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CMA
2010
183views more  CMA 2010»
13 years 1 months ago
Ramanujan's class invariants and their use in elliptic curve cryptography
Complex Multiplication (CM) method is a frequently used method for the generation of elliptic curves (ECs) over a prime field Fp. The most demanding and complex step of this metho...
Elisavet Konstantinou, Aristides Kontogeorgis
EUROCRYPT
2009
Springer
14 years 4 months ago
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
Abstract. Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert-Vanstone (GLV) method. Iijima, Matsuo, Chao and...
Steven D. Galbraith, Xibin Lin, Michael Scott
IACR
2011
113views more  IACR 2011»
12 years 4 months ago
Implementing 4-Dimensional GLV Method on GLS Elliptic Curves with j-Invariant 0
Abstract. The Gallant-Lambert-Vanstone (GLV) method is a very efcient technique for accelerating point multiplication on elliptic curves with eciently computable endomorphisms. G...
Zhi Hu, Patrick Longa, Maozhi Xu
ASIACRYPT
2001
Springer
13 years 8 months ago
Supersingular Curves in Cryptography
Abstract. Frey and R¨uck gave a method to transform the discrete logarithm problem in the divisor class group of a curve over Fq into a discrete logarithm problem in some finite ...
Steven D. Galbraith
PKC
2004
Springer
151views Cryptology» more  PKC 2004»
13 years 9 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