# Felix Fontein's Homepage

Welcome! I was working as a postdoc at the University of Zurich from February 2011 until February 2014. For more up to date information, please refer to my personal homepage.

Before being a postdoc at the University of Zurich, I was a postdoc at the Department of Mathematics & Statistics at the University of Calgary in Canada. In Calgary, I was a member of the Institute for Security, Privacy and Information Assurance. I did my PhD student at the Institut für Mathematik at the the Universität Zürich, where I was a member of the Applied Algebra work group, which is lead by Prof. Dr. Joachim Rosenthal. Before this I was studying mathematics and computer science at the University of Oldenburg, Germany.

My research interests are mainly focused on the arithmetic in global fields. I want to increase the understanding of the infrastructure, in particular of baby steps, as well increase the efficiency of computation in the infrastructure and the divisor class group of a global field. Besides this, I am interested in computing fundamental units of global fields, in particular their absolute values, using baby step-giant step strategies. Besides this, I am also interested in applications of this theories to Public Key Cryptography.

Besides these special topics, I am interested in Algebraic and Analytic Number Theory, Arithmetic and Algebraic Geometry and their applications to Cryptography.

## Publications

- F. Fontein:
*Groups from Cyclic Infrastructures and Pohlig-Hellman in Certain Infrastructures.*Advances in Mathematics of Communications, 2 (3), p. 293-307, 2008. (Preprint at arXiv, article in journal.) - F. Fontein:
*The Infrastructure of a Global Field of Arbitrary Unit Rank.*Math. Comp. 80 (2011), no. 276, 2325–2357 (Preprint at arXiv, article in journal.) - F. Fontein:
*Holes in the Infrastructure of Global Hyperelliptic Function Fields.*2009. (Preprint at arXiv.) - F. Fontein:
*Explicit Methods for Radical Function Fields over Finite Fields.*2009. (Preprint at arXiv.) - F. Fontein, E. Landquist, R. Scheidler:
*Class Number and Regulator Computation in Purely Cubic Function Fields of Unit Rank Two.*2010. (Preprint at arXiv.) - F. Fontein, M. J. Jacobson, Jr.:
*Rigorous Computation of Fundamental Units in Algebraic Number Fields.*2010. (Preprint at arXiv.) - F. Fontein, P. Wocjan:
*Quantum Algorithm for Computing the Period Lattice of an Infrastructure.*2011. (Preprint at arXiv.) - F. Fontein, K. Marshall, J. Rosenthal, D. Schipani, A.-L. Trautmann:
*On Burst Error Correction and Storage Security of Noisy Data.*2012. (Preprint at arXiv, MTNS2012 proceedings.) - F. Fontein, M. Schneider, U. Wagner:
*A Polynomial Time Version of LLL With Deep Insertions.*Preproceedings of the International Workshop on Coding and Cryptography, WCC 2013. (Preprint at arXiv.) - F. Fontein, P. Wocjan:
*On the Probability of Generating a Lattice.*Journal of Symbolic Computation, 2013. (Article in journal and preprint at arXiv.) - F. Fontein, M. Schneider, U. Wagner:
*PotLLL: A Polynomial Time Version of LLL With Deep Insertions.*Designs, Codes and Cryptography, 2014. (Online first article in journal.)

## Software

- A patch for fplll 4.0.1 which adds an PotLLL implementation.

## Coauthors

- Michael J. Jacobson, Jr. (University of Calgary)
- Eric Landquist (Kutztown University)
- Kyle Marshall (University of Zurich)
- Joachim Rosenthal (University of Zurich)
- Renate Scheidler (University of Calgary)
- Davide Schipani (University of Zurich)
- Michael Schneider (Technical University of Darmstadt)
- Anna-Lena Trautmann (University of Zurich)
- Urs Wagner (University of Zurich)
- Pawel Wocjan (University of Central Florida)

## Theses

- F. Fontein:
*Elliptic Curves over Rings with a Point of View on Cryptography and Factoring.*Diplomarbeit, Carl von Ossietzky-Universität Oldenburg, June 2005. (PDF, 2.0 MB) - F. Fontein:
*The Infrastructure of a Global Field and Baby Step-Giant Step Algorithms.*Dissertation, Universität Zürich, March 2009. (PDF, 1.0 MB) (Zentralbibliothek Zürich)

## Teaching

- In the spring term 2013, I was teaching the Aspects of Computer Algebra (MAT 007).
- In the spring term 2012, I was teaching the MATLAB course (MAT 116) preceding the lecture on numerical analysis.
- In the fall term 2011, I was teaching Einführung in die Algebra (MAT 211).
- In the spring term 2011, I was teaching the MATLAB course preceding the lecture on numerical analysis.
- In the fall term 2008, I was in charge for one exercise group of the module Kryptographie (MAT001).
- In the fall term 2007, I was in charge for one exercise group of the module Algebra I (MAT211).
- In the summer term 2007, I was in charge for one exercise group of the module Lineare Algebra II (MAT111).
- In the winter term 2006/07, I was in charge for the exercises of the module Elliptische Kurven (MAT512).
- In the summer term 2006, I was in charge for one exercise group of the module Zahlentheorie (MA 460).
- In the winter term 2005/06, I was in charge for one exercise group of the module Algebra I (MAT221).

## Links

- My math blog.
- My personal homepage.
- MatheRaum: a community for discussing, asking questions and answering questions related to math.

## Contact

You can contact me by snail mail by using the following address:

Felix Fontein

Institut für Mathematik

Universität Zürich

Winterthurerstrasse 190

8057 Zürich

Switzerland

Other ways to contact me are the following:

E-Mail: felix.fontein@math.uzh.ch

Phone: +41-(0)44-63 55859

Or just find me in my office, Y27-K52.

In case you want to send me encrypted emails, you can download
my GPG/PGP public key. It's fingerprint
should be `9F6E FA02 A8C7 BAAA 758F EA16 DFDA 115C 9957 EBA7`

.