When quantum computers start breaking classic cryptography, then we better already have something stronger at hand - like quantum cryptography. The good news is that quantum cryptography is more simple than quantum computing.
For starters there are the quantum crypto protocols BB84 and E91.
|BB84||Charles Bennet and Gilles Brassard||Polarized Photons|
|E91||Artur Ekert||Entangled Photon Pairs|
On BB84 I wrote a seminar report in the course of my Bachelor studies.