Some thoughts about Anthropic’s new cryptanalysis results

Some thoughts about Anthropic’s new cryptanalysis results

Yesterday Anthropic published two new cryptanalysis results, both outputs of Claude Mythos, their (still) unreleased advanced model. The first of these results attacks a signature scheme called HAWK, while the second is an improved attack against reduced-round AES. Anthropic also released a blog post describing the research process that produced these results. A few people online have asked me what this all means. While I’m not sure I have all the answers, I figured it wouldn’t hurt to write a bit about my current understanding. These are only my thoughts and other folks will probably differ (including domain experts in the two areas at issue) so take them for what they are.

The two new results cover two very different areas, and are overall just very different in quality. Before we get to broad statements about the world, and whether you should sell all your cryptocurrency, let’s take a minute to talk about the substance.

Hawk. The first is a new key recovery algorithm against the non-standard signature scheme HAWK. HAWK is a proposed post-quantum-safe signature scheme that’s based on the module Lattice Isomorphism Problem (module-LIP). For a brief Claude-written summary of the result itself, see here. There are five things you need to know about this result:

  1. HAWK is not a deployed or standards-adopted algorithm, it’s a proposed algorithm. It is related to the Falcon signature scheme, which is being standardized, but the attack does not transfer to that setting (which is based on a different hard problem.)
  2. However, HAWK was somewhat far along in the process of being evaluated for a future standard.
  3. The attack does not break “real deployed” HAWK in the sci-fi sense. The resulting attack is still exponential time, but roughly halves the number of “bits” of security in the algorithm. That means it could theoretically be fixed by doubling key sizes. The downside is that this makes the scheme less efficient, and, since HAWK is entirely justified by being more efficient than alternatives, that makes the existence of the scheme much harder to justify.
  4. The attack produced real code that runs in a few hours of wall-clock time against a weakened “challenge instance” of HAWK that the authors provided for this purpose. While this instance doesn’t use the parameters that were proposed for real deployment, it does demonstrate the cryptanalytic weakness well enough.
  5. What’s particularly concerning (and so especially ripe for AI) is that the attack does not invent fundamentally new mathematics. It simply extends a bunch of tools that were lying around and well-known, and gets a good result.

This last part is important. I asked Claude for its thoughts, and it doesn’t mince words: “what makes this genuinely interesting — and, frankly, a little embarrassing for the field — is that none of the ingredients are exotic.” The TL;DR is that someone just did a much more thorough job applying all of our known tools. In short: the sort of things that attack AIs are wonderful at.

AES. The second result is a new attack on reduced-round AES. This result initially sounds more exciting, since most people hear “attack on AES” and panic. However, this is also the result that’s much, much less interesting.

Most folks reading this blog will know that AES is a standard block cipher that’s used just about everywhere. It’s been a standard since 2001, and the deployed version has so far withstood everything significant that’s been thrown at it: that includes a substantial amount of non-public testing performed by the NSA. Since attacking full ciphers is very difficult, it’s standard for cryptanalysts to do their work against weakened, or “reduced-round” versions of a cipher. The full AES cipher runs for either 10, 12 or 14 rounds depending on key size. The new Anthropic result attacks a weaker 7-round variant of the cipher.

Critically, attacks against 7-round AES are not new: there have been several of these. In fact, this new Anthropic result is a modest constant-factor improvement on previous work from back in 2013. To give you a sense of how far these attacks are from really “breaking” AES, I’d note the headline results: the new attack requires 289 cipher operations and, even worse, this work is only possible after you’ve somehow convinced a real encryptor to produce 2105 encryptions of chosen plaintexts under their secret key! Neither of these things is remotely practical in the real world. And while the new result modestly speeds up this attack over the previous result, it’s not even clear how “real” the speedup in this result is: since the actual attack requires 289 operations and can’t really be “run”, what we have is an on-paper analysis that may or may not yield an actual runtime improvement if all details are actually worked out.

This does not make the result bad! In fact it’s still interesting from a techniques point of view. But it is very much a small increment in our knowledge, not a practical new attack like the HAWK work. So TL;DR: no wildly new mathematical results here. But still, real cryptanalytic progress of the sort that make scientists excited. And certainly the HAWK result is very meaningful, since that scheme had a real chance at standardization and is now (very likely) not going to be.

Now let’s talk about how we got here, and what it all means.

How did Anthropic get these results?

The Anthropic post is detailed about what they did, and honestly, it’s kind of hilarious. No, the team at Anthropic was not a large set of domain experts that carefully tuned their AI to find novel results. They appear to have just told it to get some results and then strapped its nose to the grindstone until it found some. If you doubt me, here are some examples of the prompts they used (cited from their post):

So yes, the AIs are getting pretty good. In short: they are now capable of understanding existing cryptanalysis results, synthesizing them into real new attacks, and even extending them. They can apparently do this without detailed human intervention. This isn’t yet super-intelligent cryptanalysis. but it’s pretty damn impressive.

Verifiability is now the bottleneck

As a researcher I’ve also been spending a lot of time with models, talking through various ideas. I don’t think I will surprise anyone when I say that they’re obviously getting better, even over the course of the past few months. While I don’t have Mythos and $100k to spend, I have been able to query at least one new advanced unreleased model, and I also have received some surprising new “results” to questions that I’ve been interested in for a few years.

Which brings me to the real problem: just because a model spits out an apparent new result, this does not mean the result is real. Even if models are good at producing real results, they’re much better at producing results that look real but are misleading. This can be enormously frustrating, and often means that human attention is more necessary than ever.

There are exceptions to this rule: for “full” attacks like HAWK, where the attack runs in a few hours (against a weaker version of the scheme), verification is extremely easy. You can just send over the code and let anyone check that it recovers keys and signs real chosen messages. For more subtle speedup attacks like the AES result, checking validity is not so easy. Here the approach is more specific: formally-verifiable Lean proofs can help here, but (even where these proofs are easy to make), such proofs are still highly sensitive to how you’ve formulated the theorem statement, and that often requires human experts to check.

You’ll probably notice that many of the exciting recent mathematical results have had this flavor: they either include a machine-checkable proof of a well-understood theorem, or (like the Jacobian conjecture) they involve finding a simple counterexample you can compute on. Alternatively, a bunch of experts spent a lot of time reviewing the result and were eventually convinced by it. This need for some humans to check the work is going to slow down our progress. For non-devastating examples of cryptanalysis, this is probably where we’re going to be for a while.

What are the implications for the real world?

The answer to this question really depends on whether you’re talking about the consumers of cryptography, scientists, or humanity at large. Let’s take these one at a time.

For users of cryptography: there are two pieces of good news and some mixed news. The first is that our symmetric ciphers are very messy and robust. Imagine a farmer who drags a tractor out into a patch of quicksand, and then buries it under cement. That’s what symmetric cipher design is like; it’s deliberately designed to come up with structures that are quick and easy to apply, but very messy and hard to untangle. The addition of many new raw intelligence-hours probably aren’t going to magically improve this. AIs may be able to eventually make real progress against these problems using entirely new techniques, but so far they’re not demonstrating the truly groundbreaking intuition that would be required to do so. And even if they do: there’s a good reason to hope that they’ll be able to improve the ciphers themselves to make them much harder to break.

Public-key cryptography is messier. Public-key crypto requires a mathematical object that admits fast calculations in one direction, but not the other, and yet has a convenient “trapdoor” that lets one party reverse the process. We humans have come up with only a handful of very conveniently-structured mathematical objects to enable this: they involve conjectured “hard problems” like the (EC)DLP problem, RSA, lattice problems, and various problems from the domain of coding theory. While we’ve given these our all, there simply have not been enough human beings dedicated to analyzing these problems (even the older ones like RSA!), such that we can be absolutely certain there are no more good attacks out there. This is particularly true for the novel areas like code-based crypto and even lattice-based cryptography.

That means there’s a lot of fertile ground for AIs to make real progress.

With that said, I said there was good news, and I meant it. Right now we’re in the midst of a historic transition from traditional public-key algorithms based on EC-based cryptography and RSA, moving over to new post-quantum algorithms based on novel problems. This is why there are so many standards like HAWK being considered. If there was ever a perfect time for a massive new public cryptanalysis capability to come on line, we’re in it. So unless AIs succeed in undermining all of our hard problems altogether (or we live in Impagliazzo’s Minicrypt) then this could not be a better time for AI to get good at cryptanalysis. In the best case, the result is that we gain real confidence in the problems we’ve identified, and the cryptanalysis literature gets a lot more robust. Hopefully.

For scientists: this is also a wonderful time. You now have a plastic pal who’s fun to be with, and you can talk over your hardest problems. At the same time it’s not yet smart enough that it can solve all of them without your assistance. And even better, the pace of new findings is speeding way up. This is mostly good! If you’re energetic. I still have many questions, like: “who should get credit for these new results” and “who will review all of these new results” but so far I’m not panicked. The world is getting modestly better. For now.

For the world: I don’t know. If you’re under the impression that these models are “glorified autocomplete” or that progress is slowing down, I need to urge you: stop thinking that. The models are very intelligent and capable, they are getting better at a fast clip. I can cite measurable and impressive progress over just the past five months on specific types of problem I’ve asked them to look at. If there’s a ceiling out there, I don’t yet see evidence of it. The people who think models are dumb are mostly using Google’s free AI search results, and not interacting with the high-end stuff (which only costs $20, so it’s not out of reach.) And they’re mostly not working in new areas.

On the other hand: if you think that models are super-intelligent or that AGI is already here, you should also stop thinking that. Working with these tools is like swimming in a pond where the ground drops off sharply. One minute you’re wading comfortably and there’s support under your feet. Then suddenly you cross a specific line, and you’re back to swimming on your own. This analogy is my best way to explain what it feels like when the model goes from helpful to clueless. Right now it’s easy for a human being to find that line if you’re doing advanced research, so you know where the intelligence drops off. But the line is moving. You can feel it slowly drifting outwards under your feet.

Whether this is good or bad depends whether you prefer that human beings should wade or swim, and also, whether you should be comfortable swimming in a pond where the ground itself is moving.

The only good news I can share with you is that we’re all in the same boat, scientists, lawyers, salespeople, even plumbers. Whatever happens next, it’s probably going to happen to us all. Let’s hope it’s a good thing.

The future of Siri, or: why private inference isn’t private enough

The future of Siri, or: why private inference isn’t private enough

Yesterday Apple announced a big step towards deploying real AI in their Siri ecosystem. In most ways this is good and inevitable: Siri is one of the world’s most widely-used voice agents, and it would be good if it didn’t suck. The idea that Apple would boost its capabilities with frontier models wasn’t so much a matter of if, but a question of when and who.

The who turns out to be Google: Apple looks like it will use some combination of Google Gemini models, combined with Google’s Confidential Inference and Apple’s own Private Cloud Compute for private hosting. These systems will process both your queries and evaluate private data from your devices. Apple’s marketing pitches the advantages as follows:

  1. First, since your phone already has context about you — meaning, your private information, schedules, email, text messages — an AI-enabled Siri can potentially offer more useful answers to your practical requests than external LLMs. Want to schedule a reservation for next week’s birthday party? In theory, a future Siri-AI might already know who’s coming, and what kind of cake they like.
  2. Of course, what Apple calls “context” is also the raw data of your life. This is deeply private data from all of your apps, and that data can’t just be shipped to random adtech companies (or Sam Altman) for processing. Your context needs to be protected, and Apple bills itself as a privacy company.

There’s some tension between these goals. Apple has addressed this by marketing a service it calls Private Cloud Compute, or PCC. PCC was introduced in 2024 as a private model inference system that ran entirely on Apple Silicon, using a set of “trusted” hardware security modules running in Apple’s datacenters. The goal of this system is to ensure that your data never leaves Apple’s hardware: it’s encrypted from your phone to a dedicated server, and then it disappears once a response reaches your phone. The stateless design of PCC ensures (in theory) that your data doesn’t linger, and the design of the hardware prevents even Apple from seeing the inputs.

Apple has since “expanded” PCC to encompass Google’s hardware as well. I will confess that I find the details of the new “expanded” PCC just a bit vague. It sounds a lot like Apple is primarily going to rely on Google’s existing confidential compute (running in Google datacenters) to process this data, but they’re bolting on a new layer of technical security to control which models are actually running. In any case: security experts can argue about whether this is good enough to keep Cozy Bear away from your data. What I will grant is that it’s probably good enough to keep Google and Apple from accessing your stuff, which is what most people are worried about in the first place.

So why am I so nervous?

A brief scenario involving private agents

To illustrate how agents might work, it’s helpful to consider an example use case. Let’s imagine that you’re planning a business dinner for six people. This involves several subtasks:

  1. You need to juggle the participants’ schedules, know when they’re in town and available to meet.
  2. You need to choose the appropriate restaurant based on menu and location. This might depend on what you know about the participants’ preferences: Mike is wildly allergic to szechuan peppercorn, for example, which rules out quite a few options.
  3. With these time/cuisine/location constraints in place, you’ll need to search for a restaurant that actually has a table for six in the right place.
  4. Finally, you’ll need to book the reservation, mark your calendar, and alert your attendees.

In the past, this type of scheduling required a significant amount of human effort. The beauty of AI agents is that, in theory, this is exactly the sort of project that can be automated. The agent can first scan your recent conversations to answer the questions needed for steps (1) & (2), then it can conduct the searches described in step (3). With a nod from you, it can even author the calendar invites and text messages required to complete step (4).

So what’s the problem here?

The first and unsurprising observation is that being useful on these tasks requires your agent to have context, which means: relatively unrestricted access to your private data. You know about your invitees’ availability because they texted it to you. You know about Mike’s allergy because you’ve talked about it with him or jotted it down somewhere. (This could mean iMessages, email, contacts, or personal notes.) Re-entering all of this data into an agent would be annoying and time consuming and the whole point of an agent is to save you time. The winning personal assistant doesn’t win just because it’s smart: it wins because it “already knows” the things you need it to know, like a personal assistant who sits next to your desk.

Allow me to dig into the details just a bit deeper. The agent might scan your messages database to learn the parameters needed to schedule your dinner. Or, in a more token-efficient system, it might read your messages continuously and store a “memory” that distills useful facts that it might need later. Both can be functionally equivalent, but one produces an artifact that may be highly sensitive. And keep in mind that the set of facts that might be useful is very broad. For example, Mike’s allergy is one of those facts. But there are many others. For example, the private conversation you had where you discovered that Mike was having an affair is potentially another fact that could be stored or accessed by a system. Memory or not, this data will all be within the agent’s view, and you’ll have to hope that it knows which one to operate on.

With this data at its fingertips, your agent (which is really an LLM running on a server in a data center somewhere, combined with a bunch of local state and prompting) will need to perform inference over this data, either to summarize it, or to respond to the query itself. This is where Private Cloud Compute and Confidential Inference are designed to protect you. The purpose of these technologies is to ensure that this data, and any inference results, are restricted to you alone. The inputs and outputs should be wiped as soon as inference is done, and the only remaining copy of any of it should exist on your phone.

So far I find this to be a compelling story, as long as you never plan to do anything else beyond inference.

Private inference is nice, but to be useful, agents need to talk to things

An AI that performs only inference is like a human assistant that can read your private files, but is otherwise locked in a windowless room, with no Internet access and no outbound phone. Your data is perfectly safe, but your assistant is worthless for all but the simplest tasks: for example, summarizing inbound messages for your consumption, or helping draft text messages. (In short, what Apple Intelligence does today.)

Now imagine a personal assistant who can actually get things done. This assistant will need Internet access: at minimum the ability to query search engines, or in the future, search LLMs like Gemini or ChatGPT. To accomplish the later steps of our task, you’ll need it to schedule public calendar invites and draft messages to share with your contacts. This assistant is now useful, but the wonderful PCC guarantees of “no private data is accessible to others” are no longer so applicable. The privacy of your data no longer depends on the design of some silicon, but rather, on your assistant’s discretion and judgement.

Let’s move back to our hypothetical business dinner. To accomplish step (3) your agent will need to visit a search engine or non-private LLM, perhaps asking it several queries, each of which leaks some information about your specific requirements. The nature of the data leakage really depends on how cautious the “private” agent is in authoring its queries. A perfectly reasonable case would be for the model to simply collect a series of useful facts, and upload them all to a more powerful “open” search LLM like Gemini, ChatGPT or Claude, as follows:

Hey, LLM search engine, here is a list of thirty detailed facts about my attendees and the purpose of this meeting, find me a restaurant that works for everyone.

This would be an incredibly efficient (and somewhat natural) design, since the non-private LLM is most likely going to be more powerful and capable than the private one. Unfortunately, it will also reveal an absurd amount of information about your private data, including some that may not be strictly necessary to get it done. (Is Mike’s affair relevant to the seating chart?) Put differently: private inference can work perfectly, and yet valuable (monetizable) data can still flow outward to a public search engine or LLM, simply because the agent was programmed to do its job in a slightly non-privacy-preserving way.

Ok, so search engines may learn some private data. So what?

You probably don’t care very much if a search engine learns that Mike is allergic to Szechuan food. But there are things you really should care about. In security parlance, they both have to do with different adversaries.

Let’s begin with the most obvious “adversary”. Imagine you’re Mark Zuckerberg or Sundar Pichai, or whoever runs Apple’s advertising business. You have billions of users with piles of deeply useful data stored on their phones. This data is extremely valuable for targeted advertising, something that is about to become wildly more lucrative thanks to generative AI. At the same time, a big chunk of this data is inaccessible, simply because users don’t love the idea of you scanning their private conversations. And so while you might have access to some public data (like web browsing) you can’t read those years worth of intimate private conversations that many users store on their devices.

Now imagine deploying an agent to users’ phones. That agent will have access to all that data. It’ll have access to everything the user does. To do its job, it will literally need to divine each user’s preferences and then operationalize them into queries that will repeatedly hit your search engine or “search LLM”. Whoever operates this search engine will learn a vast amount of useful information about the users’ desires, some of which will come from the most intimate private conversations — even conversations that happened years ago, and that you’ve forgotten about. If the person who operates the search engine is also the person who designs the model and its prompting, then you really have a best-case scenario for data monetization. It’s hard for me to believe that the major tech CEOs are unaware of this.

If your agent can talk to people, then strangers may talk to it

Some folks will shrug at the threat of Google learning more about them. I don’t subscribe to this viewpoint, but I understand it. From the outside, at least, Google has been a reasonably good steward of users’ data. To my knowledge, there have been no major data breaches where our most intimate Google searches were dumped all over the Internet (in the style of AOL‘s search breach.) The company deserves a lot of credit for this.

So while I object to the idea that Google or Meta or Apple may learn even more about us from our private data, it’s at least possible that our most intimate secrets won’t be revealed to the entire world. But this does not mean your private data won’t become public: and that’s why we need to talk about a second adversary. This adversary isn’t a search engine that your agent talks to, it’s all the other people who will talk to your agent.

Simon Willison describes a condition that he calls the lethal trifecta. This occurs when you have a combination of (a) access to private data, (b) untrusted content an LLM must parse, and (c) the ability to send external communications. These together create the perfect storm for data-exfiltration attacks, where a remote attacker simply “tricks” the LLM by sending it instructions to ship out confidential data. Although LLM technology is getting better, it’s still quite common for even frontier LLMs to fall for simple prompt injection attacks in which a malicious user includes text (as part of a website or a piece of data) that causes your LLM to reveal things it should not. This problem is very much alive. Just today, OpenAI recently unveiled a “lockdown mode” feature, where ChatGPT is restricted from making web searches due to the risk that it might upload your sensitive documents.

Agents like the one Apple is building (whether they use confidential inference or not) are a nightmare case of the lethal trifecta. These systems will need to ingest a vast amount of data, much of which will come from highly untrustworthy sources: think incoming emails and text messages. They will have access to everything on your system, like your encrypted messages and documents. And, to be useful, they will need to handle all sorts of actions that have visible external effects, like scheduling calendar invites and sending text messages.

The result is that your private data isn’t just vulnerable to the person who controls the agent, it’s potentially vulnerable to anyone who can cause your agent to misbehave. This problem exists regardless of how well-designed the private inference engines are. And OpenAI’s recent example illustrates that it’s far from solved. It’s possible that we’ll be able to solve these problems technically, or through some careful element of human observation — read all your outbound calendar invitations carefully — but right now we have not.

Or let me put this differently: if you think spam directed at humans is bad, wait until it’s spam directed at agents.

Who does your agent really work for?

So far we’ve discussed two adversaries: the misaligned designers of private agents (such as search operators), and the possibility of remote prompt injection attacks. But of course, in any discussion of technical privacy systems we need to talk about the last elephant in the room: your government.

We live in a society, and that society has laws. If an agent has access to all of your data, messages and actions, then technically speaking it has the ability to detect criminal activity. That criminal activity might include sharing of CSAM, or terrorism-related activity, or it could include tax fraud or any other form of crime. These agents make a perfect one-stop shop for crime detection, since they can identify patterns of bad behavior and also report them.

Is this farfetched? Well, as I’m fond of repeating on this blog, this is more or less what existing rules published by the UK’s OFCOM require for encrypted messengers, and there have been proposals in the EU Commission to do similar things. The UK also maintains a vigorous regime of Technical Capability Notices (TCNs) that allow it to demand that providers make changes to their systems, changes that could potentially affect devices worldwide. Apple is in the midst of a battle with the UK over its other encrypted services.

Traditionally in the United States we’ve shied away from this sort of thing, partly because it’s creepy and mostly because it seems like a direct attack on the Fourth Amendment. With that said, the Fourth Amendment applies only to governments: in theory a private company like Apple or Google could configure their agents to report crimes to them, and then pass along the serious ones to the government. This is more or less what Apple proposed to do in 2021, when they designed a system to monitor photos for CSAM.

At the risk of saying more obvious things, the difference between a helpful private agent, a corporate advertising bot, and a government spy comes down mainly to a matter of prompting, and maybe a bit of model fine-tuning. Once you combine private data access and the ability to send messages, there is essentially no technical protection that private inference alone can offer.

So what does this have to do with cryptography?

For decades the point of cryptography has been to remove trust: to replace “I promise not to look” with “I can’t.”

Private inference is the most ambitious version of that promise. Against the adversary it was designed for — the provider who performs the inference itself — I believe that it probably does what it says. All I’m trying to say in this post is that this adversary is a very small piece of any agentic system.

The adversaries we care about are the ones that deal with the model directly, or even the ones who designed the model or specified its technical requirements. There is no cryptographic primitive that protects you from “upload your search facts to Google” or “report anything suspicious to the government because I programmed you that way.” That protection, if it exists at all, lives in law and politics and corporate incentives: the exact messy human institutions that cryptography was invented to let us stop trusting.