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» Supersingular Elliptic Curves in Cryptography
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PKC
1998
Springer
95views Cryptology» more  PKC 1998»
15 years 3 months ago
Overview of Elliptic Curve Cryptography
In this article, we look at the elliptic curve cryptography, which is believed to be one of the most promising candidates for the next generation cryptographic tool. The following ...
Kiyomichi Araki, Takakazu Satoh, Shinji Miura
ANTS
2004
Springer
114views Algorithms» more  ANTS 2004»
15 years 5 months ago
Montgomery Scalar Multiplication for Genus 2 Curves
Using powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for scalar multiplication to the jacobian of these curves. Previously this metho...
Sylvain Duquesne
IMA
2007
Springer
94views Cryptology» more  IMA 2007»
15 years 5 months ago
Optimised Versions of the Ate and Twisted Ate Pairings
The Ate pairing and the twisted Ate pairing for ordinary elliptic curves which are generalizations of the ηT pairing for supersingular curves have previously been proposed. It is ...
Seiichi Matsuda, Naoki Kanayama, Florian Hess, Eij...
EUROCRYPT
2003
Springer
15 years 4 months ago
Improved Algorithms for Efficient Arithmetic on Elliptic Curves Using Fast Endomorphisms
Mathieu Ciet, Tanja Lange, Francesco Sica, Jean-Ja...
IEICET
2008
147views more  IEICET 2008»
14 years 11 months ago
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k = 9 or curves w...
Xibin Lin, Changan Zhao, Fangguo Zhang, Yanming Wa...