Mathpocalypse Now? OpenAI’s Big Claims Stoke Crypto Prep Debatee
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WHAT HAPPENED
The latest claim of mathematical progress from a frontier AI lab has triggered a broad and heated debate on the soundness and durability of the cryptography that secures digital assets.
On Tuesday, OpenAI released 719 math results on GitHub, following September’s high-profile claimed solution of the Navier-Stokes Millennium Prize problem. With roughly 4,000 problems posed, OpenAI used an internal frontier model to attempt solutions, on average spending about three hours of ChatGPT Pro compute per result.
The results span 17 mathematical subfields, and OpenAI claimed progress on the famous longstanding open questions related to Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, and the Hodge conjecture. Out of the 719 results, none of them explicitly relates to cryptography, but there are adjacent discoveries.
One day after the math drop, Justin Drake, a senior researcher at the Ethereum Foundation who has deep expertise in cryptographic protocol and consensus design, wrote on X urging “the blockchain industry to calmy begin planning for ‘bunker mode’” as the “OpenAI drop made it clear that mathematical superintelligence is upon us.” Drake's concern is that AI will find a classical computer algorithm that can break ECDSA, the elliptic-curve signature scheme behind Bitcoin and Ethereum. Vitalik Buterin, one of the founders of Ethereum, echoed Drake's worry that the threat extends beyond “quantum-vulnerable cryptography” to “potentially AI-vulnerable cryptography.” Scott Aaronson, a theoretical computer scientist, further mentioned that, according to his unnamed sources, “AI companies have now started, gingerly and discreetly, investigating whether their latest internal models can break important cryptographic protocols and primitives.”
Meanwhile, Yehuda Lindell, the Head of Cryptography at Coinbase, pushed back on Drake’s stance and claimed that there is no evidence that ECDSA is going to fail.
OUR TAKE
While the speed of AI development is real, the fear of AI posing a near-term threat to cryptography (or humanity, for that matter) is more of an extrapolation than reality.
From the Hugging Face incident to Jacob Coxon’s warning of AI massacring humanity to frontier labs’ collective call to “pace the frontier,” some marketing incentives likely sit behind the scary headlines. It is also curious that frontier labs have been pushing hard on mathematical discoveries rather than those of other sciences such as physics or chemistry. Aside from the fact that math results do not require wet lab experiments, there is a possibility that mathematical breakthroughs are being advertised and used as a strong signal of model capability for the frontier labs’ own benefit, as the field carries a reputation for difficulty and purity.
Where incentives are involved, hype and truth often coexist. However, this does not invalidate the truth, and each claim should be evaluated on its own merits. Drake’s concern about AI’s threat to cryptography can be described as follows.
Essentially, encryption in cryptocurrency transactions is a one-way function. When a transaction is initiated, the private key signs the transaction, and the public key, which is generated with the private key using elliptic-curve math, is used to verify signatures. The public key stays hidden behind the address until the first time the owner spends any coins. In the transacting process, the math runs one way and has been historically infeasible to reverse, so it cannot be worked backward to generate the private key, which holds access to funds. This assumption lays the foundation of cryptographic security.
All in all, the only things to fear are fear itself and its opposite, complacency.
The industry sees two threats to the security of private keys. One, quantum computers, which could run Shor’s algorithm to solve the underlying math and recover the private key from the public key. Two, a classical algorithmic discovery that finds a mathematical shortcut to reverse the process that could run on ordinary hardware. Drake’s claim is about the second.
Notably, the examples Drake cited of math breakthroughs that caused him to worry – n log(n) bound for integer multiplication and the 3SUM conjecture – were not directly related to cryptography. They are, rather, long-assumed mathematical barriers that got broken, suggesting AI is getting better at math than the public realizes. His argument implies that ECDSA’s security rests on an unproven assumption that there is not a faster approach to generate the private key with public key information. If math was falling victim to AI, it’s certainly possible that this assumption fails too. Yet there is no current evidence of such a failure.
Drake also noted that OpenAI’s math drop said little to nothing about cryptography-related discoveries. Aaronson also noticed this, remarking that “cryptography is a subfield that’s extremely conspicuous by its absence.” The absence fueled speculation that the government is censoring cryptographic breakthroughs due to the potential damage to broadly used technologies, such as transport layer security (TLS), which powers the HTTP protocol. When such breakthroughs are ultimately made public, it could catch the cryptocurrency industry off guard and force disorganized, rushed migration of assets. All of these worries are tied to the speed of AI development and distrust of institutions and frontier labs. OpenAI’s methods in breaking through math problems have been obscure, and its operations and narratives are also unclear. At the time of writing, none of the 719 math results are externally verified by mathematicians; they are only validated by Lean, a computer program that verifies formalized proofs. The Navier-Stokes solution has also not yet been accepted by the Clay Mathematics Institute.
However, there is room for concern regarding cryptographic asset safety as AI capabilities advance. Against this backdrop, Drake’s call to prepare for “bunker mode” and move funds to new addresses is simply a wise practice. Indeed, Satoshi Nakamoto also advocated using a new key pair for each transaction and consequently new addresses in the original Bitcoin whitepaper. The fear of AI’s threat to crypto security also accelerates work on the defensive side alongside solutions for a post-quantum world.
All in all, the only things to fear are fear itself and its opposite, complacency. But fear, rightly channeled, is also what turns a warning into preparation before the warning proves true. – Jianing Wu
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