Shor's Algorithm

Shor's algorithm, published by mathematician Peter Shor in 1994, is a quantum algorithm that solves integer factorization and discrete logarithms in polynomial time, tasks believed intractable for classical computers. On a large enough quantum machine it would break RSA and elliptic curve cryptography, the systems securing banking, the internet, and bitcoin.

How it works

The algorithm reduces code-breaking to period finding, which a quantum computer performs efficiently using the quantum Fourier transform across superposed states. Against bitcoin, it would derive a private key from a known public key, reversing the one-way function at the heart of ownership. Running it at cryptographic scale requires thousands of error-corrected logical qubits sustaining millions of operations, far beyond any hardware demonstrated publicly as of 2026.

Only exposed public keys are at risk. Coins behind unspent hashed addresses give the algorithm nothing to attack until the moment of spending, a window that researchers also analyze for short-exposure attacks.

In the gold vs bitcoin debate

Shor's algorithm is the strongest purely technical argument for gold over bitcoin, since no algorithm threatens a metal. Bitcoin's defenders answer that the same machine would break the wider financial system's cryptography first, that migration to post-quantum signatures is possible, and that the visible pace of qubit progress makes an overnight surprise unlikely.