Quadratic Fields and Cryptography

In this work we look at cryptographic schemes that
are based on the
mathematics of quadratic number fields. These schemes
were
proposed by Johannes Buchmann and Hugh Williams in
the late 1980s.
After summarizing the necessary background, we
describe the actual
schemes and give some reasons why we think that they
are secure at
present. Finally, we investigate what happens with
the security once we
allow quantum computations into the picture, where we
mention some
recent results.
While the present work contains nothing new and is
completely
expository, we hope that it will provide a good
summary of this
exciting subject. We believe that giving the reader a
feel for the big picture will motivate him or her to go the local
library armed with the
present book go ahead and read the more technical
papers on the
subject.

Autorentext
Aleksandar Petrov received his BA in Mathematics from Reed
College in Porland,
Oregon in 2006. He is currently a graduate student in mathematics
at the University of
Arizona, Tucson.

Klappentext
In this work we look at cryptographic schemes that are based on the mathematics of quadratic number fields. These schemes were proposed by Johannes Buchmann and Hugh Williams in the late 1980s. After summarizing the necessary background, we describe the actual schemes and give some reasons why we think that they are secure at present. Finally, we investigate what happens with the security once we allow quantum computations into the picture, where we mention some recent results. While the present work contains nothing new and is completely expository, we hope that it will provide a good summary of this exciting subject. We believe that giving the reader a feel for the big picture will motivate him or her to go the local library armed with the present book go ahead and read the more technical papers on the subject.