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‘If Anything Happens to This Guy … Everyone Is Screwed’

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On Tuesday, the world found out about two massive security vulnerabilities in PHP, a programming language that is used by roughly 70 percent of websites. The flaw was discovered by cybersecurity researchers using a frontier model from OpenAI. If they exploited it, attackers could gain full control of servers, stealing or copying anything inside or simply taking sites offline.

The PHP Foundation, the organization that maintains the programming language, had recently learned about the security flaws, but the disclosure was leaked on a forum before a patch could be released. What happened next was a frantic race with numerous participants: the foundation, which needed to create and release a patch; developers around the world, who would need to deploy it; and attackers looking to exploit these vulnerabilities in the interim. Matthew Prince, the CEO of the hosting company Cloudflare, wrote that in the 10 hours before the flaws were publicly announced, “we saw thousands of attempts to exploit it. That jumped to tens of thousands in the 45 minutes post announcement, hundreds of thousands within 2 hours, and millions now.”

Once the patch was released yesterday, websites everywhere went offline to implement the fix. These included government websites in Germany and Finland, some hospital and school websites in Europe, and international sites such as 4chan. During this race to secure the majority of the internet, I noticed one name pop up in posts on Reddit and X: Ondřej Surý.

“Explaining to my wife how there’s this one guy. And he alone is responsible for most of the world’s distribution of PHP,” a software developer named Ian Landsman wrote on X. “And if anything happens to this guy, that’s just it. Everyone is screwed.” He was referring to Surý.

Surý, who lives in Czechia, does not work for the PHP Foundation. But alongside his day job as director of domain-name-system engineering at the nonprofit Internet Systems Consortium, in a volunteer capacity, he maintains and helps automate patches for the coding language. His work, with that of just a handful of others, has allowed countless websites and organizations to fix these vulnerabilities quickly. Over the past 48 hours, he’s become arguably the unsung hero of the entire internet—despite the fact that the only compensation he receives is from modest donations. “Ondřej will save the internet today,” a user in the PHP Subreddit wrote.

I spoke with Surý today from his home about the unfolding AI-cybersecurity crisis, how the internet’s infrastructure is maintained by small crews of volunteers such as himself, and how it feels to go to bed after saving the web as we know it.

Our conversation has been edited for length and clarity.

Charlie Warzel: Explain to me what has happened in layman’s terms over the past 72 hours.

Ondřej Surý: Earlier this week, I got notified by the PHP project that there was a serious security vulnerability in the coding. On Tuesday, it became apparent that someone had leaked information about the upcoming vulnerabilities, and it was decided inside the PHP project that it needed to accelerate the release process from Thursday to Wednesday. This is when it became a little bit crazy, because now we were one day short suddenly.

Warzel: I want to try to put this into perspective: So basically, the PHP programming language that kind of undergirds the web is used by up to 70 percent of websites?

Surý: That’s what I heard as well.

Warzel: So people search for cybersecurity vulnerabilities, not necessarily for offensive-attack opportunities but maybe just defensive opportunities. And someone found a vulnerability—that’s not super abnormal. But the real issue here was how widely it was disclosed and the amount of time before people had to patch this, right?

Surý: Let me clarify that: It’s the severity. The severity is unusual. Remote Code Execution is the most severe type of vulnerability, because the attacker is able to execute their own code on the server that’s running PHP. That’s why this caused such panic throughout the internet. As you said, if about 70 percent of websites are running PHP, the impact would be huge if attackers would actually be able to execute code on these servers.

Warzel: You said that despite the panic online, it has not been a crazy 48 hours. From the outside, that’s surprising. I keep seeing people saying, There’s one person who is in charge of fixing this—and he’s supporting himself through Patreon. They may have been exaggerating, but there’s some truth to that: Your work was single-handedly helping millions of people. How could this not be a crazy time for you?

Surý: There are a couple of reasons. One is that I’ve been doing this for a long time, over 20 years. A lot of the stuff that I do is automated. But the reason it was not crazy for me was that I actually don’t have any system running PHP myself. So for me, it was like, sure, I feel a responsibility toward the users of the internet. It would be a crazy day for me if I was on a boat in the middle of the Adriatic Sea. That could happen. But I had time to prepare the packages.

Warzel: That’s kinda wild.

Surý: And even without me, people would still be able to get PHP from other sources and compile it themselves. But it would be more complicated for everyone. And some people don’t immediately have the skill to upgrade the PHP. What the PHP project did was release the source code for the language. What I am doing is preparing it into these things called packages that people can install on their servers. It’s very convenient, and it’s faster, and you can automate it and can install the same package over hundreds and thousands of servers, and you don’t have to compile it. If I was not available, it would take more time; some of them wouldn’t have the skills. Really, the thanks go to the PHP project that invited me into this secret cabal who knew about the vulnerabilities and had access before the public release.

Warzel: When you got invited, was it a real Oh, crap moment for you?

Surý: I’m in the stage of my life where I was like, This is bad. It needs to be fixed. But it doesn’t cause panic, at least for me. It did cause panic for a lot of people. But you know, it was more like, We have a situation, it needs to be solved, and this is how we do it. And I have time to properly prepare. If I didn’t have time to properly prepare, then it would cause a lot of stress. From where I stand, it was not stressful, because I’m doing this as a volunteer, and if I get hit by a bus, then it will be someone else’s problem.

Warzel: Every time I dabble in writing about the world of cybersecurity and open-source software, I discover these groups of maintainers: people such as yourself who do this work because they care. Often, nobody knows their name. But is there a line of people who would take your place if, say, you did get hit by a bus?

Surý: I am actually thinking about contingency plans. And we are talking with Raphaël Hertzog from the software company Freexian. My advantage is that I have a lot of expertise, and I know where to touch the thing to make it work. But Freexian has a lot of expertise, and they would be able to take over if anything happens.

People have been donating small amounts, and larger amounts, like crazy since yesterday. I would like to thank them all.

Warzel: Have the donations been overwhelming?

Surý: Not Silicon Valley levels of money, but I got a serious amount of contributions that I’ve never seen before. It’s like one year of the contributions gathered over the past 24 hours.

[Matteo Wong: Read this website while you still can]

Warzel: What would have happened if this wasn’t patched as quickly as it was?

Surý: A lot of things could have happened. The very basic thing is that there would be vandalism, that the sites would be taken down. And we are seeing this every day on the internet now. The other stuff that happens is that someone gets access and runs a botnet out of these devices. I would say it’s mostly organized crime doing that now—it’s not like a small guy in the basement doing this for fun. There are financial incentives for these people to sell the botnet services or to do the crypto-mining on these servers for a profit. And this still could happen, because it’s not like everyone has patched and updated their PHP.

Warzel: I saw a post on X that said not all PHP releases are patched, and one-third of the internet is kind of permanently either broken or vulnerable. Is that correct?

Surý: That initial information is not correct. There are ways to patch even the old versions.

Warzel: So one-third of the internet is not permanently screwed. Okay.

Surý: No, that’s not accurate. If people care enough, they are able to even update these old versions of PHP.

Warzel: It’s a scary moment for cybersecurity. I’ve seen people online referring to this vulnerability and other AI-agent hacks as “Black October,” and there’s concern that defensive or attacking agents can find these vulnerabilities. There is this feeling that I am noticing from the cybersecurity community that their fears of a future where things are being exploited or discovered quicker than people can handle is coming true—that we are living in that moment. And then separately, there’s a contingent of people who are saying there is an equilibrium here: If you have very persistent agents that are very good at identifying and exploiting vulnerabilities, you also have very persistent agents that are very good at defending against them.

Surý: What we’ve seen is that things have accelerated—that’s absolutely right. The defenders are also able to use the large language models to find the vulnerabilities for themselves. I believe it boils down to the simple fact that IT infrastructure is often being taken for granted.

There’s not enough priority and money going to properly maintain the IT infrastructure in various places. It’s not only companies; it’s also a lot of outdated consumer electronics that are going to be attacked. I kind of agree that everything’s moving fast now, and it’s taking a toll on the people who are defending the stuff. At the same time, maybe this is the turning point where we actually start caring about this.

[Ian Bogost: Invasion of the self-replicating AI-malware botnet]

Warzel: Do you feel like that will actually happen?

Surý: I might be wrong, but I’m an optimist that people will finally realize that we can’t go like this forever. This has been a disaster waiting to happen for a really, really long time. And this is just one of the many wake-up calls that came and will be coming.

Warzel: I am amazed by how much the infrastructure in certain areas of the internet can hinge on one or two people. There is a fragility to all of this that is concerning. So what do you want to see?

Surý: When I started doing open-source, it was fun. And it kind of still is. But the environment has shifted. Open-source sometimes feels like exploitation. What I would like to see is to find a new model where people working on open-source would be awarded for their work and the hours and hours they put into it from the people who most benefit from their work. I would like companies to realize that this is exploitation. Any exploitation is not sustainable. And it will end up badly if this continues, because the people doing the open-source will stop being motivated to actually do anything in the end.

Warzel: It sounds like you don’t have an ego about all of this. But you did some work, and you helped out a tremendous amount of people in every corner of the world yesterday. How did it feel to go to bed last night after all of that, knowing the role that you played?

Surý: Well, my wife says that I’m emotionally dead, but I’m not. And it felt nice. Like, seeing my social network filling up with thank-you notes, and getting emails with thank-yous, that feels really nice. It puts some sense into what I do. I felt that what I do has a purpose.

Warzel: The whole internet appreciates your efforts. Is there anything that you would recommend normal people do at this moment to improve their internet hygiene?

Surý: I would recommend that they rely on the experts. That’s what we all do in a crisis: We talk to experts and trust them. Rely on people, that people who take care of this stuff know what they are doing. And that’s all we can do.



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denubis
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On the demise of Contemporary Professional Mathematics

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From the Fall of the Berlin Wall until about a decade ago my animating intellectual question was pretty much, ‘how did a small number of natural sciences become qualitatively more impressive than the social sciences?’ Because I met the late George Smith relatively early in my thinking about this (as an undergraduate), I often formulated this question in terms of evidence; he liked his version of my question as ‘how to turn data into high-quality evidence?’ And his striking answer was (to simplify) that deviations from theoretically significant expectations through theory-mediated measurement were made informative in an iterative process over time in the sciences that succeeded in achieving lift-off. While I was much more interested in the social organization of the sciences than George, I never did much better than he did in answering my own question. But I did make sure his version was published in the best possible form and with full detail (see his ‘Closing the Loop.’)

Along the way, I became an expert on Newton and his reception and on developments in twentieth century economics, and I found a home in professional philosophy (as a ‘historian of philosophy,’ a ‘philosopher of social science,’ and ‘HPS-type’). At least this is a way one can tell my professional story before I switched (or returned) to political theory. Once in political theory I recognized that Machiavelli’s great contribution to the art of government — that in the right conditions, which includes considerable layers of social opacity, social disorder can itself be informative — anticipates George’s insight into how successive approximation can be fruitful.

Be that as it may, the way professional philosophy is organized, there is no list of ‘open’ questions that are treated as ‘important.’ In fact, there are ways of posing my animating question in terms that made it sound vaguely Popperian (viz. ‘is there a scientific method;’ ‘a logic of discovery?;’ ‘could concepts be stress tested?’)—and so discarded. Sometimes I was directed to others — Alison Wylie, Nancy Cartwright, and Hasok Chang back in the day — whose projects had a family resemblance with my own.

There are some subfields in philosophy where through the force of personality and/or institutional entrenchment (or donor/foundation persistence) some questions do feel significant and open. But more often than not these are treated (after the fact) as evidence of ‘fashion’ in philosophy. Because there is no consensus on what really matters philosophically, and great jobs are scarce in the profession, lots of professional philosophers are in the business of artificially producing prestige (by keeping acceptance rates for the really important journals ridiculously low).

The previous was not really meant to be polemical.

Professional philosophers often think of themselves as constituting a field that’s not very far from professional mathematics. One of our core areas — mathematical logic — even has some overlap with foundational practices in mathematics. And I am just old enough to remember the time when some wise folk thought that having mathematical logicians around in philosophy was a thing thought good, perhaps standards-protecting (even standards-raising), for a department. And I was taught by and mentored for a long time by a philosopher, Jody Azzouni who himself studied mathematical practice, and found that useful in debating what other professional philosophers argued about philosophically important topics.

But judging by the reactions collected at ‘Proofs and Prompts’ to the Open AI math dump last week, the way enquiry is organized in professional mathematics is quite distinct from the relative lack of organization in philosophy. Or to put it differently, professional mathematics has much more of a closed guild structure than we do in philosophy. (Some evidence for this can be gleaned from the way the mathematicians use ‘community’ in ‘mathematical/mathematics community’—no philosopher would speak of our profession as such as a community unless it were in order to be satirical.) There who you study with and what ‘open’ problems you work on have a rather tight connection and, these in turn, have a rather tight connection to one’s professional identity and trajectory. To put it in terms of the economists: barriers to entry and, once in, path-dependent endowment effects are rather steep.

Having a list of such open problems, and an implied sense of their significance to the community, allows for much coordination, including the distribution of honors, jobs, and grant proposals. While there is, undoubtedly, a political economy to the institutions that fund all of this, it has allowed for a non-trivial amount of bottom-up intellectual and collective self-governance as well as exploration. It is, for example, pretty clear that quite a few leading mathematicians have been early adopters of LLMs in their own research and, thereby, have indirectly helped train the next generation of these.

The situation described in the previous paragraph is fairly unique in human history. Few civilizations have invested in pure mathematics to the degree ours has with the rise of the modern research university and dedicated research institutions since (say) the late nineteenth century. (By ‘civilization’ I am happy to be very inclusive.) But by making its official problems explicitly legible (to adopt social science jargon), the ‘mathematical community’ became sitting ducks when the barriers to entry were huge for individual researchers but a relatively easy technological hurdle for a few for-profit corporations with no hard budget constraint (relative to the mathematical community). These companies now control a vital resource that enables one to be on the leading edge of the mathematical frontier. My use of ‘one’ is, of course, a weasel word—because it is wholly unclear if any human can have any leading role on that frontier henceforth.

Perhaps the implied guild structure explains the unseemly schadenfreude with which the demise of professional mathematics has been welcomed by so many commentators. Cheering on the misfortune of those who harm nobody, and who are engaged in a noble activity, is itself evidence of the advanced corruption (recall) of our age.

One sometimes hears from economic historians and sociologists of technology that the technological disruption to the mathematical community, if it is one, is no big deal all things considered. The mathematicians turn out to be no different from the hand-weavers, the loom operators, and the human (mostly female) ‘computers’ that got displaced by machines in the context of progress. But while there is more than a kernel of truth in this (and there is quite a bit of intellectual labor embodied in modern machinery, etc.), this is one of the first times since the rise of the modern research university that a ‘pure’ field risks being overtaken and displaced by one of the (applied) technologies it partially birthed. Philosophers are somewhat used to being told by the practitioners in the fields it helped birth that philosophy is useless and pointless; but it may hit the mathematicians harder. Many mathematicians are in a state of “shock,” “loss,” and depression (as well as anger), but a guild that gets undermined also opens up new opportunities for those impatient or sidelined under the old regime.

As regular readers know (recall here), I argue that the structural (Humphreys) opacity that is inherent in LLMs enhances genuine expertise. But it doesn’t follow from this that the remaining place for human mathematical expertise is on the research frontier of commonly defined open questions. My own scholarly work (with Russo and Wagemans here) suggests that in such conditions there will be more work for certification and less for production. For, opaque systems, when used to produce results, systematically secrete new layers of opacity that need to be checked and monitored.

I increasingly suspect professional mathematics will turn into practiced and idiosyncratic virtuosity, where math slides back into modern art.1 (Danny Calegari’s examples of animations are worth pondering.) Since modern universities find ways to hire, evaluate, and promote all kinds of artists, this may require less administrative adjustment than one might fear.

Of course, if the cutting edge LLMs become more like a utility, then, alternatively, maybe credentialling within mathematics disappears entirely. Automated iterative feedback from deviations then mops it all up.

What about professional philosophy and the scholarship about it (i.e. history of philosophy)? Prestige producers and the journals they control are fighting a rearguard action against the use of LLMs. I expect more and more ‘professional philosophy’ to be co-produced by professional philosophers and LLMs, until we reach the point where LLMs ‘edit,’ referee, and summarize all such papers and are effectively the only ones actually reading them. Given the way it is organized the good news is professional philosophy is not so vulnerable to a hostile takeover; but the bad news is that it is vulnerable to increasing (ahh) hollowing out of its mode of production because that mode is not itself intrinsic to philosophy. (Okay that was polemical.)

That last claim is too strong undoubtedly. Such legibility to outsiders is, of course, a matter of degree and intensity, and one wonders if the philosophical contributions of (say) Jorge Luis Borges will be re-evaluated in light of such considerations (not to mention the fortunes of bits of continental philosophy). By emphasizing Borges here I do not mean to focus on his brilliant thought experiments, but rather on how he indicates new ways of discernment. That means, but this is self-serving, that philosophers will increasingly value and gravitate toward judgment and voice—but I would say that.

Let me rephrase that. You may think that if we take Liam Kofi Bright’s famous distinction between basically pleasant bureaucrats and Sexy Murder Poets seriously, I am predicting the demise of the former and the renewed attraction of the latter within professional philosophy. But while that result would greatly amuse me, it’s not what I am predicting. Rather I am claiming (recall my treatment of synthetic philosophy) that philosophy will rediscover that its vocation is in the tending, nurturing, and monitoring of the machinery of governance of the bureaucratic structure (including the LLMs) that is opaque to society.

 

 

 

1 In some ways this would be a return to Hardy’s perspective, but also with a different conception of art and beauty underwriting it. That is, mathematics will become more like painting in response to the development of photography and the newer digital technologies. (The second half of this footnote was suggested by a token of Opus 5.5.)

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denubis
7 days ago
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(Post-Quantum) Cryptographic Right Answers

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Publishing “Cryptographic Right Answers” for developers is a tradition by now. Colin Percival started in 2009, Thomas Ptacek followed up in 2015, and then Latacora carried on in 2018 and 2024.

It might feel too soon for an update, but so much has changed. The timeline of the post-quantum transition dramatically shifted in early 2026, and there is now consensus that it needs to complete by 2029. 2029! We have three years!

The good news is that, despite what you might have heard, symmetric cryptography is going to be fine, because Grover does not matter. The bad news is that all asymmetric answers changed compared to 2018 and most even compared to 2024.

The answers below assume you are not constrained by any specific compliance regime, although they are mostly compatible with FIPS 140.1 If you need to follow something stricter like CNSA 2.0, you’ll know. Just substitute as appropriate.

Finally, remember the other big change of 2026: LLMs are very good at finding bugs now. “Get a review from the best model you can afford” is now firmly a Cryptographic Right Answer, along with the long-time classic “use a memory-safe language.”

If you’re in a rush, here’s the cheat sheet:

  • Encrypting data: If you’re in the cloud, KMS. Otherwise, XAES-256-GCM or XChaCha20Poly1305 with random nonces. If you’re encrypting more than a few MB, use Cobblestone-128.
  • Symmetric key length: Don’t stress it. 256-bit keys if you need to pick.
  • Symmetric “signatures”: HMAC-SHA-256.
  • Hash algorithm: SHA-2 is still fine, but use a real multihash (SequenceHash) if needed.
  • Random IDs: 32 random bytes, a.k.a. 256-bit random numbers.
  • Password handling: Argon2id or scrypt. But have you considered passkeys instead?
  • Key exchange: X25519+ML-KEM-768 in a secure, standard protocol.
  • Asymmetric encryption: HPKE with (MLKEM768-X25519 a.k.a. X-Wing, HKDF-SHA256, AES-128-GCM), or age with PQ keys.
  • Asymmetric signatures: ML-DSA-44.
  • Website or client-server application security: If you’re in the cloud, use its ALB/NLB. Otherwise, rustls, Go’s crypto/tls, BoringSSL, AWS-LC, or s2n-tls with a popular, updated ACME client.
  • Online backups: restic with a long random password.

Now let’s dive in.

Encrypting data

If you’re in the cloud, KMS. Otherwise, XAES-256-GCM or XChaCha20Poly1305 with random nonces. If you’re encrypting more than a few MB, use Cobblestone-128.

Percival, 2009: AES-CTR with HMAC.
Ptacek, 2015: NaCl/libsodium default, or ChaCha20Poly1305, or AES-GCM.
Latacora, 2018: KMS, or XSalsa20+Poly1305.
Latacora, 2024: KMS, or NaCl’s secretbox, or XChaCha20Poly1305.

Latacora’s reasoning for why and when you’d use your cloud’s KMS is still solid, so start there.

If you’re encrypting locally, you want an AEAD where you can avoid worrying about tracking nonces or how many messages you encrypted, so you want random nonces of at least 128 bits.2

NaCl/libsodium’s secretbox is just a paper-thin wrapper around a less common AE construction (XSalsa20+Poly1305), so instead I recommend XAES-256-GCM or XChaCha20Poly1305. The former is an efficient composition of a standard KDF and AES-GCM, packaged as an extended-nonce AEAD, so even if your library doesn’t provide it under that name you can assemble it from the KDF and AES-GCM APIs.3

Regular AES-GCM and ChaCha20Poly1305 with random nonces are only ok if you know for certain you won’t encrypt more than a billion messages with one key. AES-GCM-SIV is also a good AEAD choice if you happen to have it everywhere you need it, but that’s kinda unlikely. Some even newer options have nice properties like key commitment, but are not commonly available yet.

Since you have an AEAD, consider putting context in the additional data, like the user ID you’re encrypting for, or the version of the protocol. Anything not secret that you will definitely still know at decrypt time.

Very important is how you handle large messages, which KMS will not solve for you. Do not pass one large message to an AEAD, or you might be forced to process or store the plaintext before having authenticated it at decrypt time. Absolutely do not use unauthenticated stream ciphers. Instead, you should use STREAM (which is not a stream cipher but a way to use AEADs on a stream… I know, I know, terrible name). There are a lot of options—too many, in fact—and shamefully none are the consensus answer. Tink has one, libsodium has one, the AWS Encryption SDK has one, FLOE is one, age has one, and the list goes on. I recommend Cobblestone-128, which is a STREAM variant derived from TLS, and is available in pyca/cryptography and soon in the Go standard library (and in the meantime at filippo.io/cobblestone).4

Avoid: unauthenticated modes (CBC, CTR, raw stream ciphers), random 96-bit nonces unless you spent a lot of time thinking about how many messages you encrypt, rolling your own AEAD construction.

Symmetric key length

Don’t stress it. 256-bit keys if you need to pick.

Percival, 2009: 256-bit AES keys.
Ptacek, 2015: 256-bit keys.
Latacora, 2018: 256-bit keys.
Latacora, 2024: 256-bit keys.

Remember that Grover doesn’t actually matter and 128-bit brute-force attacks don’t exist. Still, 256-bit keys rule out multi-target attacks, which is nice.

However, don’t make other decisions based on this. For example, the recommended Cobblestone suite uses 128-bit keys and that’s fine because it has a careful analysis of multi-target attacks. Likewise, don’t go changing the default cipher suite preferences of your TLS library to enforce 256-bit keys; there’s no need.

AES-256 is slower than AES-128 because unfortunately Rijndael ties the number of rounds to the key size, but this probably won’t matter in practice.

Avoid: anything other than 128 or 256 bits, worrying too much about size, keys that are not uniform (e.g. using a password or ASCII hex string directly as a key).

Symmetric “signatures”

HMAC-SHA-256.

Percival, 2009: HMAC.
Ptacek, 2015: HMAC.
Latacora, 2018: HMAC.
Latacora, 2024: HMAC.

Yay for HMAC.

Just be careful to sidestep canonicalization and parser alignment bugs by always authenticating a verbatim string of bytes, not something you need to recompute.

Good:

{
    "inner": "{\"foo\":123}",
    "hmac": "MbPsZq7QGCllJgDnSSy/cyM10HjqiVu35UO7yyY5d3w="
}

Check the HMAC and then process or store or forward just {"foo":123}.

Bad:

{
    "foo": 123,
    "hmac": "MbPsZq7QGCllJgDnSSy/cyM10HjqiVu35UO7yyY5d3w="
}

You can use KMAC or keyed BLAKE3 if you already had a reason to use their underlying hashes. HMAC-SHA-512 is also fine.

Remember to compare tags with dedicated constant-time functions.

Avoid: rolling your own YoloMAC, encrypted hashes, standalone one-time MACs like Poly1305 or GMAC.

Hash algorithm

SHA-2 is still fine, but use a real multihash if needed.

Percival, 2009: SHA-256 (SHA-2), plan on SHA-3.
Ptacek, 2015: SHA-2.
Latacora, 2018: SHA-2.
Latacora, 2024: SHA-2.

The best option, if you have it available, is still SHA-512/256, which isn’t vulnerable to length-extension attacks. Otherwise, SHA-256 and SHA-512 are both fine.5

SHA-3 is unnecessary (because SHA-2 is fine) and slow,6 but not wrong. If you already have Keccak (SHA-3) around for ML-KEM and ML-DSA, and you want to use it for hashing, draw 32 bytes from SHAKE128.

BLAKE2 is a weird choice these days. BLAKE3 is very fast, but complex and uncommon enough that you want to have a good reason to use it and a good reason to trust your implementation.

Multihashing is when you need to hash multiple things at once. For example, multiple columns of a row, or a filename along with the file contents. It’s subtler than it sounds, so use SequenceHash with SHA-2, or TupleHash (SP 800-185) with SHA-3.

Avoid: SHA-1, MD5, all other hash functions, rolling your own multihash, truncating to less than 256 bits unless a cryptographer told you collisions are not a concern.

Random IDs

32 random bytes, a.k.a. 256-bit random numbers.

Percival, 2009: 256-bit random numbers.
Ptacek, 2015: 256-bit random numbers.
Latacora, 2018: 256-bit random numbers.
Latacora, 2024: 256-bit random numbers.

Note that UUIDv4 and APIs like rand.Text will give you ~128-bit values instead. That’s usually fine, unless you need more than 280 trillion (2⁴⁸) unique values. 256 bits is overkill, but why not.

Use your operating system’s CSPRNG: getrandom on Linux, ProcessPrng on Windows, arc4random_buf on macOS and BSD, getRandomValues on the web. A good library will wrap these for you.

Avoid: non-cryptographic PRNGs, userspace random number generators like OpenSSL’s, haveged, CPU jitter entropy.7

Password handling

Argon2id or scrypt. But have you considered passkeys instead?

Percival, 2009: scrypt or PBKDF2.
Ptacek, 2015: scrypt, then bcrypt, then PBKDF2 if you must.
Latacora, 2018: scrypt, then Argon2, then bcrypt, then PBKDF2 if you must.
Latacora, 2024: Argon2id, then scrypt, then bcrypt, then PBKDF2 if you must.

Everything my predecessors said is still spot on: “you can throw a dart at a wall to pick one of these.” I dropped bcrypt because the 72-byte truncation bites. One tip: you could argue to your auditors that scrypt is FIPS 140 compliant because its actual KDF step is PBKDF2, which is what they want. I heard it works.

For parameters, ignore RFC 9106 which apparently wants to murder your production system, and use m=64 MiB, t=2, p=1 for Argon2id (libsodium’s INTERACTIVE preset) or N=2^16, r=8, p=1 for scrypt. They use the same memory, but the scrypt ones will take ~1.5× the CPU time and ¼ the GPU time, which is why you should prefer Argon2id. If you’re doing non-interactive key derivation, feel free to crank up Argon2id’s m, and then t (or just N8 for scrypt) as far as tolerable.

Much more importantly, do you really need passwords? If you only need them for logins, could you use phishing-proof passkeys instead? Maybe with email magic links as a fallback? Or just support SSO (as long as it’s OIDC and not SAML)?

(Note that in 2026, passkeys are still not PQ. That’s mostly fine. They’re still phishing-proof and credential-stuffing-proof. All a quantum attacker can do is log in to a specific site if they obtain its database or intercept a login.)

Avoid: regular hashes, spending time thinking about password hashes instead of focusing on passkeys, phishable variants of email-based logins.9

Key exchange

X25519+ML-KEM-768 in a secure, standard protocol.

Percival, 2009: 2048-bit Group #14 with a generator of 2.
Ptacek, 2015: Probably still DH-2048, or NaCl.
Latacora, 2018: Probably nothing. Or Curve25519.
Latacora, 2024: X25519+ML-KEM-768.

The 2018 version of the Latacora answers is correct in asking “why are you as a developer thinking about this, and what does it even mean?!” Don’t roll your own key exchange protocol. Just pick X25519MLKEM768 in TLS, mlkem768x25519-sha256 in SSH, and/or MLKEM768-X25519 in HPKE and age. If you really need to obtain some keys and you know what you’re doing, both TLS and HPKE have “exporters” to derive them.

Non-PQ solutions are an active, urgent liability due to harvest-now-decrypt-later attacks, and PQ alternatives range from impractical (HQC-KEM, FrodoKEM) to impractical and broken (Classic McEliece).

For key exchange, using an ECC hybrid is cheap enough to be worth it, and indeed ML-KEM is usually deployed alongside ECDH. However, if picking or implementing the hybrid is going to make you stay even a single month longer on a classical, non-PQ key exchange, go straight to pure ML-KEM-768 now.

P-256+ML-KEM-768 is also fine, just less common. NIST P curves got a bad rep for many years, but I think it’s 90% because they came out before we knew how to do cryptography engineering particularly well (and because of… let’s say non-NPOV proselytizing). Almost none of the attacks against ECDH on NIST P curves even matter for ephemeral key exchanges.

Avoid: anything and everything without ML-KEM or X-Wing (a specific X25519+ML-KEM-768 combiner) in its name.

Asymmetric encryption

HPKE with (MLKEM768-X25519 a.k.a. X-Wing, HKDF-SHA256, AES-128-GCM), or age with PQ keys.

Percival, 2009: RSAES-OAEP with SHA-256, MGF1+SHA-256, and exponent 65537.
Ptacek, 2015: NaCl.
Latacora, 2018: NaCl/libsodium (box / crypto_box).
Latacora, 2024: Tricky, wait for established PQ solutions.

This is one of the most improved answers in recent years, as we now have a standard to do hybrid encryption: HPKE. (“Hybrid” as in asymmetric + symmetric, not as in classical + post-quantum, yay for overloaded names.)

MLKEM768-P256 is also ok as a choice of KEM, but less available. Pure ML-KEM-768 is fine if it’s all you have. All KDF and AEAD choices are fine, as well.

If your message is large, do the same chunking Cobblestone does, with multiple sequential HPKE Seal/Open calls in place of the AEAD.

Note that the PQ HPKE KEMs are maddeningly still a draft.10 Worse, they are unnecessarily spread over four drafts, such that I had to write filippo.io/hpke-pq. However, I made the authors solemnly swear they will not change the wire format, and then we all shipped them in our cryptographic libraries, so you can and should use them.

If you need something higher-level, with multiple recipients or a CLI, use age11 with its new age1pq-prefixed keys, based on MLKEM768-X25519. PQ support is also rolling out for plugins like the YubiKey and the Secure Enclave ones.

Avoid: again anything not based on ML-KEM (RSA and NaCl’s box12 in particular), OpenPGP, encrypting emails.

Asymmetric signatures

ML-DSA-44.

Percival, 2009: RSASSA-PSS with SHA-256, MGF1+SHA-256, and exponent 65537.
Ptacek, 2015: NaCl, Ed25519, or RFC 6979.
Latacora, 2018: NaCl or Ed25519.
Latacora, 2024: Ed25519 if short-lived, otherwise Ed25519+ML-DSA-65.

In January 2026, I would have told you to wait and see, and then everything started moving a lot faster. You need to move to PQ for auth, too.

Just use ML-DSA-44. If your message needs pre-hashing, use “external-μ (Mu)” signing, not HashML-DSA. Store keys as 32-byte seeds exclusively.

The two PQ alternatives are FN-DSA, which is stuck somewhere in the US Department of Commerce, and SLH-DSA, which is based on hash functions. The latter can make sense for some specialist use cases, but is slow, large, and not widely available in implementations.

Why not a hybrid or “composites”? Hybrid auth is more complex and less useful than hybrid key exchange. I need to write a long-form post about this, but in short either you already have a key rotation strategy that you can use to rotate back to RSA/ECDSA/Ed25519 in the unlikely case of a cryptanalytic break, or you have such a long time horizon that you should assume quantum computers will break the classical half anyway.

Also, ML-DSA is just such a better signature algorithm than its predecessors. It has hedged randomness (which is better than both random and deterministic nonces), built-in context, extra properties like SUF-CMA, and is relatively simple to implement and test.

Why the -44 parameter set, when I’m recommending ML-KEM-768? Unlike ML-KEM-512 (NIST category 1), ML-DSA-44 sits at NIST category 2, with some margin above the 128-bit security level already.

The one exception to the no-composites rule is SSH keys. OpenSSH 10.6 picked ssh-mldsa44-ed25519. I think they made a mistake, but it would be a mistake for you to go off the beaten path there.

Note that asymmetric signatures are overused, and especially now that they are not cheap, you should try to avoid them. Consider whether you could use a simple HMAC. Maybe you can replace signed JWTs with random session tokens. If instead you do want to commit to something publicly, consider whether you should use a transparency log, and get a more practically useful notion of non-repudiability (and potentially smaller sizes, if you amortize the signature over multiple proofs).

Avoid: all non-PQ options like RSA/ECDSA/Ed25519, stateful signatures (LMS/XMSS), HashML-DSA, ML-DSA “semi-expanded keys,” composite signatures, OpenPGP.

Website or client-server application security

If you’re in the cloud, use its ALB/NLB. Otherwise, rustls, Go’s crypto/tls, BoringSSL, AWS-LC, or s2n-tls with a popular, updated ACME client.

Percival, 2009: OpenSSL for websites, custom RSA protocol for applications.
Ptacek, 2015: OpenSSL, or BoringSSL if you can. Or just AWS ELBs.
Latacora, 2018: AWS ALB/ELB or OpenSSL, with Let’s Encrypt.
Latacora, 2024: AWS ALB/ELB or OpenSSL, with Let’s Encrypt.

Not recommending OpenSSL will probably be my least practical suggestion, but OpenSSL has been making consistently puzzling and problematic choices for years now. The pyca/cryptography authors, in a long post about OpenSSL’s issues, summarize it as:

Our experience with OpenSSL has been on a negative trajectory for several years.

They even presented at the 2025 OpenSSL Conference (!?), apparently fruitlessly. They’re not alone in criticizing OpenSSL: here are HAProxy from the server side, and curl from the client side.

I recommend rustls or Go’s crypto/tls,13 which are memory safe. If you need to stick to C, both BoringSSL and AWS-LC are very competently maintained OpenSSL forks, and the latter, unlike BoringSSL, has versioned releases. s2n-tls and rustls-ffi are interesting options if you don’t need libssl compatibility.

Whatever you use, make sure it prioritizes the X25519MLKEM768 key exchange, which requires TLS 1.3. Your cloud load balancer might require you to select a PQ security policy. On RHEL 9 and derivatives, you need to opt in.

Previous lists split websites and client-server applications. I merged them because these days you’ll just use the same TLS stack for both. What changes is the PKI. For applications where you control both ends, consider making your own ML-DSA-44 X.509 certificates, self-signed or from a private root. For websites, wire up a popular, well-supported ACME client and keep it up to date. Merkle Tree Certificates will roll out in 2027, and you want to be well positioned to be included in the transition.

Avoid: rolling your own transport protocol, TLS libraries that failed at their core job before (GnuTLS14, Mbed TLS15 16 17, wolfSSL18 19 20 21 22 23 24 25, Botan26 27), offbeat TLS libraries, OpenSSL before version 3.5 (the first with X25519MLKEM768), any OpenSSL if you can, TLS 1.0–1.1, TLS 1.2 if you can, rolling your own ACME client.

Online backups

restic with a long random password.

Percival, 2009: Tarsnap.
Ptacek, 2015: Tarsnap.
Latacora, 2018: Tarsnap.
Latacora, 2024: Tarsnap.

I checked restic’s encryption a very long time ago and it was slightly weird but good. Fully symmetric, so it’s not scared of quantum computers. Doesn’t look like anything changed since. If you need cloud storage, rsync.net has a “secret” plan for restic users, and they support an append-only mode.

We all love Tarsnap, and I feel like I am betraying my elders right now… but its asymmetric cryptography layer is all RSA. Technically, I think the only things that truly break are the lower-capability keys: a write-only key can decrypt archives and a read-only key can forge archives. Server authentication is HMAC, and the RSA public keys are never sent to the server. In that sense, Tarsnap is as secure as restic, which is an impressive feat for a 2008 design. However, this feels like a major footgun with impending quantum computers.

The picture

Kinda incredible that you can just walk up to this thing.

The Colosseum, at night, pictured from the ground looking up.

Follow me on Bluesky at @filippo.abyssdomain.expert or on Mastodon at @filippo@abyssdomain.expert.


  1. FIPS 140 still has some very ugly bits around module validation (runtime self-tests, the integrity check, and the worsening RNG mess) but the actual cryptography algorithms these days are “good, actually.” ↩

  2. You might read that GCM can take 128-bit nonces, but when you do that it doesn’t have a separate CTR counter anymore, and messages with different GCM nonces can end up sharing CTR keystream, which makes the analysis more complicated. ↩

  3. Full disclosure: XAES-256-GCM is my design, but there are now multiple third-party implementations, including as part of Google’s Tink libraries, there’s a security analysis by Amazon Web Services, and it’s used by Microsoft in an official SDK. ↩

  4. Again, full disclosure, this is my design, but it’s adopted externally enough that I feel comfortable recommending it. ↩

  5. On 64-bit machines, SHA-512/256 and SHA-512 should be faster than SHA-256 thanks to their larger block size, except right now hardware support for SHA-256 is more widespread, so SHA-256 is faster in practice. They are both fast, so you probably don’t care. ↩

  6. Partially because of choices NIST made to make SHA3-256 strictly as secure as SHA-256, even where SHA-256 was overkill. SHA-256 and SHA3-256 have 128 bits of collision resistance and 256 bits of second preimage resistance. It’d be enough to have 128 bits of both, which is what you get from 256 bits of SHAKE128 output. Unfortunately, it doesn’t have a SHA name. TurboSHAKE128 (RFC 9861) would be even better, but it is neither FIPS 140 nor widespread. ↩

  7. People outside the FIPS 140 circle of hell don’t seem to have noticed, but new NIST rules require FIPS 140 modules to have an “internal” entropy source now. If your FIPS 140 “module” is a piece of software… what do you do? Everyone’s answer is “CPU jitter”: run a tight loop that accesses uncached memory and take high-resolution timestamps, hoping the frequency mismatch between CPU and main memory will make the measurements unpredictable. IMHO, this is the worst part of FIPS 140 since the module integrity hash, and it will hurt people. The one sane way to do it is to go through the motions, and then at the last moment mix the result with kernel entropy, like Go does. However, that’s harder to justify to the validation labs than doing just CPU jitter, so I’m afraid we’ll see pure CPU jitter in production a lot. ↩

  8. Argon2id parameters mostly do what you’d imagine, scrypt parameters do not. ↩

  9. A link with an opaque random token that logs in the opening browser is very hard to phish. A link that logs in the browser that started the login is very easy to phish. Short numeric codes are moderately easy to phish. (You can get the best of both worlds by using the Broadcast Channel API to pass the token from the new tab to the original one.) ↩

  10. In a different venue I said a serious engineering community would have a post-mortem about having wasted two of the five years we had for the transition to post-quantum cryptography, only to produce specs that changed nothing compared to what we had in 2024. But that’s for another time. ↩

  11. Again again, full disclosure: my design, but pretty uncontroversial pick. ↩

  12. I truly don’t understand why my predecessors recommended NaCl’s box. It’s an incredibly sharp and low-level API, pretending to be a high-level safe API. ↩

  13. One last time, full disclosure: I am a crypto/tls maintainer. ↩

  14. CVE-2020-13777, GnuTLS 3.6.4–3.6.13: the session ticket key is all zeroes, breaking confidentiality in TLS 1.2 and allowing authentication bypass in TLS 1.3. ↩

  15. CVE-2023-45199, Mbed TLS 3.2–3.4: pre-auth remote code execution via an oversized key share in the TLS 1.3 handshake. ↩

  16. CVE-2026-34873, Mbed TLS 3.5.0–4.0.0: TLS 1.3 session resumption allows client impersonation. ↩

  17. CVE-2026-25835, Mbed TLS 2.18.0–3.6.5 and 4.0.0: the RNG state is cloned across fork, so parent and child produce the same random values. ↩

  18. CVE-2026-5194, wolfSSL 3.12.0–5.9.0: signatures by ECDSA certificates can be forged by providing an ML-DSA or Ed25519 signature algorithm identifier and a trivial ECDSA signature over the zero-length digest. ↩

  19. CVE-2026-5501, wolfSSL through 5.9.0: the OpenSSL compatibility layer skips the leaf’s signature check when any valid end-entity cert is supplied as an “intermediate.” ↩

  20. CVE-2026-11310, wolfSSL 5.8.4–5.9.1: the OpenSSL compatibility layer lets caller-supplied untrusted intermediates act as trust anchors. ↩

  21. CVE-2026-11999, wolfSSL 5.7.4–5.9.1: the OpenSSL compatibility layer accepts any chain longer than the maximum path depth of 100, without reaching a trust anchor. ↩

  22. CVE-2026-55960, wolfSSL 5.6.4–5.9.1: a raw public key is always accepted in place of a certificate, bypassing authentication. ↩

  23. CVE-2026-93302, wolfSSL 5.3.0–5.9.2: trusted-peer certificates are matched by name rather than public key. ↩

  24. CVE-2026-89136, wolfSSL 5.6.0–5.9.2: clients still accept an unsolicited raw public key from the server, bypassing authentication. ↩

  25. CVE-2026-89135, wolfSSL 5.8.4–5.9.2: a failed chain verification in the OpenSSL compatibility layer permanently adds the attacker’s CA to the trust store used by native TLS, OCSP, and CRL checks. ↩

  26. CVE-2026-34580, Botan 3.11.0: an end-entity certificate whose DN matches a trusted root is accepted as if it were that root. ↩

  27. CVE-2026-34582, Botan before 3.11.1: TLS 1.3 servers process application data before Finished, so a client can skip Certificate, CertificateVerify, and Finished entirely, a full client authentication bypass. ↩

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denubis
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The Mathocalypse

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Updates (Oct. 9): To address some questions that keep coming up…

No, I’m not aware of any direct practical implications of any of these results. I certainly don’t expect the O(n log0.9999999999999 n)-time Fourier Transform algorithm to get practically deployed anytime soon! But anyone who harps on this, simply doesn’t understand what mathematical progress looks like, or how it eventually pulls the rest of science and technology and human civilization with it. If and when the relevant human mathematicians understood the clever new ideas in all 372 of these papers, I have no doubt that they’d be able to use the ideas to do all sorts of new things, and that some of those things would have practical value. That’s yet another reason to try to keep human understanding at the center of our enterprise—unless, of course, you’re happy to outsource the task of understanding and applying the ideas to AI models as well.

Meanwhile, something calling itself the Association for Human Mathematics put out a statement condemning OpenAI for its release. The statement included a sentence that’s since been widely mocked on social media: “Mathematicians did not ask for this work to be done.” (Imagine G. H. Hardy saying to Ramanujan, “who asked you to prove all these bizarre new identities?”)

If it wasn’t clear, the members of AHM speak for themselves, not for the math community as a whole. For my part, I think the math and CS theory communities should absolutely hold the AI companies’ feet to the fire to behave better, both within our little domains, and (much more consequentially) in pacing AI progress, figuring out alignment, and preventing a catastrophe for our whole civilization. So I’m glad that our communities have increasingly been doing that, and I hope to have played a tiny part.

At the same time, I regard the position “no one should spoil our fun by solving our open math problems using AI models” to be totally untenable. It offers no argument for why refraining would be in the broader public interest—as opposed to various mathematicians’ narrow career interests. It violates the core principle that math problems are there for absolutely anyone (yes, even a hated corporation) to try to solve. And of course, it’s not enforceable anyway, in a world where these capabilities will rapidly diffuse to anyone with a GPT or Claude subscription.

We will need to adapt to this new world.


… then they came for Navier–Stokes and I said nothing because I never worked on Navier–Stokes. But when they came for RL vs. L I realized that things are serious

–friend-of-the-blog Omer Reingold (shared with permission)


Last night my 9-year-old son was taunting my wife, complexity theorist Dana Moshkovitz, as follows: “mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!”

While my son was being a brat, he also wasn’t wrong. Whether you’re thrilled, depressed, angry, or whatever else about it, yesterday was surely one of the biggest days in mathematical history. And yes, among the 372 huge results released yesterday by OpenAI, on the recommendation of its advisory group of Timothy Gowers, Edward Witten, and other distinguished mathematicians, was a proof of Subhash Khot’s Unique Games Conjecture (UGC), a statement that my wife has worked toward proving for the entire time I’ve known her. (The UGC implies that a whole slew of optimization problems really are NP-hard, even if you just want an approximation that’s slightly better than what you get from semidefinite programming relaxation, which is one of our main tools.)

Or at least, we’re pretty sure that it’s a proof! There’s a Lean certificate, as there are for some of the other 372 breakthrough results (not all of them). But it also appears that no human has understood just about any of these proofs yet; the race to do so has just started. If you want an on-the-ground sense of what that race is going to be like, here’s some of what Dana texted me last night:

It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results

Basically the paper is so horribly written that it’s impossible to read it without AI help

I asked Astra for reasonable completeness and soundness claims of the noise gadget and it gave them by combining claims from all over the paper

They also have direct optimal NP hardness of approximation proofs for the main applications of the UGC (Max Cut and all CSP) that bypass the UGC.

The UGC proof invents a completely new bizarre code with a noise test. It’s some crazy recursive construction.

It’s not the long code, not the short code – some alien craziness

I still think that there maybe is a proof that uses the half space code (which is natural)

The citations are often irrelevant and confusing

A possible future is a math world that’s heavenly if you have vision/creative ideas that AI could help check and implement.

And of course there’s a lot for us to learn from the aliens

If you’re wondering what emotions Dana is feeling—well, probably all of them! Even while a central career aspiration has fallen to a robot, there are at least two mitigating factors for her. First, she can feel vindicated that the UGC was true after all, something she never doubted even while many of her colleagues did! Second, all of us in math and theoretical computer science and mathematical physics, at least those who cared about solving crisply-stated problems, are now in the same boat.


Besides the Unique Games Conjecture, here’s a small sampling of the treasures from Aladdin’s cave that I’ll probably be paying the most attention to over the coming weeks:

Any of the above, alone, could easily have been “result of the year” in some area (and in some cases, like Unique Games and L=BPL, in all of CS theory). And there’s a lot that I’ve left out—feel free to share in the comments whatever is making your eyes bug out! There are equally astounding wonders in number theory, combinatorics, algebraic geometry, analysis, and pretty much every other area of math, most of which I’ll never understand, although I’ll note that it includes partial progress toward the Riemann hypothesis and the Hodge Conjecture and the Birch-Swinnerton-Dyer Conjecture (i.e., the majority of the remaining Millennium Problems).

We can take solace in what’s missing from the list. P≠NP isn’t there, nor even P=BPP or NEXP⊄P/poly, and surely not for lack of trying. Apparently the greatest open problems of theoretical computer science are indeed pretty hard!


Oh, lest I forget: one day before the OpenAI dump, meaning Monday evening, Virginia Williams and Josh Alman posted an arXiv preprint that solves the 3SUM problem in O(n1.9992) time, and the All-Pairs Shortest Paths problem in O(n2.9995) time, refuting half-century-old conjectures that the correct answers were n2-o(1) and n3-o(1) respectively. In this case, it wasn’t an OpenAI model that supplied the crucial idea; it was an Anthropic one! But Anthropic then took a different approach from OpenAI: rather than post the undigested solutions to the world, it gave Virginia and Josh the opportunity to write and announce a digested version in exchange for compensation.

These have emerged as the two main models for communicating AI math breakthroughs, and they both have strengths and weaknesses. The “OpenAI model” sets up a crazy race among humans to digest and explain a messy AI proof (work that could easily be some combination of thankless, barely-credited, competitive, and unfun), while the “Anthropic model” puts a private company in the position of picking and choosing which human mathematicians get to be the emissaries of the AI. Dunno, what do you guys think?


For those who are wondering: apparently, the AI model that produced all these wonders was not bespoke contraption of 10,000 agents burning millions of dollars worth of compute, as was used for example to construct a finite-time blowup for the Navier-Stokes equations. Instead, it was simply the latest internal OpenAI model—one that might be released to paying ChatGPT customers within the next couple of months, depending on the recommendations of OpenAI’s safety board! (My 9-year-old son: “Oh they definitely shouldn’t release that. If it could solve all those math problems, it can’t possibly be safe.”) Apparently they used about 3 hours of GPT-Pro level compute on average per problem solved.

Also, if you were wondering: apparently they tried the model on about 8,000 problems. So, right now it “merely” solves ~5% of the longstanding open mathematical problems that it’s asked about, the problems that whole communities have spent years on, after a single 3-hour attempt on them.


I’ve been glad to see the CS theory community rising to the occasion. At the Simons Institute in Berkeley, here at UT Austin, and elsewhere, I’ve hearing stories of researchers rushing to pore over the manuscripts and make sense of them and explain them—because what else do we do? How else do we continue the craft to which we’ve devoted much of our lives?

If you want some sense of what things feel like now in math, imagine a hunter-gatherer who’s spent his entire life learning to survive deep in an unforgiving rainforest, then a giant resort hotel springs up right next to him with a helipad and heated pools and AirBnBs, and without missing a beat, the hunter-gatherer says: “alright fine, so now my new job is to run wilderness retreats for the tourists, or something.”

In Quanta magazine, Jordana Cepelewitz attempted a different metaphor:

It’s as if you were teleported to the peak of a tall mountain. Surrounded by fog, you have no idea where you are, or what’s around you. You do not know how your mountain connects to others, and you have no equipment to help you explore, no way to help someone else join you. If you had climbed the mountain yourself, you would have experienced how the human body adapts to altitude and changes in oxygen levels. You might have had to invent tools to navigate, to climb steep cliffs, or to make a shelter. You might have encountered a fellow explorer, gotten lost together in a hidden valley, and found a plant that could be turned into a life-saving medicine.

Instead you’re perched on the peak but in the dark, while the maker of the teleportation machine tells you that it can explore the wilderness better than any human.

For any one of these mountains, if we care enough, I feel optimistic that we can do as we always have: clear the fog and figure out the path, except now using the teleportation machine to help guide us. The bigger challenge will be to nurture a community that still cares about the heroic adventure of finding the paths up these mountains in the world with the machine. (Oh, and I think one place where the metaphor breaks is that we still do have each other, as much as we ever did before!)


Experience has shown that, even now, there will still be people explaining in patronizing tones why none of this is real and none of it counts. If such people were capable of being impressed by anything that happens in the empirical world, of updating on anything, they would’ve already been impressed and already updated several years ago, long before things had reached the point of an actual Mathocalypse.

So, they’ll say, maybe the alleged solutions are not solutions at all, but just “AI slop.” Or maybe none of the 372 well-known open problems that were solved were real math problems, they were all just glorified contest puzzles and trivialities. (After all, there’s still no Riemann Hypothesis!) Or maybe the entire 4000-year-old discipline of mathematics needs to be jettisoned: turns out that it was all just puzzle-solving and trivialities; all that’s different is that now the triviality stands unmasked. In any case, what really matters is that the true inner sanctum of human creativity hasn’t been breached and probably never will be, and also, that Sam Altman and Dario Amodei are contemptible little nerds.

If you’re still a proponent of that doomed worldview, still aboard the sinking ship, I encourage you in the strongest possible terms to read yesterday’s other great contribution to AI discourse, besides the OpenAI Mathocalypse dump: namely, Scott Alexander’s open letter to Steven Pinker. I feel some responsibility for this, as the person who first introduced Steven Pinker to the existence of the rationalist community, and who also first introduced Steven Pinker and Scott Alexander to one another (they had both been fans of each other’s writing). And now Scott is challenging Steve to a literal duel, with guns!

For whatever it’s worth: Steve is a lifelong intellectual hero of mine, just as he is for Scott, and I also have to privilege of calling Steve my friend. But I found Scott’s post to be one of the most devastating rejoinders to anything that I’ve ever read. And I thought Scott’s conclusion was exactly right: when it comes to AI risk, Steve’s great challenge is now to accept and start using a more “Pinkerite” epistemology.


Last night, while I should’ve been poring over some of OpenAI’s hundreds of papers and/or writing this post, I decided to spend some time with my kids instead. They wanted a movie night, so I suggested something they’d never seen before (and that I hadn’t seen for decades), and that seemed chock-full of no-nonsense, practical guidance for the world in which they’re going to grow up: Terminator 2.


Update: As several people have pointed out, cryptography is a subfield that’s extremely conspicuous by its absence from OpenAI’s list of 376 papers! But my sources tell me that the AI companies have now started, gingerly and discreetly, investigating whether their latest internal models can break important cryptographic protocols and primitives. If they can, then it would certainly be nice to get ahead of things before the rest of the world figures out the same.

Another Update: The statement put out the Advisory Group on Mathematics and Artificial Intelligence is very carefully phrased, neither endorsing nor condemning what OpenAI did, and is worth a read:

As announced a few weeks ago, OpenAI has released a large collection of mathematical results generated by an internal model, reporting solutions to hundreds of open questions. This is an important event for mathematics, with consequences both for mathematics and for the mathematical community that extend far beyond the individual results.

AGMAI’s advisory role should not be interpreted as a judgment of the impact of these results or an endorsement of the process by which OpenAI obtained them. We do not speak on behalf of the entire mathematical community, and only the mathematical community can undertake the assessment that is needed. 

Making this work public is a first step. This release is the beginning, not the completion, of the process of human understanding and the incorporation of the work into mathematical knowledge. At the same time, the future of mathematical research cannot consist only of understanding results produced by AI labs. Mathematicians must be able to formulate their own questions, develop their own approaches, and explore directions that have not been selected as examples of an AI system’s capabilities. Equitable access to powerful research tools and adequate computational resources are essential to that freedom.

We reaffirm our published recommendations on responsible release. We have discussed them with OpenAI and appreciate the company’s willingness to engage. While we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest. We remain committed to engaging with any frontier AI lab on these questions and have already been in contact with several of them.

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A Cray-1 supercomputer replica from 30 "obsolete" Mac Minis

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The Museo de Historia de la Computación in Spain has unveiled a 1:1 scale visual replica of the famous Cray-1 supercomputer from 1976. Instead of sourcing expensive, cutting-edge tech to run the system, the creative team powered the project with 30 2012-era Mac Minis. Developed over 18 months, the project serves as a 50th-anniversary tribute to the Cray-1 and Apple's founding.

Mac Minis from over a decade ago might not seem like the obvious first choice for building a cluster supercomputer, but when networked together, the developers can orchestrate the 64 active processing cores into a combined 1.3 teraflops of performance in their most recent tests. The museum reportedly achieved 1.5 teraflops previously using all 70 available cores, prior to one node going offline. Benchmarks were obtained using a custom matrix-multiplication Python script. Five PCs are quad-core i7s, and the remaining 25 are dual-core i5 models. Except for two units from 2014, the rest of the array dates to 2012.

The replica is a valuable tool for museum-goers to understand the shifts in computer architecture since 1976. The original Cray-1 used vector processing, applying a single instruction to multiple data elements simultaneously, whereas the replica distributes work across independent processors in a parallel cluster. The peak theoretical performance of the original Cray-1 was approximately 160 megaflops. What was originally a purpose-built research machine has been re-created with consumer hardware that's vastly more capable than the machine that inspired it.

Rather than opting for a more standard Linux distribution, the team found that macOS Mojave (10.14) met their project needs by harnessing macOS's built-in support for MPI (Message Passing Interface), the software layer that allows all the nodes in the cluster to pass tasks to one another.

Photograph of the museum's mac mini-powered Cray display The Cray-1 replica, complete with iconic padded bench seating. The only thing missing is Robert Redford and Ben Kingsley having a discussion on SECTEC Astronomy. Credit: Museo de Historia de la Computación Credit: Museo de Historia de la Computación

Guests at the Museo de Historia de la Computación can watch in real time as the system runs matrix algorithms, mapping the scale of system performance from a single core to the full suite running in parallel.

Stealth supercomputing

Combining 30 consumer PCs into an operational cluster wasn't the only engineering challenge the team faced. If you've ever stepped inside a server room, or, like me, foolishly installed one in your own basement, you know that fan cooling can be loud. The museum team used passive convection cooling via a steel rack chassis and aluminum tray mounts for each Mac Mini. Compared to the roaring thunder of a modern data center, this cluster is nearly inaudible.

Cray-1_Tower_Unit14 Macs are mounted vertically on aluminum racks in a steel chassis. Credit: Museo de Historia de la Computación

The secret to the near-silence comes from vertical mounting. The PCs' vertical orientation, combined with the steel chassis and aluminum trays, allows the tower to act as a natural thermal chimney. Hot air rises through the structure and out of the top grills without the need for added mechanical fans. According to the museum, the only noticeable noise inside the Cray-1 replica comes from two gigabit Ethernet switches at the base of the unit that register between 30–33 decibels, though the team plans to replace them with silent models. The fully assembled replica is said to make so little audible sound that you have to get right up next to the tower to be able to hear anything. While exact dB  measurements from inside the exhibit weren't available, each individual PC is stated to produce 12–15 dBA of noise at idle.

Mission control

To manage this quiet giant, designers built a custom terminal that looks straight out of a Cold War control room. The team combined elements of the DEC VT05 and Processor Technology Sol-20 Terminal Computer designs of the 1970s, even incorporating an analog control panel, with future plans to add original lamps from an IBM System/3. One master Mac Mini resides in the terminal and serves to direct all the other cluster nodes.

Cray-1_Terminal_and_Tower_Background Classic design elements lend the Cray-1 control terminal some retro style. Credit: Museo de Historia de la Computación

The original design had planned for the terminal to feature CRT monitors for added authenticity, but modern flat Samsung displays eliminated the connectivity headaches that come from attempting to bridge different technological eras. Future design plans will see 3.5- and 5.25-inch floppy drives mounted to the underside of the desk, and a 3D-printed shell will encase the keyboard to mimic the look of the classic HP 250 design.

A mockup in 3D printing software of a potential keyboard cover design. Mockup of the shell that will fit over the existing PowerMac G4 keyboard. Credit: Museo de Historia de la Computación

Targeting the TOP500

The Cray-1 team hopes to fill the currently empty second half of the tower through a crowdfunding campaign to secure 70–80 additional M4 Mac Minis. The goal: create a cluster capable of ranking on the TOP500 supercomputers list.

Cray-1_Replica_Bright_Room_PCs The Cray-1 replica among its classic computing peers. Credit: Museo de Historia de la Computación

The replica is on permanent display in the museum, alongside two unused authentic Cray CX1 systems. The Museo de Historia de la Computación offers guided tours on Saturdays from 11:30 am to 2 pm. Additional project information can be found on the museum website.

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denubis
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Muse, Meta's extraordinarily privileged AI assistant, has a serious 0-day

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Meta founder and CEO Mark Zuckerberg has gone to great lengths to hype the security of its new AI assistant Muse, claiming it is “built from the ground up for privacy and security.” A zero-day vulnerability that gives locally run apps and terminal commands complete control of the agent raises serious doubts. Further raising questions, Amazon on Sunday began blocking Muse from its site.

Meta introduced Muse a few weeks ago. The assistant “books appointments, fills out forms and handles customer service,” “proactively takes tasks off your plate,” and can “make purchases, generate images, create documents, and connect with your favorite apps and services.” The macOS app (curiously, there’s no Windows version) also works with a user’s WhatsApp, email, calendar, and social media accounts. When a task requires a tool that doesn’t exist, Muse creates one on the fly.

Meta doth hype Muse security too much

Of course, for Muse to do any of these things, users must first give it access to their accounts. This includes authenticating the assistant to each service and, because the app runs on macOS, giving it permissions to a broad range of operating system-restricted device resources like writing files to disk, accessing the mic and camera, and monitoring location and calendars. Apple has spent years developing these defenses to prevent installed apps or commands entered into the terminal from accessing these resources, clearly because the company considers them a security threat. Muse completely undoes these default measures.

The zero-day allows any app or terminal command to gain access to the token that authenticates users to their Muse account. Meta developers designed the assistant so that any locally installed app or executed code, regardless of the macOS permissions it has, can change a long list of undocumented settings. Most of them are fairly innocuous, such as controlling dark mode. One setting, however, is anything but innocuous. It allows processes to change the endpoint where transcription occurs. Normally, it’s a server address operated by Meta. Attackers can exploit this flaw by changing the location to their own endpoint. Once that happens, the attackers have the token that gives complete control over the Muse account.

“We can manipulate the agent and leverage its privileges to do whatever we want,” Patrick Wardle, the macOS security expert who discovered the zero-day, told Ars. “So instead of us having to write a very comprehensive Mac malware stealer, we can just leverage the AI assistant itself.” Wardle said he has developed several proof-of-concept attacks that do things like writing malicious files to disk and snapping pictures, in many cases with no indication to even an alert user.

Meta representatives didn't answer emailed questions.

Meta has published two posts in as many weeks documenting the design decisions that went into ensuring an assistant with such extraordinary access to user data and resources is secure and private. The posts come amid revelations that internal testing of models from Anthropic and Google has resulted in security breaches of external, third-party networks that the engineers involved never intended to target. In traditional human-only hacking, these actions could likely result in the filing of criminal charges. The Meta posts are likely mindful of the resulting blowback and the calls to slow down AI development in response.

Wardle said that Meta developers made several design decisions that made his exploit possible. One is the choice for Muse dictation to occur in the cloud, where Meta can log it. macOS has long provided a simple means for apps to handle dictation and transcription in processes that stay securely on the device. Had the developers chosen this safer alternative, the attack wouldn’t have been possible.

Another flawed decision is for any app to control all of the undocumented settings. It’s likely Meta intended for apps working with Muse to control UI settings, and for understandable reasons. The ability for any app or command to control an endpoint where sensitive user speech is processed is an entirely different matter. Together, the design decisions raise questions about just how much effort developers put into designing and testing the security and privacy of the new assistant.

“To me, the bar is infinitely higher in terms of the security of these apps. They don’t have to be perfect, but when you take a look at Muse, it’s like they didn’t, in my opinion, think about security, which is really worrisome," Wardle said. "At the very least, they should be thinking about security from the very start, and they are just not.”

Roughly 12 hours before Wardle disclosed the zero-day, Amazon started blocking people from using Muse to shop on the site. Users who tried received a message saying Muse was an “unauthorized AI agent [that] violates Amazon’s Conditions of Use.”

“We think it's fairly straightforward that third-party applications that offer to make purchases on behalf of customers from other businesses should operate openly and respect service provider decisions about whether or not to participate,” Amazon said in an emailed statement. "This helps ensure a safe, secure, and reliable customer experience, and it is how others operate including food delivery apps and the restaurants they take orders for, delivery services apps and the stores they shop from, and online travel agencies and the airlines they book tickets with for customers. Agentic third-party applications such as Muse have the same obligations, and we've requested that Meta remove Amazon from the experience."

A single ClickFix is all it takes

There are several ways for attacks to work. One is for an attacker's server to act as a proxy that’s placed between the Muse user and Meta endpoint. Once the user enters the voice prompt, the attacker's server adds a prompt invoking a malicious command, such as sending an archive of all WhatsApp messages to the attacker. Once that happens, the attacker gains permanent control over the Muse account because the token is automatically sent to the malicious server as well.

Wardle is the creator of the Objective-See Foundation, a nonprofit focused on macOS security. He is also the author of the "The Art of Mac Malware" book series, and a former employee of NASA and the National Security Agency. Wardle said he plans to discuss the vulnerability in more detail and other AI assistant threats at the Objective by the Sea security conference in November.

One of the counterarguments raised by developers of apps that can be exploited once a device is compromised is that once that happens, all security bets are off. This standard doesn’t fit well in this case. Wardle found that a simple variation of ClickFix attack—a technique that has become remarkably effective in tricking people into infecting their devices—is all that’s required for an attacker to take control of a Muse account.

Credit: Patrick Wardle

Credit: Patrick Wardle

In the first image above, Wardle can be seen using a simple terminal command to surreptitiously send a prompt to the Meta endpoint. The second image shows the response. To prevent attackers from cutting and pasting the prompt in live attacks, Wardle's prompt asks only how it's possible it's coming from an unprivileged attacker. Muse incorrectly responds that such an action isn't possible.

As already noted, the extraordinary access Muse requires to work as intended places an additional burden on its designers. Like most such AI agents—and contrary to Meta’s claims—Muse can’t be trusted. It’s not clear when or if it ever will.

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denubis
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