The 15th workshop on Elliptic Curve Cryptography

Summer school
ECC 2011 will be preceded by a summer school on Elliptic and Hyperelliptic Curve Cryptography. The summer school will be hosted at the same place. The course is intended for graduate students in cryptography and mathematics, and will take place September 1216. Introductory topics on elliptic curves and cryptographic applications will be covered, with an emphasis on providing a strong background in support of the research talks at ECC.
The summer school lecturers are:
 Laurent Imbert: Efficient finite field and
elliptic curve arithmetic
(slides:
part1,
part2)
This course gives an overview of some common techniques used to speedup computations over finite fields and elliptic curves of cryptographic interest. In the first part, we present some algorithms for computing the basic arithmetic operations (multiplication, division, gcd) over both prime and binary fields. The second part, dedicated to fast elliptic curve arithmetic, covers various curve models and several scalar multiplication algorithms.
 François Morain: Algorithms for computing
the cardinality of hyperelliptic curves
(slides)
Efficient point counting algorithms date back to the work of Schoof around 1985 for genus 1 and later Pila for genus 2. In practice, computing the cardinality of elliptic curves over finite fields of cryptographic size became possible after improvements by Atkin and Elkies. Later, padic methods appeared that are faster for finite fields of small characteristic and were not limited to genus 1. The aim of the course is to give an overview of the history of point counting and the algorithms used as well as some light on recent progress.
 Damien Robert: Isogenies and endomorphism rings
of elliptic curves.
(slides)
Isogenies are non trivial morphisms between elliptic curves. They have many applications in cryptography: transferring the discrete logarithm problem to a weaker curve, faster point counting algorithm... The first part of the course will deal with isogeny computations from an algorithmic point of view. The second part of the course will deal with the computation of the endomorphism ring of an elliptic curve (the ring of all isogenies from a curve to itself). The endomorphism ring is a finer invariant than the number of points, and can be used to assess better the security of a curve.
 Benjamin Smith: Curves and Abelian Varieties
from a Cryptographic Point of View
(slides)
We recall the algorithmic theory of algebraic curves over finite fields, their jacobians, and more general abelian varieties, with a view to their constructive and destructive applications in cryptography. (This course will serve as an introduction and foundation for the other summer school courses.)
 Marco Streng: Complex multiplication
(blackboard talk, no slides)
I will explain how cryptographic curves can be constructed using the theory of complex multiplication
 Frederik Vercauteren: Pairings (slides: part1, part2)
 Vanessa Vitse: A survey of existing attacks on
the curvebased discrete logarithm
problem
(slides)
Except for generic methods, all known attacks of the DLP on Jacobians of curves fall into the two categories of index calculus methods and transfer to weaker groups. We begin by presenting the basics of index calculus, and by explaining how it applies naturally to the Jacobians of large genus hyperelliptic curves. For the small genus case, the large prime variations are also introduced. A second part is devoted to decomposition attacks, or how to use index calculus for curves defined over small degree extension fields. Finally, we review the transfer methods, with an emphasis on the GHS cover technique that allows to transfer the DLP from an elliptic curve defined over an extension field to the Jacobian of a larger genus curve defined over the base field.
Besides classical lectures, there will be some Coding sprints based on the Sage software. They are coordinated by Paul Zimmermann and volunteers, please contact him if you are interested. Some possible topics are discussed on http://www.loria.fr/~zimmerma/ecc.html ; introductory slides for practical info on the coding sprints are here.
Schedule
The following embeds a Google Calendar version for viewing both the ECC Summer School and ECC workshop schedules. For your convenience, it is also possible to download both calendars as a .ics file (thanks to Nicolas Estibals for suggesting this).