Publication1800-38A: “Migration to Post-Quantum Cryptography: Preparation for Considering the Implementation and Adoption of Quantum Safe Cryptography.” It’s only four pages long, and it doesn’t have a lot of detail—more “volumes” are coming, with more information—but it’s well worth reading.

We are going to need to migrate to quantum-resistant public-key algorithms, and the sooner we implement key agility the easier it will be to do so.

News article.

Posted on May 2, 2023 at 10:10 AM • View Comments

Side-Channel Attack against CRYSTALS-Kyber

CRYSTALS-Kyber is one of the public-key algorithms currently recommended by NIST as part of its post-quantum cryptography standardization process.

Researchers have just published a side-channel attack—using power consumption—against an implementation of the algorithm that was supposed to be resistant against that sort of attack.

The algorithm is not “broken” or “cracked”—despite headlines to the contrary—this is just a side-channel attack. What makes this work really interesting is that the researchers used a machine-learning model to train the system to exploit the side channel.

Posted on February 28, 2023 at 7:19 AM • View Comments

Breaking RSA with a Quantum Computer

A group of Chinese researchers have just published a paper claiming that they can—although they have not yet done so—break 2048-bit RSA. This is something to take seriously. It might not be correct, but it’s not obviously wrong.

We have long known from Shor’s algorithm that factoring with a quantum computer is easy. But it takes a big quantum computer, on the orders of millions of qbits, to factor anything resembling the key sizes we use today. What the researchers have done is combine classical lattice reduction factoring techniques with a quantum approximate optimization algorithm. This means that they only need a quantum computer with 372 qbits, which is well within what’s possible today. (The IBM Osprey is a 433-qbit quantum computer, for example. Others are on their way as well.)

The Chinese group didn’t have that large a quantum computer to work with. They were able to factor 48-bit numbers using a 10-qbit quantum computer. And while there are always potential problems when scaling something like this up by a factor of 50, there are no obvious barriers.

Honestly, most of the paper is over my head—both the lattice-reduction math and the quantum physics. And there’s the nagging question of why the Chinese government didn’t classify this research. But…wow…maybe…and yikes! Or not.

“Factoring integers with sublinear resources on a superconducting quantum processor”

Abstract: Shor’s algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglogN ), which is sublinear in the bit length of the integer N , making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.

In email, Roger Grimes told me: “Apparently what happened is another guy who had previously announced he was able to break traditional asymmetric encryption using classical computers…but reviewers found a flaw in his algorithm and that guy had to retract his paper. But this Chinese team realized that the step that killed the whole thing could be solved by small quantum computers. So they tested and it worked.”

EDITED TO ADD: One of the issues with the algorithm is that it relies on a recent factoring paper by Claus Schnorr. It’s a controversial paper; and despite the “this destroys the RSA cryptosystem” claim in the abstract, it does nothing of the sort. Schnorr’s algorithm works well with smaller moduli—around the same order as ones the Chinese group has tested—but falls apart at larger sizes. At this point, nobody understands why. The Chinese paper claims that their quantum techniques get around this limitation (I think that’s what’s behind Grimes’s comment) but don’t give any details—and they haven’t tested it with larger moduli. So if it’s true that the Chinese paper depends on this Schnorr technique that doesn’t scale, the techniques in this Chinese paper won’t scale, either. (On the other hand, if it does scale then I think it also breaks a bunch of lattice-based public-key cryptosystems.)

I am much less worried that this technique will work now. But this is something the IBM quantum computing people can test right now.

EDITED TO ADD (1/4): A reporter just asked me my gut feel about this. I replied that I don’t think this will break RSA. Several times a year the cryptography community received “breakthroughs” from people outside the community. That’s why we created the RSA Factoring Challenge: to force people to provide proofs of their claims. In general, the smart bet is on the new techniques not working. But someday, that bet will be wrong. Is it today? Probably not. But it could be. We’re in the worst possible position right now: we don’t have the facts to know. Someone needs to implement the quantum algorithm and see.

EDITED TO ADD (1/5): Scott Aaronson’s take is a “no”:

In the new paper, the authors spend page after page saying-without-saying that it might soon become possible to break RSA-2048, using a NISQ (i.e., non-fault-tolerant) quantum computer. They do so via two time-tested strategems:

  1. the detailed exploration of irrelevancies (mostly, optimization of the number of qubits, while ignoring the number of gates), and
  2. complete silence about the one crucial point.

Then, finally, they come clean about the one crucial point in a single sentence of the Conclusion section:

It should be pointed out that the quantum speedup of the algorithm is unclear due to the ambiguous convergence of QAOA.

“Unclear” is an understatement here. It seems to me that a miracle would be required for the approach here to yield any benefit at all, compared to just running the classical Schnorr’s algorithm on your laptop. And if the latter were able to break RSA, it would’ve already done so.

All told, this is one of the most actively misleading quantum computing papers I’ve seen in 25 years, and I’ve seen … many.

EDITED TO ADD (1/7): More commentary. Again: no need to panic.

EDITED TO ADD (1/12): Peter Shor has suspicions.

Posted on January 3, 2023 at 12:38 PM • View Comments

NIST’s Post-Quantum Cryptography Standards

Quantum computing is a completely new paradigm for computers. A quantum computer uses quantum properties such as superposition, which allows a qubit (a quantum bit) to be neither 0 nor 1, but something much more complicated. In theory, such a computer can solve problems too complex for conventional computers.

Current quantum computers are still toy prototypes, and the engineering advances required to build a functionally useful quantum computer are somewhere between a few years away and impossible. Even so, we already know that that such a computer could potentially factor large numbers and compute discrete logs, and break the RSA and Diffie-Hellman public-key algorithms in all of the useful key sizes.

Cryptographers hate being rushed into things, which is why NIST began a competition to create a post-quantum cryptographic standard in 2016. The idea is to standardize on both a public-key encryption and digital signature algorithm that is resistant to quantum computing, well before anyone builds a useful quantum computer.

NIST is an old hand at this competitive process, having previously done this with symmetric algorithms (AES in 2001) and hash functions (SHA-3 in 2015). I participated in both of those competitions, and have likened them to demolition derbies. The idea is that participants put their algorithms into the ring, and then we all spend a few years beating on each other’s submissions. Then, with input from the cryptographic community, NIST crowns a winner. It’s a good process, mostly because NIST is both trusted and trustworthy.

In 2017, NIST received eighty-two post-quantum algorithm submissions from all over the world. Sixty-nine were considered complete enough to be Round 1 candidates. Twenty-six advanced to Round 2 in 2019, and seven (plus another eight alternates) were announced as Round 3 finalists in 2020. NIST was poised to make final algorithm selections in 2022, with a plan to have a draft standard available for public comment in 2023.

Cryptanalysis over the competition was brutal. Twenty-five of the Round 1 algorithms were attacked badly enough to remove them from the competition. Another eight were similarly attacked in Round 2. But here’s the real surprise: there were newly published cryptanalysis results against at least four of the Round 3 finalists just months ago—moments before NIST was to make its final decision.

One of the most popular algorithms, Rainbow, was found to be completely broken. Not that it could theoretically be broken with a quantum computer, but that it can be broken today—with an off-the-shelf laptop in just over two days. Three other finalists, Kyber, Saber, and Dilithium, were weakened with new techniques that will probably work against some of the other algorithms as well. (Fun fact: Those three algorithms were broken by the Center of Encryption and Information Security, part of the Israeli Defense Force. This represents the first time a national intelligence organization has published a cryptanalysis result in the open literature. And they had a lot of trouble publishing, as the authors wanted to remain anonymous.)

That was a close call, but it demonstrated that the process is working properly. Remember, this is a demolition derby. The goal is to surface these cryptanalytic results before standardization, which is exactly what happened. At this writing, NIST has chosen a single algorithm for general encryption and three digital-signature algorithms. It has not chosen a public-key encryption algorithm, and there are still four finalists. Check NIST’s webpage on the project for the latest information.

Ian Cassels, British mathematician and World War II cryptanalyst, once said that “cryptography is a mixture of mathematics and muddle, and without the muddle the mathematics can be used against you.” This mixture is particularly difficult to achieve with public-key algorithms, which rely on the mathematics for their security in a way that symmetric algorithms do not. We got lucky with RSA and related algorithms: their mathematics hinge on the problem of factoring, which turned out to be robustly difficult. Post-quantum algorithms rely on other mathematical disciplines and problems—code-based cryptography, hash-based cryptography, lattice-based cryptography, multivariate cryptography, and so on—whose mathematics are both more complicated and less well-understood. We’re seeing these breaks because those core mathematical problems aren’t nearly as well-studied as factoring is.

The moral is the need for cryptographic agility. It’s not enough to implement a single standard; it’s vital that our systems be able to easily swap in new algorithms when required. We’ve learned the hard way how algorithms can get so entrenched in systems that it can take many years to update them: in the transition from DES to AES, and the transition from MD4 and MD5 to SHA, SHA-1, and then SHA-3.

We need to do better. In the coming years we’ll be facing a double uncertainty. The first is quantum computing. When and if quantum computing becomes a practical reality, we will learn a lot about its strengths and limitations. It took a couple of decades to fully understand von Neumann computer architecture; expect the same learning curve with quantum computing. Our current understanding of quantum computing architecture will change, and that could easily result in new cryptanalytic techniques.

The second uncertainly is in the algorithms themselves. As the new cryptanalytic results demonstrate, we’re still learning a lot about how to turn hard mathematical problems into public-key cryptosystems. We have too much math and an inability to add more muddle, and that results in algorithms that are vulnerable to advances in mathematics. More cryptanalytic results are coming, and more algorithms are going to be broken.

We can’t stop the development of quantum computing. Maybe the engineering challenges will turn out to be impossible, but it’s not the way to bet. In the face of all that uncertainty, agility is the only way to maintain security.

This essay originally appeared in IEEE Security & Privacy.

EDITED TO ADD: One of the four public-key encryption algorithms selected for further research, SIKE, was just broken.

Posted on August 8, 2022 at 6:20 AM • View Comments

SIKE Broken

SIKE is one of the new algorithms that NIST recently added to the post-quantum cryptography competition.

It was just broken, really badly.

We present an efficient key recovery attack on the Supersingular Isogeny Diffie­-Hellman protocol (SIDH), based on a “glue-and-split” theorem due to Kani. Our attack exploits the existence of a small non-scalar endomorphism on the starting curve, and it also relies on the auxiliary torsion point information that Alice and Bob share during the protocol. Our Magma implementation breaks the instantiation SIKEp434, which aims at security level 1 of the Post-Quantum Cryptography standardization process currently ran by NIST, in about one hour on a single core.

News article.

Posted on August 4, 2022 at 6:56 AM • View Comments

NIST Announces First Four Quantum-Resistant Cryptographic Algorithms

NIST’s post-quantum computing cryptography standard process is entering its final phases. It announced the first four algorithms:

For general encryption, used when we access secure websites, NIST has selected the CRYSTALS-Kyber algorithm. Among its advantages are comparatively small encryption keys that two parties can exchange easily, as well as its speed of operation.

For digital signatures, often used when we need to verify identities during a digital transaction or to sign a document remotely, NIST has selected the three algorithms CRYSTALS-Dilithium, FALCON and SPHINCS+ (read as “Sphincs plus”). Reviewers noted the high efficiency of the first two, and NIST recommends CRYSTALS-Dilithium as the primary algorithm, with FALCON for applications that need smaller signatures than Dilithium can provide. The third, SPHINCS+, is somewhat larger and slower than the other two, but it is valuable as a backup for one chief reason: It is based on a different math approach than all three of NIST’s other selections.

NIST has not chosen a public-key encryption standard. The remaining candidates are BIKE, Classic McEliece, HQC, and SIKE.

I have a lot to say on this process, and have written an essay for IEEE Security & Privacy about it. It will be published in a month or so.

Posted on July 6, 2022 at 11:49 AM • View Comments

The NSA Says that There are No Known Flaws in NIST’s Quantum-Resistant Algorithms

Rob Joyce, the director of cybersecurity at the NSA, said so in an interview:

The NSA already has classified quantum-resistant algorithms of its own that it developed over many years, said Joyce. But it didn’t enter any of its own in the contest. The agency’s mathematicians, however, worked with NIST to support the process, trying to crack the algorithms in order to test their merit.

“Those candidate algorithms that NIST is running the competitions on all appear strong, secure, and what we need for quantum resistance,” Joyce said. “We’ve worked against all of them to make sure they are solid.”

The purpose of the open, public international scrutiny of the separate NIST algorithms is “to build trust and confidence,” he said.

I believe him. This is what the NSA did with NIST’s candidate algorithms for AES and then for SHA-3. NIST’s Post-Quantum Cryptography Standardization Process looks good.

I still worry about the long-term security of the submissions, though. In 2018, in an essay titled “Cryptography After the Aliens Land,” I wrote:

…there is always the possibility that those algorithms will fall to aliens with better quantum techniques. I am less worried about symmetric cryptography, where Grover’s algorithm is basically an upper limit on quantum improvements, than I am about public-key algorithms based on number theory, which feel more fragile. It’s possible that quantum computers will someday break all of them, even those that today are quantum resistant.

It took us a couple of decades to fully understand von Neumann computer architecture. I’m sure it will take years of working with a functional quantum computer to fully understand the limits of that architecture. And some things that we think of as computationally hard today will turn out not to be.

EDITED TO ADD (6/14): Since I wrote this, flaws were found in at least four candidates.

Posted on May 16, 2022 at 6:34 AM • View Comments

Breaking 256-bit Elliptic Curve Encryption with a Quantum Computer

Researchers have calculated the quantum computer size necessary to break 256-bit elliptic curve public-key cryptography:

Finally, we calculate the number of physical qubits required to break the 256-bit elliptic curve encryption of keys in the Bitcoin network within the small available time frame in which it would actually pose a threat to do so. It would require 317 × 106 physical qubits to break the encryption within one hour using the surface code, a code cycle time of 1 μs, a reaction time of 10 μs, and a physical gate error of 10-3. To instead break the encryption within one day, it would require 13 × 106 physical qubits.

In other words: no time soon. Not even remotely soon. IBM’s largest ever superconducting quantum computer is 127 physical qubits.

Posted on February 9, 2022 at 6:25 AM • View Comments

Update on NIST's Post-Quantum Cryptography Program

NIST has posted an update on their post-quantum cryptography program:

After spending more than three years examining new approaches to encryption and data protection that could defeat an assault from a quantum computer, the National Institute of Standards and Technology (NIST) has winnowed the 69 submissions it initially received down to a final group of 15. NIST has now begun the third round of public review. This “selection round” will help the agency decide on the small subset of these algorithms that will form the core of the first post-quantum cryptography standard.

[…]

For this third round, the organizers have taken the novel step of dividing the remaining candidate algorithms into two groups they call tracks. The first track contains the seven algorithms that appear to have the most promise.

“We’re calling these seven the finalists,” Moody said. “For the most part, they’re general-purpose algorithms that we think could find wide application and be ready to go after the third round.”

The eight alternate algorithms in the second track are those that either might need more time to mature or are tailored to more specific applications. The review process will continue after the third round ends, and eventually some of these second-track candidates could become part of the standard. Because all of the candidates still in play are essentially survivors from the initial group of submissions from 2016, there will also be future consideration of more recently developed ideas, Moody said.

“The likely outcome is that at the end of this third round, we will standardize one or two algorithms for encryption and key establishment, and one or two others for digital signatures,” he said. “But by the time we are finished, the review process will have been going on for five or six years, and someone may have had a good idea in the interim. So we’ll find a way to look at newer approaches too.”

Details are here. This is all excellent work, and exemplifies NIST at its best. The quantum-resistant algorithms will be standardized far in advance of any practical quantum computer, which is how we all want this sort of thing to go.

Posted on July 24, 2020 at 6:36 AM • View Comments

Factoring 2048-bit Numbers Using 20 Million Qubits

This theoretical paper shows how to factor 2048-bit RSA moduli with a 20-million qubit quantum computer in eight hours. It’s interesting work, but I don’t want overstate the risk.

We know from Shor’s Algorithm that both factoring and discrete logs are easy to solve on a large, working quantum computer. Both of those are currently beyond our technological abilities. We barely have quantum computers with 50 to 100 qubits. Extending this requires advances not only in the number of qubits we can work with, but in making the system stable enough to read any answers. You’ll hear this called “error rate” or “coherence”—this paper talks about “noise.”

Advances are hard. At this point, we don’t know if they’re “send a man to the moon” hard or “faster-than-light travel” hard. If I were guessing, I would say they’re the former, but still harder than we can accomplish with our current understanding of physics and technology.

I write about all this generally, and in detail, here. (Short summary: Our work on quantum-resistant algorithms is outpacing our work on quantum computers, so we’ll be fine in the short run. But future theoretical work on quantum computing could easily change what “quantum resistant” means, so it’s possible that public-key cryptography will simply not be possible in the long run. That’s not terrible, though; we have a lot of good scalable secret-key systems that do much the same things.)

Posted on October 14, 2019 at 6:58 AM • View Comments

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Sidebar photo of Bruce Schneier by Joe MacInnis.