The Algorithms That Change Everything

Discovered by Peter Shor in 1994, this algorithm factors large numbers exponentially faster than any known classical algorithm. Why it matters: RSA encryption (used by HTTPS, banking, email) relies on the fact that multiplying two large primes is easy, but factoring the result is computationally infeasible. A 2048-bit RSA key would take a classical computer millions of years to crack. A large enough quantum computer running Shor's algorithm could do it in hours. Current status: Today's quantum computers can't run Shor's at scale (too many qubits needed, too much noise). But 'harvest now, decrypt later' attacks are already happening — adversaries collect encrypted data today to decrypt once quantum computers mature.

Grover's algorithm searches an unsorted database of N items in √N steps instead of N/2 steps classically. Practical example: cracking a 128-bit AES key classically requires 2¹²⁸ operations. Grover's reduces this to 2⁶⁴ operations — still enormous, but the effective key strength is halved. This is why post-quantum standards recommend 256-bit AES instead of 128-bit. Broader impact: Any problem that can be framed as 'search for a solution among many candidates' benefits from Grover's. This includes optimisation problems in logistics, finance, and machine learning.