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» Hardware Factorization Based on Elliptic Curve Method
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PKC
2004
Springer
151views Cryptology» more  PKC 2004»
14 years 1 months ago
On the Optimal Parameter Choice for Elliptic Curve Cryptosystems Using Isogeny
The isogeny for elliptic curve cryptosystems was initially used for the efficient improvement of order counting methods. Recently, Smart proposed the countermeasure using isogeny f...
Toru Akishita, Tsuyoshi Takagi
ANTS
2010
Springer
250views Algorithms» more  ANTS 2010»
14 years 15 days ago
A Subexponential Algorithm for Evaluating Large Degree Isogenies
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...
David Jao, Vladimir Soukharev
WAIFI
2010
Springer
160views Mathematics» more  WAIFI 2010»
14 years 15 days ago
Speeding Up Bipartite Modular Multiplication
Abstract. A large set of moduli, for which the speed of bipartite modular multiplication considerably increases, is proposed in this work. By considering state of the art attacks o...
Miroslav Knezevic, Frederik Vercauteren, Ingrid Ve...
PKC
2009
Springer
121views Cryptology» more  PKC 2009»
14 years 9 months ago
Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication
Recently, the new Multibase Non-Adjacent Form (mbNAF) method was introduced and shown to speed up the execution of the scalar multiplication with an efficient use of multiple bases...
Patrick Longa, Catherine H. Gebotys
CHES
2010
Springer
132views Cryptology» more  CHES 2010»
13 years 9 months ago
Efficient Techniques for High-Speed Elliptic Curve Cryptography
In this paper, a thorough bottom-up optimization process (field, point and scalar arithmetic) is used to speed up the computation of elliptic curve point multiplication and report ...
Patrick Longa, Catherine H. Gebotys