What is Shor's algorithm, and why does it worry every cybersecurity team on the planet?

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Shor's algorithm is a quantum algorithm published by mathematician Peter Shor in 1994 that can efficiently factor large integers and solve the related discrete logarithm problem, the two mathematical problems that underpin RSA, Elliptic Curve Cryptography and Diffie-Hellman key exchange, the encryption schemes securing the overwhelming majority of internet traffic today. Classically, factoring a large number like a 2048 bit RSA key is considered computationally infeasible, taking longer than the age of the universe with any known classical method. Shor's algorithm reduces that same problem to something a sufficiently powerful quantum computer could solve in a practical amount of time

The algorithm works by reframing factoring as a period finding problem, something quantum computers are naturally well suited to because of a tool called the Quantum Fourier Transform, which quantum hardware can apply to many possibilities simultaneously thanks to superposition. No quantum computer today is anywhere close to running Shor's algorithm against real world key sizes, current estimates still require somewhere in the range of a million or more high quality physical qubits with extremely low error rates, well beyond what any existing machine has achieved

The threat is not purely theoretical or purely future facing though, because of a strategy security researchers call harvest now, decrypt later, where encrypted data intercepted and stored today could simply be decrypted once a capable enough quantum computer eventually exists. That risk is exactly why post quantum cryptography, new encryption schemes designed to resist Shor's algorithm even in principle, is already being standardized and rolled out well before the hardware that could actually break today's encryption exists

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