Google certified a quantum attack on elliptic curve cryptography without disclosing the algorithm

A zero-knowledge proof does one narrow thing. It convinces a verifier that a prover holds a valid proof of some statement, and it conveys nothing about that proof ^[11]. The convincing happens through interaction: information is exchanged step by step, and with each step the verifier's conviction that the claim is true grows, with algorithms handling the exchange in practice ^[12]. Cryptographers have had the idea since the mid-1980s ^[10].

The certificate Google published in March was itself wrong. Keegan Ryan's team showed that the first version could be used to prove false claims, among them that the encryption could be cracked without any Toffoli gates, which is impossible because the algorithm would then perform no logical operations ^[9]. Google's developers and colleagues corrected it and put a valid zero-knowledge proof in its place in mid-April 2026 ^[13]. Scientific American reports the original claim came through intact, with the error confined to the implementation of the method ^[13].

The claim is a resource count: 1,175 logical qubits and more than two million Toffoli gates ^[6]. Experts had previously put the requirement at 20 times that qubit figure or more, which is about 23,500 ^[7][14]. Hardware is nowhere near either number. The record as of July 2026 is just under 100 logical qubits ^[8], roughly a twelfth of Google's count ^[15] and about one 235th of the older estimate ^[16].

Google's researchers argued that publishing the algorithm carried too great a risk of misuse, or of being rapidly developed further by others ^[4]. By Scientific American's account, the algorithm stayed secret for only a few days ^[18]. Everyone outside the company was left with what the proof carries, which is that such an algorithm exists, and could not use the method to do anything else ^[5].

Whether this becomes a way of publishing is a separate question from whether it worked once. Scientific American reports that some experts asked afterward whether Google's use would remain an isolated case, or whether zero-knowledge proofs would become the norm in a research world where companies with secrets to keep matter more and more ^[17]. The instrument is general, since any verifiable proof admits a zero-knowledge version ^[11]. On one white paper, revised once, whose secret lasted days, I would not yet describe the meaning of publication as reopened.