The 20th McGill Invitational Workshop on Computational Complexity will be held at Bellairs Research Institute of McGill University, Holetown, St. James, Barbados, West Indies from March 2nd to March 9th, 2008. Participants are expected to arrive on Sunday afternoon, March 2nd. The subject of this year's workshop will be elliptic curves.

Speaker:

René SchoofAddress:

Università di Roma "Tor Vergata"Proposed outline

Dipartimento di Matematica

Via della Ricerca Scientifica

I-00133 Roma, ITALY

- Basics:

- Definition of elliptic curves.
- Weierstrass equations to represent elliptic curves.
- Group law for the points on the curve.
- Endomorphisms on a curve.
- Algorithms for elliptic curves over finite fields:

- Computing order of the group of points on the curve.
- Solving the discrete log problem on a curve.
- Elliptic curve cryptography:

- El Gamal encryption and signature scheme using the group of points on the curve.
- Applications of elliptic curves:

- Goldwasser-Kilian algorithm for primality testing.
- Lenstra's algorithm for integer factoring.
- Weil pairing:

- Definition.
- Computing pairing function.
- Application of the pairing in cryptography including cryptosystem, signature scheme, ...
- Fun stuff:

- Zeta function for curves over finite fields.
- A proof of Riemann hypothesis for these zeta functions.
- Zeta function for curves over Q. Connection to Fermat's Last Theorem.
- Outline of Wiles proof.

- Participants
- Contact Information
- Information about the Facility
- Background Reading Material
- Map of Barbados