Classical Cryptosystems In A Quantum Setting

Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum computing indicate that many of the public key cryptosystems currently in use could easily be broken if large-scale quantum computers become technologically feasible. Further, encrypted messages captured and stored in the past could also be decrypted by a future quantum attacker. Since large-scale quantum computers may one day be developed, We need to prepare for that eventuality by analysing modern cryptosystems with respect to attacks with a quantum computer. In this thesis, submitted in fulfilment of the requirements for the degree of Master of Mathematics in Combinatorics & Optimisation at the University of Waterloo, we examine the quantum strengths and vulnerabilities of several of the most popular classical public key cryptosystems.