The recent introduction of Edwards curves has significantly reduced the cost of addition on elliptic curves. This paper presents new explicit formulae for pairing implementation in Edwardsâ€¦ (More)

The Gallant-Lambert-Vanstone (GLV) algorithm uses efficiently computable endomorphisms to accelerate the computation of scalar multiplication of points on an abelian variety. Freeman and Satohâ€¦ (More)

Scott uses an efficiently computable isomorphism in order to optimize pairing computation on a particular class of curves with embedding degree 2. He points out that pairing implementation becomesâ€¦ (More)

This paper presents the first study of pairing computation on curves with embedding degree 15. We show that pairing computation on these curves has loop length r and we use a twist of degree 3 toâ€¦ (More)

An isogeny graph is a graph whose vertices are principally polarizable abelian varieties and whose edges are isogenies between these varieties. In his thesis, Kohel describes the structure of isogenyâ€¦ (More)

Given a sextic CM field K, we give an explicit method for finding all genus 3 hyperelliptic curves defined over C whose Jacobians are simple and have complex multiplication by the maximal order ofâ€¦ (More)

Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the l-Tate pairing in terms of the action of the Frobenius on the l-torsion of the Jacobian of a genus 2â€¦ (More)

Isogeny volcanoes are graphs whose vertices are elliptic curves and whose edges are `-isogenies. Algorithms allowing to travel on these graphs were developed by Kohel in his thesis (1996) and laterâ€¦ (More)