IACR
2011
12 years 4 months ago
2011
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...
MOC
2010
12 years 11 months ago
2010
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...
PAIRING
2010
Springer
13 years 2 months ago
2010
Springer
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...
AAECC
2005
Springer
13 years 4 months ago
2005
Springer
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...
IEICET
2008
13 years 4 months ago
2008
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....
FOCM
2008
13 years 4 months ago
2008
Let
AAECC
2007
Springer
13 years 4 months ago
2007
Springer
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...
ISSAC
1995
Springer
13 years 7 months ago
1995
Springer
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) · · ...
EUROCRYPT
2000
Springer
13 years 8 months ago
2000
Springer
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...
EUROCRYPT
1999
Springer
13 years 8 months ago
1999
Springer
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...