Seminar Advanced Topics in Crytography

Lecture

First meeting: Thursday, 16 April 2009, 10⁰⁰, b-it 1.25.

Basic knowledge of cryptography and fast understanding of mathematical and computer science topics is required.

We plan to learn more about either

The decision is taken: We deal with

As a starting point we read Chapter 1 and 2 of Cohen, A course in computational algebraic number theroy.

7 May 2009, 10⁰⁰.
Daniel Loebenberger, Michael Nüsken, Konstantin Ziegler.
Basics on Pairings on Elliptic Curves; report of a workshop in Essen.
13 and 27 May 2009, 15³⁰, and 28 May, 10⁰⁰.
Laila El Aimani & Yona Raekow,
Summary of the basics.
10 June 2009, 15³⁰ and 18 June 2009, 10⁰⁰.
Thorsten Fiolka.
Factoring methods.
25 June and 2 July 2009, 10⁰⁰, and 15 July 2009, 15³⁰.
Konstantin Ziegler.
The number field sieve (including some algebraic number theory).
16 July 2009, 10⁰⁰, 22 July 2009, 15³⁰, 23 July 2009, 10⁰⁰, 29 July 2009, 15³⁰, and 30 July 2009, 10⁰⁰.
Michael Nüsken.
Counting primes and evaluating Riemann's zeta function.
(Basics, relations, and algorithms.)
Moved to following semester.
Daniel Loebenberger.
The Schnorr factoring proposal.

Eric Bach & Jeffrey Shallit (1996). Algorithmic Number Theory, volume 1: Efficient Algorithms. MIT Press. ISBN 0-262-02405-5.
Henri Cohen (1993). A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics 138. Springer-Verlag.
Richard Crandall & Carl Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001, ISBN 0-387-94777-9.
Victor Shoup (2005). A Computational Introduction to Number Theory and Algebra. Cambridge. ISBN 0-521-85-154-8.
Hans Riesel (1994). Prime Numbers and Computer Methods for Factorization. Second edition, Birkhäuser. ISBN 0-8176-3743-5, ISBN 3-7643-3743-5.

S2.