The CHIC project

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The members of the CHIC project

Scientific goals

Some recent improvements have strengthen the importance of elliptic curves in asymmetric cryptography. The main objective of the project Hyperelliptic Curves Isogenies, point Counting (CHIC) is to bridge the gap in terms of performance and security between the genus one and small genus cases over prime fields. We project to expand the algorithmic toolbox applicable to small genus abelian varieties with new algorithms aiming at:
  • improving the representation and group law computation;
  • obtaining efficient point counting for curves.

The project is divided in four main tasks:
  • The arithmetic of hyperelliptic curves and their Jacobians;
  • Isogeny computation between general abelian varieties;
  • General point counting algorithms over prime fields;
  • Special curves and point counting.
For more details, we refer the reader of this page to the pdf document describing all the goals of the project as well as its management.