How Quantum Computers Pose a Threat to Bitcoin Security in Under 10 Minutes

The first part of this series provided an overview of quantum computing principles. This piece focuses on the application of quantum computing to compromise bitcoin's security, specifically how quantum algorithms can break the encryption that safeguards bitcoin transactions. Understanding this requires knowledge of bitcoin's encryption methodology and the weaknesses it presents to quantum computing. Bitcoin employs elliptic curve cryptography, which involves a pair of keys: a private key known only to the owner and a public key that can be shared without compromising security. The relationship between these keys is based on complex mathematical operations on a specific curve, known as 'secp256k1.' The process of deriving a public key from a private key is relatively straightforward, but reversing this process to find the private key from the public key is virtually impossible for classical computers due to the elliptic curve discrete logarithm problem. However, a quantum algorithm known as Shor's algorithm can efficiently solve this problem, thereby breaking the encryption. Shor's algorithm exploits the properties of quantum mechanics, including superposition, entanglement, and interference, to find the period of a function related to the elliptic curve, which in turn reveals the private key. Although Shor's algorithm has been known for decades, its application has been hindered by the requirement for a large number of stable qubits to maintain coherence throughout the calculation. Recent research by Google has significantly reduced the estimated number of qubits needed, from millions to fewer than 500,000, making the threat more plausible. This reduction, combined with the design of quantum circuits that can implement Shor's algorithm against bitcoin's specific elliptic curve, introduces a practical attack scenario. The attack can be divided into two parts: the first part can be precomputed and stored, waiting for a target public key to appear. Once a public key is broadcast, the second part of the calculation can be completed in approximately nine minutes, according to Google's estimates. This timeframe is critical because it coincides with bitcoin's average block confirmation time, giving a quantum attacker a window of opportunity to derive a private key and submit a competing transaction. The vulnerability is particularly concerning for the 6.9 million bitcoin whose public keys have already been exposed on the blockchain, as these are susceptible to attack without the need for real-time calculation. The implications of these findings and the evolving landscape of quantum computing's threat to bitcoin security will be explored further in the next part of this series.