A quantum algorithm that factors large integers in polynomial time — exponentially faster than the best known classical algorithms. The basis for quantum's threat to RSA encryption.
Shor's Algorithm, discovered by Peter Shor in 1994, reduces integer factorization to period-finding, which a quantum computer can perform exponentially faster than classical computers via the Quantum Fourier Transform. RSA, the most widely-used public-key cryptosystem, depends on the hardness of factoring large integers — so a sufficiently large fault-tolerant quantum computer running Shor's could break RSA in hours instead of the cosmologically long time it would take classically. Current hardware is many orders of magnitude away from this scale, but post-quantum cryptography is being deployed proactively.
Demonstrating Shor's algorithm factoring the number 15 = 3×5 on a 5-qubit quantum computer — proof of concept, but still far from cryptographic relevance.
Shor's Algorithm is why governments and industries are urgently deploying post-quantum cryptography — current encryption schemes will be vulnerable when sufficient quantum hardware exists.
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