The Looming Threat of Quantum Computers to Bitcoin Security

The first part of this series delved into the fundamentals of quantum computing, explaining how it differs from classical computing by leveraging the unique properties of physics at the atomic and particle level. However, understanding how quantum computers work is only half the story; the real concern lies in how they can be utilized to breach bitcoin's security. This involves grasping the encryption methods bitcoin employs, specifically elliptic curve cryptography, and identifying the weaknesses that a quantum algorithm can exploit. Bitcoin's security is rooted in a one-way function, akin to a map that allows for easy forward movement but makes reverse navigation virtually impossible for classical computers. Each wallet has a private key, a secret number, and a public key derived from it through a mathematical operation on the 'secp256k1' curve. The public key can be shared without compromising security because classical computers cannot reverse the process to find the private key. However, the advent of quantum algorithms, such as Shor's algorithm, threatens this security model. Shor's algorithm can efficiently solve the discrete logarithm problem, which is the backbone of bitcoin's encryption, by utilizing quantum properties like superposition, entanglement, and interference. This algorithm can find the period of a function related to the elliptic curve, which in turn reveals the private key. The recent Google paper has made significant strides in this area, reducing the estimated number of qubits needed to run Shor's algorithm against bitcoin's encryption from millions to fewer than 500,000. Moreover, the paper introduced a practical attack scenario where parts of the algorithm can be precomputed, leaving only the final step to be executed once a target public key is identified. This final step can be completed in approximately nine minutes, which is crucial because it is less than the average time it takes for a bitcoin transaction to be confirmed. If a quantum computer were to exist with the capability to run Shor's algorithm, it could potentially derive a private key and submit a competing transaction within this timeframe, posing a significant threat to bitcoin's security. The situation is further complicated by the fact that approximately 6.9 million bitcoin are already vulnerable due to their public keys being exposed on the blockchain, making them susceptible to attack without the need for racing against transaction confirmation times. The implications of these findings and the potential countermeasures are of paramount importance for the future of bitcoin's security.