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Advanced
Algorithms

Shor's Algorithm: Breaking RSA with Quantum Computers

By Dr. Emily Watson 15 min read 12457 views 198
AI Summary

Shor's algorithm can factor large numbers exponentially faster than classical computers, threatening RSA encryption. It requires fault-tolerant quantum computers with millions of qubits to break real-world encryption.

Overview

Shor's algorithm, discovered by Peter Shor in 1994, can factor large integers exponentially faster than the best known classical algorithm.

Why It Matters

RSA encryption, used across the internet, relies on the difficulty of factoring large numbers. A sufficiently powerful quantum computer running Shor's algorithm could break RSA.

The Algorithm

Shor's algorithm works in three steps:

  1. ▸Classical preprocessing: Convert factoring to period-finding
  2. ▸Quantum period-finding: Use quantum Fourier transform to find the period
  3. ▸Classical postprocessing: Extract factors from the period

Current Status

Current quantum computers can only factor very small numbers (e.g., 15 = 3 × 5). Breaking RSA-2048 would need millions of physical qubits with error correction.

shors-algorithm
factoring
rsa
QFT

References

  • • Shor, P. (1994) Algorithms for quantum computation
  • • Proos & Zalka (2003) Shor's discrete logarithm algorithm

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