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cosec >students >Teaching >Winter 2006/2007 

Graduate Seminar Advances in Elliptic Curve Cryptography


Prof. Dr. Joachim von zur Gathen


Michael Nüsken

Time & Place

Thursday, 10:00-12:00, b-it 2.1.

Organizational meeting: 19 October 2006, 10:00.
First session: 2 November 2006, 10:00.


Basic knowledge of elliptic curves and their use in cryptography will be helpful. Fast understanding of mathematical and computer science topics is required.


We will discuss various topics from elliptic curve cryptography. The aim of the seminar is to get an overview over current uses of elliptic curves in particular in cryptography and the necessary background to understand these. The book "Advances in Elliptic Curve Cryptography" shall be a guideline to this. We would like to discuss those topics enhanced by the necessary background information. Since our purpose is to really understand things it may well happen that a topic extends to a further session or a background session is put inbetween as necessary. This heavily depends on the knowledge and interests of the participants.


Note that this is a working seminar. Its sessions might be less structured, talks more ad-hoc and with more discussion than usual. A session might thus expand and use another week or shrink.

02.11.2006 / 09.11.2006 :
Daniel Loebenberger, Basics about elliptic curves.
[Washington (2003), §3.]
09.11.2006 / 16.11.2006 / 23.11.2006 :
Jens Putzka, Torsion and pairings 1.
[Washington (2003), §3, §5.3. Blake et al. (2005), §IX.6, §IX.9.]
30.11.2006 :
Jamshid Shokrollahi, Factoring 1.
[Washington (2003), §7.]
07.12.2006 / 14.12.2006 :
Michael Nüsken, Point Counting 1.
[Washington (2003), §4.]
21.12.2006 / 11.01.2007 / 18.01.2007 :
Laila El Aimani, Elliptic curve cryptography.
[Blake et al. (2005), §I. Washington (2003), §6.]
25.01.2007 1500(!) / 01.02.2007 :
Daniel Loebenberger, Hyperelliptic curves...


  • Ian Blake, Gadiel Seroussi & Nigel Smart (2005). Advances in Elliptic Curve Cryptography.
  • Ian Blake, Gadiel Seroussi & Nigel Smart (1999). Elliptic Curve Cryptography.
  • Lawrence C. Washington (2003). Elliptic Curves; Number Theory and Cryptography.
  • Henry Cohen, Gerhard Frey, Roberto Avanzi, Chritophe Doche, Tanja Lange, Kim Nguyen & Frederik Vercauteren (2005). Handbook of Elliptic and Hyperelliptic Curve Cryptography.
  • Slides from ECC 2006 .


Media Informatics, Communication skills.
University of Bonn - Computer Science, ??.
University of Bonn - Mathematics, ??.

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