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EUROCRYPT
2009
Springer
14 years 5 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
PKC
2004
Springer
158views Cryptology» more  PKC 2004»
13 years 10 months ago
Faster Scalar Multiplication on Koblitz Curves Combining Point Halving with the Frobenius Endomorphism
Let E be an elliptic curve defined over F2n . The inverse operation of point doubling, called point halving, can be done up to three times as fast as doubling. Some authors have t...
Roberto Maria Avanzi, Mathieu Ciet, Francesco Sica
PAIRING
2010
Springer
133views Cryptology» more  PAIRING 2010»
13 years 2 months ago
Pairing Computation on Elliptic Curves with Efficiently Computable Endomorphism and Small Embedding Degree
Scott uses an efficiently computable isomorphism in order to optimize pairing computation on a particular class of curves with embedding degree 2. He points out that pairing implem...
Sorina Ionica, Antoine Joux
ANTS
2010
Springer
250views Algorithms» more  ANTS 2010»
13 years 8 months 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
PAIRING
2009
Springer
111views Cryptology» more  PAIRING 2009»
13 years 11 months ago
Faster Pairings on Special Weierstrass Curves
This paper presents efficient formulas for computing cryptographic pairings on the curve y2 = cx3 + 1 over fields of large characteristic. We provide examples of pairing-friendly...
Craig Costello, Hüseyin Hisil, Colin Boyd, Ju...