"Distortion maps on elliptic curves"

Denis Charles, Microsoft Research


Abstract: An important problem in cryptography is the so-called Decision Diffie-Hellman problem over a group. If the group is an elliptic curve, then this problem becomes easy provided there are certain endomorphisms called Distortion maps that can be efficiently evaluated. We give a survey of what is known about Distortion maps on elliptic curves (over finite fields), including some recent results regarding Distortion maps for ordinary elliptic curves.