This talk will serve as an introduction to the use of pairings
(especially Weil pairings on elliptic curves or abelian varieties)
in cryptography. We will mention some open questions that have
practical interest for cryptographers and should be more fully
explored by number theorists. We also show how abelian varieties
and the Weil restriction of scalars can (sometimes) be used to
"compress" points on elliptic curves.