Physical Sciences and Mathematics Commons^™

Regulators On Higher Chow Groups, Muxi Li

Arts & Sciences Electronic Theses and Dissertations

There are two natural questions one can ask about the higher Chow group of number fields:

One is its torsion, the other one is its relation with the homology of GLn. For the first

question, based on some earlier work, the integral regulator on higher Chow complexes

introduced here can put a lot of earlier result on a firm ground. For the second question, we

give a counterexample to an earlier proof of the existence of linear representatives of higher

Chow groups of number fields.

Chapter 1 gives a general picture of the two problems we are talking about. Chapter …

A Computational Introduction To Elliptic And Hyperelliptic Curve Cryptography, Nicholas Wilcox

Honors Papers

At its core, cryptography relies on problems that are simple to construct but difficult to solve unless certain information (the “key”) is known. Many of these problems come from number theory and group theory. One method of obtaining groups from which to build cryptosystems is to define algebraic curves over finite fields and then derive a group structure from the set of points on those curves. This thesis serves as an exposition of Elliptic Curve Cryptography (ECC), preceded by a discussion of some basic cryptographic concepts and followed by a glance into one generalization of ECC: cryptosystems based on hyperelliptic …