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The Brezing-Weng-Freeman method for certain genus two hyperelliptic curves
Brezing-Weng-Freeman method elliptic curve hyperelliptic curves
2009/6/12
We construct paring friendly curves of the form Y2 = X5+uX3+vX over large
finite prime fields. The ρ-value of our family is always less than 4. Our
method is based on the fact that, under a certain ...
Generating genus two hyperelliptic curves over large characteristic finite fields
hyperelliptic curve point counting
2009/6/9
In hyperelliptic curve cryptography, finding a suitable hyperelliptic
curve is an important fundamental problem. One of necessary
conditions is that the order of its Jacobian is a product of a large...
Fast explicit formulae for genus 2 hyperelliptic curves using projective coordinates （Updated）
hyperelliptic curves explicit formulae
2009/6/2
This contribution proposes a modification of method of divisors group operation in the Jacobian of hyperelliptic curve over even and odd characteristic fields in projective coordinate. The hyperellipt...
Weighted Coordinates on Genus 2 Hyperelliptic Curves
Weighted Coordinates Genus 2 Hyperelliptic Curves
2009/4/15
Weighted Coordinates on Genus 2 Hyperelliptic Curves.
Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves
Inversion-Free Arithmetic Genus 2 Hyperelliptic Curves
2009/4/15
Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves.
Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae
Efficient Arithmetic Genus 2 Hyperelliptic Curves Explicit Formulae
2009/4/15
We extend the explicit formulae for arithmetic on genus two curves of [13, 21] to fields of even
characteristic and to arbitrary equation of the curve. These formulae can be evaluated faster than the...
Low Cost Security: Explicit Formulae for Genus 4 Hyperelliptic Curves
Low Cost Security Explicit Formulae Genus 4 Hyperelliptic Curves
2009/4/9
Low Cost Security: Explicit Formulae for Genus 4 Hyperelliptic Curves.
Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves
Genus 3 Hyperelliptic Curve Cryptosystem Explicit Formulae Inversion-Free
2009/3/27
Hyperelliptic curve cryptosystem (HECC) is becoming more
and more promising for network security applications because of the common
effort of several academic and industrial organizations. With shor...
Fast computation of Tate pairing on general divisors of genus 3 hyperelliptic curves
Tate pairing hyperelliptic curves divisors resultant pairing-based cryptosystem
2008/11/12
For the Tate pairing computation over hyperelliptic curves, there are developments by Duursma-
Lee and Barreto et al., and those computations are focused on degenerate divisors.
Isogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves
Discrete Logarithm Problem Jacobians of Genus 3 Hyperelliptic Curves
2008/5/22
We describe the use of explicit isogenies to reduce Discrete
Logarithm Problems (DLPs) on Jacobians of hyperelliptic genus 3 curves
to Jacobians of non-hyperelliptic genus 3 curves, which are vulner...