44 search results - page 2 / 9 » Computing in Component Groups of Elliptic Curves |
TIT
2010
13 years 2 days ago
2010
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...
PAIRING
2009
Springer
13 years 12 months ago
2009
Springer
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 ...
JSC
2008
13 years 5 months ago
2008
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...
EUROCRYPT
2001
Springer
13 years 9 months ago
2001
Springer
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...
ANTS
2010
Springer
13 years 9 months ago
2010
Springer
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...