**Theses**

Diplomarbeit (Master's thesis): Zur Inversen Galoisschen Theorie in positiver Charakteristik: Starrheitssätze (On Inverse Galois Theory in Positive Characteristic: Rigitity Theorems) (pdf, dvi)

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

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

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) (pdf, dvi)

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

Index calculus in class groups of non-hyperelliptic curves of genus three (with Emmanuel Thomé), Journal of Cryptology **21**, 593-611 (2008) (pdf, 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)

On the use of expansion series for stream ciphers, LMS Journal of Computation and Mathematics **15**, 326-340 (2012) (pdf, dvi)

On the discrete logarithm problem for plane curves, Journal de Théorie des Nombres de Bordeaux **24**, 639-667 (2012) (pdf, dvi)

On the discrete logarithm problem in elliptic curves II Algebra & Number Theory **7**, 1281-1323 (2013) (pdf, dvi)

Bounded regularity, Journal of Algebra Journal of Algebra **423**, 1143-1160 (2015) (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.) (pdf, dvi)

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

Computation of a 768-bit prime field discrete logarithm (with T.Kleinjung, A.Lenstra, C.Priplata and C.Stahlke), Eurocrypt 2017, Part I, Springer LNCS 10210, 178-194 (2017) (pdf)

**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)

Cryptology - Methods, Applications and Challenges, Mathematics and Society (Wolfgang König, editor), European Mathematical Society Publishing House, 2016 (pdf)

**Further works**

Computing discrete logarithms with pencils (with S.Kochinke) (pdf) (**new**)

Ordinary plane models and completely split divisors (with S.Kochinke) (pdf)

Reflections on the role of statements on statements in mathematics (with C.Schulze) (pdf) (**neu**)

Abstract algorithms (pdf)

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

Computing discrete logarithms with special linear systems (with S. Kochinke) (dvi, pdf) (This work contains and expands the older work "Computing discrete logarithms with pencils". A Magma-Program for the "practical algorithm" based in pencils can be found here.)

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

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

**Talks**

On the ECDLP over Extension Fields (pdf) (This is my first public talk about my subexponentiality result for the elliptic curve discrete logarithm problem over extension fields. I gave this talk at the second day of the conference after on the first day Pierrick Gaudry mentioned my at that time heuristic result.)

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.)

Sur le problème du logarithme discret dans les courbes elliptiques (pdf)

Last modified: Thu Apr 3 15:42:56 CEST 2014