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Full-Text Articles in Mathematics
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
Rose-Hulman Undergraduate Mathematics Journal
In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.
Constructing Surfaces With (1/(K-2)^2)(1,K-3) Singularities, Liam Patrick Keenan
Constructing Surfaces With (1/(K-2)^2)(1,K-3) Singularities, Liam Patrick Keenan
Lawrence University Honors Projects
We develop a procedure to construct complex algebraic surfaces which are stable, minimal, and of general type, possessing a T-singularity of the form (1/(k-2)2)(1,k-3).
Regulators On Higher Chow Groups, Muxi Li
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
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 …