A new paper presents a polynomial-time quantum algorithm for solving certain hard lattice problems. This could be a big deal for post-quantum cryptographic algorithms, since many of them base their security on hard lattice problems.

A few things to note. One, this paper has not yet been peer reviewed. As this comment points out: “We had already some cases where efficient quantum algorithms for lattice problems were discovered, but they turned out not being correct or only worked for simple special cases .”

Two, this is a quantum algorithm, which means that it has not been tested. There is a wide gulf between quantum algorithms in theory and in practice. And until we can actually code and test these algorithms, we should be suspicious of their speed and complexity claims.

And three, I am not surprised at all. We don’t have nearly enough analysis of lattice-based cryptosystems to be confident in their security.

Last week I posted a short memorial of Ross Anderson. The Communications of the ACM asked me to expand it. Here’s the longer version .

EDITED TO ADD (4/11): Two weeks before he passed away, Ross gave an 80-minute interview where he told his life story.

Ross Anderson unexpectedly passed away Thursday night in, I believe, his home in Cambridge.

I can’t remember when I first met Ross. Of course it was before 2008, when we created the Security and Human Behavior workshop. It was well before 2001, when we created the Workshop on Economics and Information Security . (Okay, he created both—I helped.) It was before 1998, when we wrote about the problems with key escrow systems. I was one of the people he brought to the Newton Institute, at Cambridge University, for the six-month cryptography residency program he ran (I mistakenly didn’t stay the whole time)—that was in 1996.

I know I was at the first Fast Software Encryption workshop in December 1993, another conference he created. There I presented the Blowfish encryption algorithm. Pulling an old first-edition of Applied Cryptography (the one with the blue cover) down from the shelf, I see his name in the acknowledgments. Which means that sometime in early 1993—probably at Eurocrypt in Lofthus, Norway—I, as an unpublished book author who had only written a couple of crypto articles for Dr. Dobb’s Journal , asked him to read and comment on my book manuscript. And he said yes. Which means I mailed him a paper copy. And he read it. And mailed his handwritten comments back to me. In an envelope with stamps. Because that’s how we did it back then.

I have known Ross for over thirty years, as both a colleague and a friend. He was enthusiastic, brilliant, opinionated, articulate, curmudgeonly, and kind. Pick up any of his academic papers—there are many —and odds are that you will find a least one unexpected insight. He was a cryptographer and security engineer, but also very much a generalist. He published on block cipher cryptanalysis in the 1990s, and the security of large-language models last year. He started conferences like nobody’s business. His masterwork book, Security Engineering —now in its third edition—is as comprehensive a tome on cybersecurity and related topics as you could imagine. (Also note his fifteen-lecture video series on that same page. If you have never heard Ross lecture, you’re in for a treat.) He was the first person to understand that security problems are often actually economic problems . He was the first person to make a lot of those sorts of connections. He fought against surveillance and backdoors, and for academic freedom. He didn’t suffer fools in either government or the corporate world.

He’s listed in the acknowledgments as a reader of every one of my books from Beyond Fear on. Recently, we’d see each other a couple of times a year: at this or that workshop or event. The last time I saw him was last June, at SHB 2023 , in Pittsburgh. We were having dinner on Alessandro Acquisti ‘s rooftop patio, celebrating another successful workshop. He was going to attend my Workshop on Reimagining Democracy in December, but he had to cancel at the last minute. (He sent me the talk he was going to give. I will see about posting it.) The day before he died, we were discussing how to accommodate everyone who registered for this year’s SHB workshop . I learned something from him every single time we talked. And I am not the only one.

My heart goes out to his wife Shireen and his family. We lost him much too soon.

EDITED TO ADD (4/10): I wrote a longer version for Communications of the ACM .

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 .