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

The first part of this series delved into the physics of quantum computing, explaining how these machines differ fundamentally from classical computers. However, understanding the inner workings of a quantum computer doesn't reveal how it can be used to steal bitcoin. To grasp this, we need to understand the target - how bitcoin's security is constructed, why a quantum algorithm can break it, and the implications of Google's recent quantum computing paper. This piece begins with an examination of bitcoin's encryption, working through to the nine-minute window identified by Google's paper, within which a quantum computer can potentially break bitcoin's security. Bitcoin utilizes a system called elliptic curve cryptography to verify ownership. Each wallet has two keys: a private key, which is a secret 256-digit binary number, and a public key derived from the private key through a mathematical operation on the 'secp256k1' curve. This can be thought of as a one-way map, where starting from a known location on the curve, taking a private number of steps leads to a public key. Anyone can verify the endpoint but not the number of steps taken to get there. Technically, this is represented as K = k × G, where k is the private key, and K is the public key, with the 'multiplication' being a geometric operation along the curve. The crucial property of this system is that moving forward is easy, but reversing the process is effectively impossible for classical computers. If you know the public key and the generator point, figuring out the private key involves solving the elliptic curve discrete logarithm problem, which is estimated to take longer than the age of the universe for the best-known classical algorithms. This one-way trapdoor is the basis of bitcoin's security model. Your private key proves ownership, and your public key is safe to share because classical computers cannot reverse the math. When sending bitcoin, your wallet uses the private key to create a digital signature, proving knowledge of the secret number without revealing it. However, Shor's algorithm, discovered in 1994, breaks this trapdoor by efficiently solving the discrete logarithm problem. The algorithm converts the problem into finding the period of a function that takes a number as input and returns a point on the elliptic curve. As the function's outputs repeat in a cycle when fed sequential numbers, knowing the cycle length unravels the discrete logarithm problem, allowing the private key to be found almost immediately. Finding this period is exactly what quantum computers are designed for. They put their input register into a superposition, representing all possible values simultaneously, apply the function to all of them at once, and then use a quantum operation called the Fourier transform to cancel out wrong answers and reinforce the correct ones. When measured, the result reveals the period, from which ordinary math can recover the private key. The attack utilizes all three quantum properties: superposition evaluates the function on every possible input at once, entanglement links the input and output, and interference filters the noise until only the answer remains. Despite Shor's algorithm being known for over 30 years, running it has required a quantum computer with a large enough number of stable qubits, which has been out of reach. Google's paper reduced the estimated number of qubits needed from millions to fewer than 500,000, a roughly 20-fold reduction. The team designed quantum circuits that implement Shor's algorithm against bitcoin's specific elliptic curve, using approximately 1,200 to 1,450 logical qubits and tens of millions of Toffoli gates. Because qubits lose their quantum state constantly, hundreds of redundant qubits are needed to maintain a single reliable logical qubit, with most of the quantum computer existing as infrastructure to catch its own mistakes. Google's paper introduced a practical attack scenario that changes how to think about the threat. Parts of Shor's algorithm can be precomputed, allowing the quantum computer to sit in a primed state, waiting for a target public key to appear. Once a target public key is broadcast or exposed on the blockchain, the machine only needs to finish the second half of the calculation, which Google estimates takes about nine minutes. Given that bitcoin's average block confirmation time is 10 minutes, a quantum attacker has roughly nine minutes to derive a private key and submit a competing transaction. This gives the attacker a roughly 41% chance of succeeding before the original transaction confirms. The bigger concern is the 6.9 million bitcoin already vulnerable to an 'at-rest' attack, where the public key has been permanently exposed on the blockchain. A quantum computer running Shor's algorithm can turn a bitcoin public key into the private key that controls the coins, with no race against the clock needed for these coins.