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» Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
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CHES
2004
Springer
148views Cryptology» more  CHES 2004»
13 years 10 months ago
Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations
We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups,...
Roberto Maria Avanzi
PAIRING
2010
Springer
147views Cryptology» more  PAIRING 2010»
13 years 3 months ago
Generating More Kawazoe-Takahashi Genus 2 Pairing-Friendly Hyperelliptic Curves
Constructing pairing-friendly hyperelliptic curves with small ρ-values is one of challenges for practicability of pairing-friendly hyperelliptic curves. In this paper, we describe...
Ezekiel J. Kachisa
ITCC
2005
IEEE
13 years 11 months ago
Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves and Its Implementations
Recently, a lot of effort has been done to investigate all kinds of explicit formulae for speeding up group operation of hyperelliptic curve cryptosystem (HECC). In this paper, ex...
Xinxin Fan, Thomas J. Wollinger, Yumin Wang
WAIFI
2007
Springer
121views Mathematics» more  WAIFI 2007»
13 years 11 months ago
Explicit Formulas for Real Hyperelliptic Curves of Genus 2 in Affine Representation
Stefan Erickson, Michael J. Jacobson Jr., Ning Sha...
MOC
2010
13 years 1 days ago
Factorization with genus 2 curves
The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower...
Romain Cosset