Bitcoin’s quantum problem gets a recovery tool, but not for Satoshi’s 1.1 million BTC

Project Eleven and Jim Posen, lead developer of the Binius proof system, built a zero-knowledge proof around it.

The user proves they know the key material sitting above their address in the wallet's derivation tree, that it derives the address in question, and binds the proof to a specific message, so the same proof can authorize the migration transaction. None of the key material is disclosed.

The benchmarks are what make it interesting. On an M5 MacBook Air, generating the proof takes 243 milliseconds on four cores, verification takes 40 milliseconds, and the whole thing uses about 2 gigabytes of memory and no GPU at all. There is no trusted setup.

Project Eleven's runs in 910 milliseconds on the CPU alone, counting circuit construction, proof generation and self-checking, which it puts at 16 times faster. Excluding the one-time setup, which a real prover would build once and reuse, the gap widens to roughly 60 times.

Which brings it back to Satoshi. The entire trick depends on there being a key above a user’s address to prove knowledge of, and that the tree structure arrived with BIP-32, which was assigned on February 11, 2012.

Before it, as Bitcoin's own documentation puts it, wallets generated every key independently and at random.