Eric Landquist

[Contact Information] [Employer Information] [Teaching] [Research]

Contact Information

I am currently holding a position as a postdoc working with the Centre for Information Security and Cryptography at the University of Calgary. Contact information may be found here.

Email: elandqui@ucalgary.ca or eric.landquist@gmail.com 

Employer Information

Teaching

Past Courses:

Research

Ph.D. Thesis
Publications and Preprints
Unit rank 2 Infrastructure
This image represents an object called the infrastructure of principal ideal class and is a set of reduced principal ideals that almost forms a group under ideal composition, which is multiplication followed by reduction. The infrastructure exists in any number field or function field whose ring of integers has positive unit rank and is useful for computing regulators and fundamental units in these fields. In unit rank 1, by far the most understood case, the infrastructure is a cycle. In the unit rank 2 setting, however, the infrastructure is bicyclic like a torus, as the image shows. The spheres represent reduced principal ideals, the red and orange lines represent so-called baby steps in one direction, and the blue lines represent baby steps in the other direction in the infrastructure. Specifically, this is the infrastructure corresponding to the cubic function field defined by the curve:

y3 = x6 + 5x5 + 6x4 + 5x2 over F7.

Click on the image to see a larger version.
Image created using Mathematica.

My research interests fall under the general category of Computational Algebraic Number Theory and Cryptography. In the past I have studied integer factorization and the discrete logarithm problem, but my current research focuses on cubic function fields of large characteristic.

One current project looks into optimizing algorithms to compute divisor class numbers of purely cubic function fields of large characteristic. At present, 28-digit class numbers have been computed in function fields of genus 3 and 25-digit class numbers have been computed in function fields of genus 4. In both cases, we found examples in function fields of unit ranks 0 and 1, extracting the regulator and computing in the infrastructure of the function field in the latter case.

My next project will be to extend the infrastructure methods used above to compute the regulator, R, of a function field of unit rank 2 infrastructure. While current methods require O(R) infrastructure operations, I believe that we can reduce this to O(R0.5) operations and possibly as fast as O(R0.4) operations.

Factoring Papers
It was easy to find a factor!

Slides from Seminar and Conference Talks

PGP Public Key for landquis@uiuc.edu.

Last updated April 7, 2009.