Dissertation

A Study on Theoretical and Practical Aspects of Weil-Restrictions of Varieties (ps, dvi)

Habilitation

On arithmetic and the discrete logarithm problem in class groups of curves (dvi, pdf), Errata (dvi, pdf)

Publications in scientific journals

The GHS Attack in odd Characteristic, J. Ramanujan Math. Soc. 18, No.1, 1-32 (2003) (ps, dvi)

On the Structure of Weil Restrictions of Abelian Varieties (with Niko Naumann), J. Ramanujan Math. Soc. 18, No.2, 153-174 (2003) (ps, dvi)

Ordinary elliptic curves of high rank over F_p(x) with constant j-invariant (with Irene Bouw and Jasper Scholten), manuscripta mathematica 114, 487-501 (2004) (pdf)

Families of elliptic curves with genus 2 covers of degree 2, Collectanea Mathematica 57, 1-25 (2006) (ps, dvi)

A double large prime variation for small genus hyperelliptic index calculus (with Pierrick Gaudry, Emmanuel Thomé and Nicolas Thériault), Mathematics of Computation 76, 475-492 (2007) (ps)

Ordinary elliptic curves of high rank over F_p(x) with constant j-invariant II (with Jasper Scholten), Journal of Number Theory 124, 31-41 (2007) (ps, dvi)

Non-constant curves of genus 2 with infinite pro-Galois covers (with Gerhard Frey), Israel Journal of Mathematics, 164, 193-220 (2008) (ps, dvi)

Index calculus in class groups of non-hyperelliptic curves of genus three (mit Emmanuel Thomé), Journal of Cryptology 21, 593-611 (2008) (ps, dvi)

On the discrete logarithm problem in class groups of curves, Mathematics of Computation, 80, 443-475 (2011) (pdf, dvi)

On the discrete logarithm problem in elliptic curves, Compositio Mathematica 147, 75-104 (2011) (pdf, dvi)

Publications in refereed conference proceedings

The XL-Algorithm and a Conjecture from Commutative Algebra, Advances in cryptology - ASIACRYPT 2004, Springer LNCS 3329, 323-337 (2004). (For this work, I obtained the "Best Paper Award" of the conference Asiacrypt 2004.) (ps, dvi)

An Index Calculus Algorithm for Plane Curves of Small Degree, Algorithmic Number Theory - ANTS VII, Springer LNCS 4076 (2006) (ps, dvi)

Invited articles

On the notion of bit complexity, Bulletin of the European Association for Theoretical Computer Science (in the "Complexity Column") 103, 35-52 (2011) (pdf, dvi)

Preprints

On the discrete logarithm problem in elliptic curves II, submitted (pdf, dvi)

On the discrete logarithm problem for plane curves, submitted (pdf, dvi)

On the use of expansion series for stream ciphers, submitted (pdf, dvi)

On the complexity of some computational problems in the Turing model, submitted (pdf, dvi)

Index Calculus in Class Groups of Plane Curves of Small Degree. This work is an extensive preprint to the work above for ANTS VII and contains additional information (ps, dvi)

Index calculus in class groups of non-hyperelliptic curves of genus 3 from a full cost perspective, a contribution to Sharcs 2006 (ps, dvi)

Cover attacks (pdf, dvi) (with Jasper Scholten), a report for the AREHCC projekt (a former project by the EU for cryptography with elliptic and hyperelliptic curves)

Systems of polynomial equations associated to elliptic curve discrete logarithm problems (ps, dvi)

An Attack on a Trace-Zero Cryptosystem (with Jasper Scholten) (ps, dvi)

Talks

An index calculus algorithm for non-singular plane curves of high genus (pdf) (Talk for "ECC 2006")

What is Index Calculus? (pdf) (An introductory talk with a new result.)

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