In this paper we introduce the concept of an optimal pairing, which by definition can be computed using only log2 r/(k) basic Miller iterations, with r the order of the groups invo...
When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of ...
Michael Scott, Naomi Benger, Manuel Charlemagne, L...
We outline PARI programs which assist with various algorithms related to descent via isogeny on elliptic curves. We describe, in this context, variations of standard inequalities w...
Abstract. We show that finding an efficiently computable injective homomorphism from the XTR subgroup into the group of points over GF(p2 ) of a particular type of supersingular e...
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...