How Quantum Computing Threatens Bitcoin Security in Under 10 Minutes

Part 1 of this series delved into the physics behind quantum computing, revealing its fundamentally different nature compared to regular computers. However, understanding how quantum computers work doesn't necessarily explain how they can be used to steal bitcoin. To grasp this, it's essential to comprehend what they're attacking, how bitcoin's security is structured, and where the vulnerabilities lie. This piece begins with an examination of bitcoin's encryption, working through to the nine-minute window identified by Google's recent quantum computing paper. Bitcoin utilizes elliptic curve cryptography to verify ownership, with each wallet possessing two keys: a private key, which is a secret 256-digit binary number, and a public key derived from the private key using a mathematical operation on the secp256k1 curve. The process can be thought of as a one-way map, where starting from a known location, taking a private number of steps leads to a public key, making it easy to verify the endpoint but virtually impossible for classical computers to reverse-engineer the steps taken. This one-way trapdoor is the foundation of bitcoin's security model, with private keys proving ownership and public keys being safe to share due to the impracticality of reversing the math for classical computers. However, Shor's algorithm, discovered in 1994, offers a quantum solution to the discrete logarithm problem, potentially breaking this trapdoor. The algorithm works by converting the problem into finding the period of a function, which quantum computers can solve efficiently by representing all possible values simultaneously, applying the function, and then using the Fourier transform to cancel out incorrect answers. Google's paper significantly reduced the estimated number of qubits required to run Shor's algorithm against bitcoin's elliptic curve, from millions to fewer than 500,000, and introduced a practical attack scenario. The paper designed two quantum circuits implementing Shor's algorithm, one requiring approximately 1,200 logical qubits and the other 1,450, with the potential for a 'nine-minute window' where a quantum attacker could derive a private key and submit a competing transaction. This poses a significant threat, particularly to the 6.9 million bitcoin with public keys already exposed on the blockchain, which are vulnerable to an 'at-rest' attack. The implications of this and the rapidly closing gap in hardware capability will be explored in the next piece.