Felix Fontein's Homepage

Welcome! I was (past tense!) 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).

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~~ felix@fontein.de
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.