The Quantum Threat to Bitcoin: How a Powerful Computer Can Steal Your Cryptocurrency in Under 10 Minutes

Quantum computers are fundamentally different from regular computers, exploiting the rules of physics at the atomic and particle level. However, understanding how they work is not enough to grasp their potential for stealing bitcoin. To do that, one must comprehend the target: the encryption that secures bitcoin transactions. Bitcoin utilizes elliptic curve cryptography, which involves a private key and a public key derived from it through a mathematical operation on a specific curve. The relationship between the two keys is a one-way function, making it easy to generate the public key from the private key but virtually impossible to reverse the process with classical computers. This security model relies on the difficulty of solving the elliptic curve discrete logarithm problem, which is estimated to take longer than the age of the universe for classical computers. However, a quantum algorithm known as Shor's algorithm can efficiently solve this problem, thereby breaking the encryption. Shor's algorithm works by converting the discrete logarithm problem into finding the period of a function, which quantum computers can do efficiently using superposition, entanglement, and interference. The recent paper by Google's Quantum AI division reduced the estimated number of qubits required to run Shor's algorithm against bitcoin's encryption from millions to fewer than 500,000. The team designed quantum circuits that can implement Shor's algorithm with approximately 1,200 to 1,450 logical qubits. Because qubits are prone to errors, a large number of physical qubits are needed to maintain a smaller number of reliable logical qubits. Google's paper introduced a practical attack scenario where parts of the calculation can be precomputed, allowing the quantum computer to sit in a primed state. Once a target public key appears, the machine only needs to finish the second half of the calculation, which is estimated to take about nine minutes. This creates a narrow window for a quantum attacker to derive a private key and submit a competing transaction. The average block confirmation time in bitcoin is 10 minutes, giving the attacker a roughly 41% chance of succeeding. However, the bigger concern is the large number of bitcoin (approximately 6.9 million) that are already vulnerable to an 'at-rest' attack because their public keys have been exposed on the blockchain. These coins can be stolen without any time constraint, once a sufficiently powerful quantum computer is available.