Andreas Enge's Publications
Book
Elliptic Curves and Their
Applications to Cryptography – An Introduction.
Kluwer Academic Publishers, 1999.
Used by Scott Vanstone and Peter Landrock as basis for a course.
Habilitation / Professorial Dissertation
Courbes algébriques et
cryptologie.
Université Paris 7 Denis Diderot, 2007.
Doctoral Dissertation
Hyperelliptic Cryptosystems –
Efficiency and Subexponential Attacks.
Books on Demand, 2000.
Available in any German bookstore and in
Japan.
Journal articles
-
With Pierrick Gaudry and Emmanuel Thomé:
An L (1/3)
Discrete Logarithm Algorithm for Low Degree Curves.
Journal
of Cryptology 2010, to appear.
HAL-INRIA 383941
and
ArXiv 0905.2177.
- Computing
modular polynomials in quasi-linear time
Mathematics of Computation 78 (267), 2009, pp. 1809–1824.
- The
complexity of class polynomial
computation via floating point approximations.
Mathematics of Computation 78 (266), 2009, pp. 1089–1107.
- With Régis Dupont:
Provably secure
non-interactive key distribution based on pairings.
Discrete Applied Mathematics 154 (2), 2006, pp. 270–276.
Preliminary version in
Daniel Augot, Pascale Charpin and Grigory Kabatianski,
editors.
Proceedings of the International Workshop on Coding and
Cryptography, Versailles — WCC 2003.
École Supérieure et d'Application des Transmissions,
2003, pp. 165–174.
- With Reinhard Schertz:
Modular
curves of composite level.
Acta Arithmetica 118 (2), 2005, pp. 129–141
- With Régis Dupont and François Morain:
Building curves with arbitrary
small MOV degree over finite prime fields.
Journal of Cryptology 18 (2), 2005, pp. 79–89.
- With Abdolali Basiri, Jean-Charles Faugère and Nicolas
Gürel:
The arithmetic of
Jacobian groups of superelliptic cubics.
Mathematics of Computation 74 (249), 2005, pp. 389–410.
- With Reinhard Schertz:
Constructing
elliptic curves over finite fields from double eta-quotients.
Journal de Théorie des Nombres de Bordeaux 16, 2004, pp. 555–568.
- With Andreas Stein:
Smooth ideals in hyperelliptic function fields.
Mathematics of Computation 71 (239), 2002, pp. 1219–1230.
Preprint
-
Computing discrete logarithms in high-genus hyperelliptic Jacobians
in provably subexponential time.
Mathematics of Computation 71 (238), 2002, pp. 729–742.
Preprint
- With Pierrick Gaudry:
A general framework for
subexponential discrete logarithm algorithms.
Acta Arithmetica 102 (1), 2002, pp. 83–103.
- The extended Euclidian algorithm on polynomials, and the
computational efficiency of hyperelliptic cryptosystems.
Designs, Codes and Cryptography 23, 2001, pp. 53–74
Preprint
- With Petra Huhn:
A counterexample to
H. Arsham: ``Initialization of the simplex algorithm: An
artificial-free approach''.
SIAM Review Online, 40(4), 1998.
Refereed conference articles
-
With Juliana Belding, Reinier Bröker and Kristin Lauter:
Computing Hilbert class polynomials.
In: Alfred J. van der Poorten and Andreas Stein, editors.
Algorithmic Number Theory – ANTS-VIII, Lecture Notes in
Computer Science vol. 5011.
© Springer-Verlag, Berlin 2008, pp. 282–295.
HAL-INRIA 246115
and
ArXiv 0802.0979.
-
Discrete logarithms
in curves over finite fields.
In: Gary L. Mullen, Daniel Panario and Igor E. Shparlinski, editors.
Finite Fields and Applications,
Contemporary Mathematics vol. 461.
American Mathematical Society, Providence 2008,
pp. 119–139.
HAL-INRIA 201090
and
ArXiv 0712.3916.
-
With Pierrick Gaudry:
An L(1/3 + ε)
algorithm for the discrete logarithm problem for low degree curves.
In: Moni Naor, editor.
Advances in Cryptology – Eurocrypt 2007,
Lecture Notes in Computer Science vol. 4515.
Springer-Verlag, Berlin 2007, pp. 379–393.
HAL-INRIA 135324
and
ArXiv cs.CR/0703032.
- With Abdolali Basiri, Jean-Charles Faugère and Nicolas
Gürel:
Implementing the arithmetic of C3,4 curves.
In: Duncan Buell, editor.
Algebraic Number Theory – ANTS-VI, Lecture Notes in
Computer Science vol. 3076.
© Springer-Verlag, Berlin 2004, pp. 87–101.
- With François Morain:
Fast decomposition of
polynomials with known Galois group.
In: Marc Fossorier, Tom Høholdt and Alain Poli,
editors.
Applied Algebra, Algebraic Algorithms and Error-Correcting
Codes – AAECC-15, Lecture Notes in Computer Science vol.
2643.
© Springer-Verlag, Berlin 2003, pp. 254–264.
Extended version.
- With François Morain:
Comparing invariants for class
fields of imaginary quadratic fields.
In: Claus Fieker and David R. Kohel, editors.
Algebraic Number Theory – ANTS-V, Lecture Notes in
Computer Science vol. 2369.
© Springer-Verlag, Berlin 2002, pp. 252–266.
- How to distinguish
hyperelliptic curves in even characteristic.
In: K. Alster, J. Urbanowicz and H. C. Williams, editors.
Public-Key Cryptography and Computational Number
Theory.
De Gruyter, Berlin 2001, pp. 49–58.
- A general framework for
subexponential discrete logarithm algorithms in groups of unknown
order.
In: A. Blokhuis, J. W. P. Hirschfeld, D. Jungnickel and J. A. Thas,
editors.
Finite Geometries, Developments in Mathematics vol. 3.
Kluwer Academic Publishers, Dordrecht 2001, pp. 133–146.
- With Benno Büeler and Komei Fukuda:
Exact volume computation
for polytopes: A practical study.
In: Gil Kalai and Günter M. Ziegler, editors.
Polytopes – Combinatorics and Computation,
DMV-Seminars vol. 29.
Birkhäuser Verlag, Basel 2000, pp. 131–154.
Invited contributions
Communications
Review
- With Dieter Jungnickel:
Ian Blake, Gadiel Seroussi and Nigel Smart: Elliptic Curves in
Cryptography, Cambridge University Press, Cambridge 1999.
Designs, Codes and Cryptography 22, 2001, pp. 97–99
Preprints
The following preprint is in preparation.
- With François Morain:
Generalised Weber Functions. II
Last changes on 17th February 2010 by
Andreas Enge