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"Distortion maps on elliptic curves"**

Denis Charles, Microsoft Research

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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.