Shor's Algorithm
A quantum algorithm that factors large integers exponentially faster than known classical methods.
Definition
Shor's algorithm factors a large integer in time polynomial in the number of digits, an exponential speedup over the best known classical algorithms. It reduces factoring to finding the period of a function, a task a quantum circuit performs efficiently using the quantum Fourier transform.
The looming threat it poses to public-key cryptography is already driving action today, well before capable hardware exists, because encrypted data captured now could be decrypted later. This harvest-now-decrypt-later concern is why standards bodies are deploying post-quantum cryptography ahead of need.
The gap between the algorithm and its realization is instructive: factoring a cryptographically relevant number would require millions of high-quality physical qubits with error correction, far beyond current hardware. The threat is nonetheless taken seriously today because adversaries could store encrypted data now and decrypt it once machines mature, which is why standards bodies have already selected post-quantum algorithms resistant to it.
Why it works
- Factoring reduces to period-finding.
- Quantum interference extracts the period efficiently.
- Classical post-processing recovers the factors.
Why it matters
The security of RSA and much of public-key cryptography rests on factoring being hard. A large fault-tolerant quantum computer running Shor's algorithm would break it, which is driving the migration to post-quantum cryptography. Current hardware is far from the scale required.
Fusion connection
Shor's algorithm illustrates a genuine, proven quantum advantage, useful context for judging which quantum claims are credible when evaluating computing partnerships.