Bitcoin's security rests on a mathematical structure that is easy to compute in one direction and effectively impossible to reverse on classical machines. In a featured article, CryptoComLearn says the recent Google quantum computing paper points to a nine-minute window in which that assumption could be attacked.
The one-way link between private keys and public keys
The article starts with the core mechanism. Bitcoin uses elliptic curve cryptography, and every wallet has two keys: a private key and a public key. The private key is a secret number that is 256 bits long in binary form. The public key is derived from that private key through a specific mathematical operation on an elliptic curve.
CryptoComLearn describes this as a one-way map. Everyone begins from a known generator point, called G. A user takes a number of curve-defined steps that only they know; that hidden step count is the private key. The endpoint, K, is the public key. Anyone can verify the endpoint. Working backward to recover the number of steps is the hard part.
Formally, the relationship is written as K = k × G. That multiplication is not ordinary arithmetic but a geometric point operation on the curve. If k and G are known, K can be computed in milliseconds. If only K and G are known, solving for k becomes the elliptic curve discrete logarithm problem. For a 256-bit curve, the article says the best known classical methods are estimated to take longer than the age of the universe.
Why digital signatures prove control of coins
This one-way trapdoor is the foundation of Bitcoin ownership. The private key proves control over coins, while the public key can be shared because classical computers cannot reverse the math. When someone sends bitcoin, the wallet uses the private key to create a digital signature. That signature proves knowledge of the secret number without exposing it.
So the direct route for an attacker is not rewriting Bitcoin's ledger. The real target is the hidden key behind public information. Classical machines stall there. Quantum machines attack that exact bottleneck.
Shor's algorithm changes the security assumption
The piece points to 1994, when mathematician Peter Shor introduced what is now called Shor's algorithm. The algorithm can efficiently solve the discrete logarithm problem, striking at the central assumption behind elliptic curve cryptography.
On classical systems, the difficulty of the problem explodes as the numbers get larger. Under Shor's algorithm, the growth in difficulty is far more manageable. The article frames the intuition this way: given the public key K and the generator point G, the task of finding the private key k can be converted into a period-finding problem, which is well suited to quantum computation.
That is the basis of the article's nine-minute theft scenario. The issue is not that a quantum computer is simply faster than a normal computer. The issue is that it attacks the one-way property at the center of Bitcoin's cryptographic design. If that property no longer holds under quantum computation, the relationship between public keys and private keys stops being secure in the way Bitcoin currently assumes.