Anthropic's Claude Mythos cracks HAWK in 60 hours, halving key strength

Anthropic's unreleased Claude Mythos Preview model discovered a mathematical flaw in HAWK, a NIST post-quantum signature candidate, cutting its effective key strength from 2^64 to 2^38 operations in a 60-hour autonomous research run. The model also developed a new attack technique called the "Möbius Bridge" that accelerates cryptanalysis of a reduced-round AES-128 by 200 to 800 times.

"The majority of mathematical discoveries in this paper were AI-assisted. Human author contribution mainly consisted of directing, organizing and verifying AI work," the Anthropic researchers wrote in the HAWK paper. A human researcher with a theoretical computer science background but no lattice-cryptography expertise provided occasional project-management guidance.

The attack recovered a functionally equivalent signing key for HAWK-256 in about 3 hours and 42 minutes on a 96-core server. For larger parameter sets, gate-count estimates fell from 2^150 to 2^108 for HAWK-512 and from 2^288 to 2^182 for HAWK-1024. Fixing the flaw requires roughly doubling HAWK's key sizes, which eliminates the scheme's efficiency advantage — compact signatures and fast signing were its primary selling points, particularly for blockchain applications where signature size directly affects transaction fees.

The discovery has immediate implications for NIST's post-quantum standardization process, where HAWK is the sole remaining lattice-based candidate in the third round. It also raises the stakes for the broader cybersecurity industry: Anthropic says the model found thousands of zero-day vulnerabilities, including a 27-year-old flaw in OpenBSD's SACK TCP implementation and a 16-year-old bug in FFmpeg's H.264 codec, at a cost of under $50 per critical vulnerability.

The 60-hour discovery that took humans a month to verify

The HAWK attack exploits a previously unused automorphism — a symmetry preserving the lattice structure underlying the scheme — that reduces the key-recovery problem to finding a short vector in a lattice of roughly half the original dimension. Anthropic's released implementation performs the full key recovery in under four hours on a 96-core server, using lattice reduction and sieving techniques to reconstruct a secret basis capable of signing messages.

The AES finding is equally notable for how it emerged. Claude initially refused the task, arguing that "there's nothing easy to find; this is the most-studied block cipher in existence." After researchers pushed the model over three days, it produced the Möbius Bridge concept — a mathematical invariant that removes a 256-way guessing step from meet-in-the-middle attacks on seven-round AES-128. The model generated roughly one billion output tokens refining the idea.

The verification bottleneck is striking: two researchers spent nearly a month confirming the AES result, reading hundreds of hours of cryptography literature. "In just one year, language models have gone from being unable to perform cryptanalysis of even the most basic ciphers to being capable of finding flaws in cryptographic designs that have escaped discovery despite years of human expert review," Anthropic wrote.

What it means for NIST, cybersecurity, and AI governance

HAWK remains a third-round NIST candidate as of July 29, and it is unclear whether its parameters or standing will change. The attack does not compromise HAWK-512 or HAWK-1024 in practice — both remain exponential and impractical to break — but the effective key-strength reduction forces a re-evaluation of the scheme's efficiency claims.

Anthropic has restricted access to Mythos Preview under "Project Glasswing," limiting it to vetted enterprise partners and critical infrastructure organizations. The company also released CryptanalysisBench, a 191-task benchmark developed with researchers from ETH Zurich, the University of Haifa, Technische Universität Berlin, and Tel Aviv University, to measure AI cryptanalysis capability. Claude Mythos 5, the latest update, solved 85.7 percent of tasks with known solutions, compared with 65.3 percent for the weakest model tested.

The dual-use nature of the capability is not lost on national security circles. Reports suggest the U.S. National Security Agency may be evaluating Claude Mythos for offensive cyber operations. Anthropic has open-sourced proof-of-concept code for the HAWK and AES attacks, enabling independent verification while limiting distribution of the model itself.

For investors, the implications extend beyond Anthropic. The discovery accelerates the timeline for post-quantum migration across industries, creating demand for PQC-enabled hardware from vendors like SEALSQ, which embeds post-quantum cryptography into silicon. It also raises the bar for AI safety frameworks: when a model can discover mathematical flaws faster than humans can verify them, the traditional "find and fix" security model breaks down. The cost structure is the most striking part — scanning a thousand OpenBSD repositories costs under $20,000, and a single critical vulnerability costs under $50 to find.

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