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Elliptic Curve Cryptography

Corresponding entry in Aachen Campus, Bonn University (Lecture, Tutorial).


Prof. Dr. Joachim von zur Gathen


Michael Nüsken


Daniel Loebenberger

Time & Place

First meeting: Tuesday, 27 October 2009, 1330, b-it Rheinsaal.

Additional hours: Wednesday 1445-1530, b-it 1.25 on 2, 9, 16 December, 13, 20, 27 January and 3 February.

In exchange there is no course on 3, 22 and 23 December.  The first course in 2010 is on 12 January.


There will be oral exams. Dates are already set and sent to participants by email.


Basic knowledge in cryptography is required.


We intend to introduce elliptic curves as used in cryptography. That encompasses definition and properties of the group law and of pairings. The necessary maths will be discussed in the course.

The computationally interesting part starts when we try to implement elliptic curve arithmetic as good as possible.  The last few years have brought up quite a few surprising developments.  One of those was the rise of Edwards curves.  They are very close relatives of elliptic curves but more symmetric than the former in their shape and -more important- in their arithmetic (no special cases!).

All times subject to agreement in class.


The screen notes (PDF) contain all handwritten stuff (last updated 28 January 2010, 18:20).

There is also a sketch (PDF) of the course (last updated 01 February 2010, 18:41).




We will put each member on the mailing list

[Sorry, you need to enable Javascript to see this.]
, but you can also subscribe yourself: . The list is intented for all participants of the course as a platform for discussions around the topic. Furthermore, announcements regarding the course are made here.


4+2 SWS, 8 credits. Optionally, 3+2 SWS, 6 credits.

Successful completion of the course yields 8 credit points. For students who only want 6 credit points, a breakpoint at about 3/4 of the teaching time will be defined, and only the course material up to that point will be relevant for their exams and grades.

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