The article’s first part detailed what quantum computers are—not merely faster versions of traditional computers, but a different type of machine that leverages unique physical properties at the atomic level.
Understanding quantum computing doesn’t directly explain how it might facilitate bitcoin theft. It’s crucial to grasp the aspects of bitcoin’s security structure and identify the vulnerabilities it may expose.
The One-Way Map
Bitcoin employs elliptic curve cryptography to validate ownership. Each wallet contains two keys: a private key, a 256-bit secret number, and a public key, mathematically derived from the private key using a specific curve algorithm named “secp256k1.”
This system works like a one-way map. Starting from a common point on the curve, known as the generator point G, moving a number of steps defined by the private key produces the public key. Mathematically, this is expressed as K = k × G, where k is the private key and K is the public key.
Shor’s Algorithm Opens the Door
In 1994, Peter Shor developed a quantum algorithm capable of breaking this one-way trapdoor. While conventional algorithms require an impractical amount of time to solve the discrete logarithm problem, Shor’s algorithm operates efficiently, referred to as polynomial time.
The algorithm’s effectiveness comes from its ability to discover the period of a function, which can be computed using quantum properties, enabling a quantum computer to solve the discrete logarithm problem and, in turn, reveal the private key.
The Nine-Minute Window
Google’s recent findings have highlighted a shift in how the quantum threat to bitcoin is perceived. By preparing the algorithm in a state that precomputes portions reliant on shared curve parameters, all a quantum machine needs is to complete the secondary computation once it identifies a public key during a transaction.
This process takes roughly nine minutes—less than the average ten-minute block confirmation time for bitcoin. Should a user’s public key be exposed, a hypothetical quantum attacker has that window to derive the private key and redirect funds.
Bitcoin’s Current Security
Although Shor’s algorithm has been known for decades, bitcoin remains secure as the necessary quantum computer is still under development. Recent estimates suggest that fewer than 500,000 stable qubits are required, a significant downgrade from previous projections.
However, millions of bitcoins are still at risk, particularly those in wallets where public keys are already displayed. Ongoing improvements in quantum computing hardware intensify these concerns, prompting further examination of vulnerability, especially around newly introduced features like Taproot.
