Sciweavers

Share
IACR
2011
124views more  IACR 2011»
7 years 10 months ago
Group Law Computations on Jacobians of Hyperelliptic Curves
We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the g...
Craig Costello, Kristin Lauter
MOC
2010
8 years 5 months 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
PAIRING
2010
Springer
147views Cryptology» more  PAIRING 2010»
8 years 8 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
AAECC
2005
Springer
99views Algorithms» more  AAECC 2005»
8 years 10 months ago
Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
The ideal class group of hyperelliptic curves can be used in cryptosystems based on the discrete logarithm problem. In this article we present explicit formulae to perform the gro...
Tanja Lange
IEICET
2008
126views more  IEICET 2008»
8 years 10 months ago
Skew-Frobenius Maps on Hyperelliptic Curves
The hyperelliptic curve cryptosystems take most of the time for computing a scalar multiplication kD of an element D in the Jacobian JC of a hyperelliptic curve C for an integer k....
Shunji Kozaki, Kazuto Matsuo, Yasutomo Shimbara
FOCM
2008
76views more  FOCM 2008»
8 years 10 months ago
Point Counting in Families of Hyperelliptic Curves
Let
Hendrik Hubrechts
AAECC
2007
Springer
88views Algorithms» more  AAECC 2007»
8 years 10 months ago
Hyperelliptic curves with reduced automorphism group A5
We study genus g hyperelliptic curves with reduced automorphism group A5 and give equations y2 = f(x) for such curves in both cases where f(x) is a decomposable polynomial in x2 or...
David Sevilla, Tanush Shaska
ISSAC
1995
Springer
174views Mathematics» more  ISSAC 1995»
9 years 1 months ago
Numerical Uniformization of Hyperelliptic Curves
Abstract. In this paper we derive an algorithm that computes, for a given algebraic hyperelliptic plane curve C of genus p, p > 1, defined by a polynomial y2 = (x−λ1) · · ...
Klaus-Dieter Semmler, Mika Seppälä
EUROCRYPT
2000
Springer
9 years 1 months ago
An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves
We present an index-calculus algorithm for the computation of discrete logarithms in the Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that i...
Pierrick Gaudry
EUROCRYPT
1999
Springer
9 years 2 months ago
On the Performance of Hyperelliptic Cryptosystems
In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to genera...
Nigel P. Smart
books