Project Eleven said it has built a zero‑knowledge proof system that could enable recovery of bitcoin held in addresses made vulnerable by the BIP‑361 proposal, including the roughly 1.1 million BTC linked to Satoshi Nakamoto.

BIP‑361, published in April by Jameson Lopp and five co‑authors, would block new deposits to quantum‑vulnerable addresses after three years and freeze existing coins after five years, affecting more than a third of bitcoin’s total supply.

The system creates a proof that a user knows the seed material above an address in a hierarchical derivation tree, binds the proof to a migration transaction, and does not reveal the seed. Benchmarks show proof generation of 243 ms on a four‑core MacBook Air, verification of 40 ms, and memory usage of about 2 GB, with no GPU required; the author reports the proof runs 16 times faster than prior work and up to 60 times faster when the one‑time setup is excluded.

Quantum computers could derive private keys from public keys using Shor’s algorithm, rendering signatures meaningless after a theoretical “Q‑Day”. More than 34 % of bitcoin resides in addresses whose public keys are exposed.

The prototype is unaudited, supports three address types, and does not yet recover any coins on a live network. Lopp has said he dislikes BIP‑361 because it conflicts with the principle of permanent ownership, and the main objection is that freezing coins appears to violate that promise; a functional recovery proof would turn the freeze into a lock rather than a burn.

Since the recovery relies on a derivation tree introduced by BIP‑32 in February 2012, it cannot be applied to Satoshi’s coins or to wallets created before that date, and the proposal still awaits consensus changes before it could protect any coins.