Plain-Language Intuition
Why is online banking and internet communication secure today?
Because multiplying two huge prime numbers together is easy, but factoring their product N = p × q back into primes takes classical supercomputers billions of years!
In 1994, Peter Shor stunned the world by showing that a Quantum Computer can break this code in minutes.
Shor realized that factoring is really about finding a repeating pattern (the period r) in modular arithmetic:
a^x mod N = 1
Classical computers must calculate powers one by one like checking locks on a door.
Shor's quantum circuit evaluates ALL powers at once in a superposition wave, uses quantum interference to cancel all the wrong frequencies, and leaves only the true period r vibrating at the top! From r, classical math instantly factors the number.