Elliptic curve cryptography is cutting edge technology in close
interaction with the newest developments in computational number theory
and higher arithmetic. Some of its advantages include significant security
levels with comparatively smaller key lengths. As security policies
tighten, up to date algorithms and techniques are needed to keep in pace.
Our research focuses especially on computational aspects of elliptic and
hyperelliptic curves over finite fields, such as cardinality algorithms,
efficient halving methods, algorithms to obtain cryptographically useful
curves, applications to identity-based cryptography, etc.