Quadratic Fields and Cryptography: Classical and Quantum Aspects

In this work we look at cryptographic schemes thatare based on the mathematics of quadratic number fields. These schemeswere proposed by Johannes Buchmann and Hugh Williams inthe late 1980s. After summarizing the necessary background, wedescribe the actual schemes and give some reasons why we think that theyare secure at present. Finally, we investigate what happens withthe security once we allow quantum computations into the picture, where wemention some recent results. While the present work contains nothing new and iscompletely expository, we hope that it will provide a goodsummary of this exciting subject. We believe that giving the reader afeel for the big picture will motivate him or her to go the locallibrary armed with the present book go ahead and read the more technicalpapers on the subject.