Bitcoin’s Quantum Problem Is a Governance Problem

Bitcoin's vulnerability to quantum computing lies in its governance structure, not its security. A powerful quantum computer could theoretically derive private keys from public keys and create valid signatures to spend coins it doesn't own. However, no current machine possesses this capability. While quantum computers are becoming more powerful, they remain far from being able to execute such attacks.

Public key cryptography is solvable, but the real challenge is migrating millions of coins and determining whether the network should reject invalid signatures. Quantum computing poses a two-fold threat: Shor's algorithm can recover private keys from public keys, while Grover's algorithm weakens hash functions used in proof of work.

Not all Bitcoin coins are equally at risk. Early pay-to-public-key outputs reveal public keys on-chain, making them easy targets for quantum attackers. Modern Taproot outputs, although containing public keys, only reveal them when spent. Pay-to-public-key-hash outputs are more secure, as the public key is hidden until spent. If an address has never been reused, the attacker must recover the private key and outpace confirmation times, requiring a faster quantum computer.

Address reuse greatly increases exposure, as coins controlled by the same key become vulnerable. Bitcoin's transition to post-quantum cryptography should begin now, as the U.S. government plans to phase out vulnerable public-key cryptography in the 2030s. Delaying migration could lead to market crises when major dormant addresses are targeted by quantum attackers.