Dr. Markus Maurer

From January 1, 2001 to May 5, 2001 I was a Postdoctoral Fellow at the Center of Applied Cryptography at the University of Waterloo, Canada.

Dr.rer.nat., TU Darmstadt, 2000,
Doctoral Thesis Regulator approximation and fundamental unit computation for real-quadratic orders

Diploma in computer science, University of Saarland, Saarbrücken, 1995,
Thesis Eine Implementierung des Algorithmus von Atkin zur Bestimmung der Punktanzahl elliptischer Kurven über endlichen Primkörpern der Charakteristik größer drei

Research interest and activities

My research interest was algorithmic number theory and its application to cryptography. For my PhD thesis I developped and programmed algorithms for approximating regulators of real-quadratic number fields with a-priori error bounds and computing fundamental units. The algorithms are implemented within the C++ library LiDIA, which I managed from April 1996 to September 1998. Afterwards, I was responsible for the cdcProvider project, i.e., a provider for the Java Cryptography Architecture (JCA), that, beside standard cryptographic schemes, contains schemes, whose security relies on the difficulty of factoring integers, computing discrete logarithms in finite fields, the group of rational points of an elliptic curve over a finite field, the class group of an algebraic number field, and on the difficulty of finding a generator of a principal ideal of an algebraic number field. The provider is part of the FlexiPKI project.

Publications and preprints

• Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree. With Alfred Menezes and Edlyn Teske. Indocrypt 2001, LNCS 2247, Springer Verlag, 2001, pp. 195 - 213.

• Cryptography based on number fields with large regulator. With Johannes Buchmann and Bodo Möller. Journal de Theorie des Nombres de Bordeaux, 12 (2000) 293-307. ISSN 1246-7405.

• Finding the Eigenvalue in Elkies' Algorithm. With Volker Müller. Experimental Mathematics, vol. 10, number 2, 2001, pp. 275 - 285.

• Wie sicher ist die Public-Key Kryptographie ? With Johannes Buchmann. In Tagungsband der Konferenz Systemsicherheit: Grundlagen, Konzepte, Realisierungen, Anwendungen, Vieweg Verlag, ISBN 3-528-05745-9, 2000, pp. 105 - 116.

• Identitätsbasierte Kryptosysteme als Alternative zu Public-Key-Infrastrukturen. With Dennis Kügler and Sachar Paulus. Tagungsband der Konferenz Sicherheitsinfrastrukturen: Grundlagen, Realisierungen, Rechtliche Aspekte, Anwendungen, Vieweg Verlag, ISBN 3-528-05709-2, 1999, pp. 201 - 212.

• A Note on the Weakness of the Maurer-Yacobi Squaring Method. With Dennis Kügler, Technical Report No. TI-15/99, TU Darmstadt, 1999, 4 pp.

• Approximate Evaluation of L(1,X_Delta). With Johannes Buchmann, Technical Report No. TI-6/98, TU Darmstadt, 1998, 17 pp.

• The logarithm function in LiDIA's bigfloat class. Technical Report No. TI-33/97, TU Darmstadt, 1997, 22 pp.

• LiDIA - A library for computational number theory. With Thomas Pfahler, and Susanne Wetzel, Poster Session of ISSAC'97, 1997, 7 pp.

• Counting the Number of Points on Elliptic Curves over Finite Fields of Characteristic Greater than Three. With Frank Lehmann, Volker Müller, and Victor Shoup. Proceedings of Algorithmic Number Theory Symposium, ANTS I, LNCS 877, 1994, pp 60 - 70.

Last modified: July 14, 2002 by Markus Maurer.