OpenAI announced on Oct. 26 that its AI system has refuted the Exponential Time Hypothesis (ETH), a longstanding assumption about the difficulty of certain logic problems. The claim has prompted researchers to organize an independent examination, but it does not establish a practical attack on Bitcoin.
What the claim actually says
The ETH posits that solving 3-SAT problems—where a computer must find true-or-false settings that satisfy a set of logical rules—requires exponential time in the worst case. OpenAI's manuscript, dated Oct. 17 and revised Oct. 25, claims a deterministic algorithm that exactly counts satisfying assignments of fixed-width Boolean formulas in subexponential time and polynomial space. In plain terms, the running time grows more slowly than an exponential bound as the problem gets larger.
OpenAI says the result was verified in Lean, a proof assistant, though its scope note describes a weaker time bound than the manuscript's sharpest claim. The researchers organizing the community's examination have expressly declined to certify it. Their letter states, “Our involvement should not be taken as certification of the claim.”
The disclosed bound does not establish a polynomial-time algorithm or settle P=NP, the question of whether every decision problem whose proposed solutions can be verified in polynomial time can also be solved in polynomial time.
Why Bitcoin is not directly affected
Bitcoin's security relies on two separate tasks: mining and spending authorization. Miners search for a block-header hash below a target, while signatures—such as ECDSA and Schnorr over the secp256k1 elliptic curve—establish authorization to spend. The security assumptions for these mechanisms concern elliptic-curve discrete logarithms and hash functions, not worst-case SAT solving.
Refuting an assumption about SAT solving does not, by itself, show how to defeat those concrete mechanisms. A practical attack would still require a suitable encoding, an implementation, and a cost comparison for the task being attacked. The variable count in a SAT formula is also not interchangeable with the bit length of a cryptographic key or hash. Substituting a familiar crypto bit count into the bound would skip the work needed to represent the actual problem.
Bitcoin's difficulty adjustment, which recalculates the mining target every 2,016 blocks, concerns block production, not signature authorization. It would not make a private mining advantage irrelevant.
Context and caveats
The distinction follows an earlier debate CryptoSlate covered on Oct. 7, when Justin Drake urged preparations for “bunker mode” after a previous OpenAI mathematics release. That warning concerned a possible future attack; the earlier announcement had not demonstrated a practical ECDSA or RSA break. The Oct. 26 ETH claim concerns a different result.
Ryan Williams, posting as @rrwilliams, said he, Russell Impagliazzo, and Mohan Paturi had been asked to organize an open, independent examination, without NDAs or compensation. In a separate post, Williams said he had asked OpenAI to check whether existing cryptosystems were compromised and relayed that they were apparently safe. That is his second-hand account of a check requested from OpenAI, not an independent cryptographic audit.
OpenAI itself says practical improvements require significant further research. Asked about benefits developers might feel, Williams said he did not know, allowing both for progress within 12 months and for no such development. The organizers intend to share findings as the examination progresses.
CryptoSlate's examination of the paper is limited to its introductory pages 1–8, rather than a review of the full proof. No attack times, encoding sizes, benchmarks, or independent cryptographic audit are established.
