搜索结果: 1-15 共查到“Jacobians”相关记录28条 . 查询时间(0.078 秒)
Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers
Hyperelliptic curve cryptography Kummer surface genus 2
2016/12/10
We give one- and two-dimensional scalar multiplication algorithms for Jacobians of genus~2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudomult...
Given a CM sextic field K, we give an explicit method for finding and constructing all genus 3 hyperelliptic curves whose Jacobians have complex multiplication by the maximal order of this field. Our ...
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
elliptic curve cryptography hyperelliptic curve cryptography scalar multiplication
2015/12/22
We give a general framework for uniform, constant-time oneand
two-dimensional scalar multiplication algorithms for elliptic curves
and Jacobians of genus 2 curves that operate by projecting to the x...
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
Elliptic curve cryptography number theory
2014/3/6
The first step in elliptic curve scalar multiplication algorithms based on scalar decompositions using efficient endomorphisms---including Gallant--Lambert--Vanstone (GLV) and Galbraith--Lin--Scott (G...
Jacobians of singular matrix transformations: Extensions
Jacobians Hausdorff measure real, complex, quaternion and octonion singular random ma-trices real normed division algebras.
2012/9/19
This article presents a unified approach to simultaneously compute the Jacobians of several singular matrix transformations in the real, complex, quaternion and octonion cases. Formally, these Jacobia...
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Pairing-based algorithms jacobians of genus 2 curves maximal endomorphism ring Number Theory
2012/4/17
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a ge...
Group Law Computations on Jacobians of Hyperelliptic Curves
Hyperelliptic curves group law Jacobian arithmetic genus 2
2012/3/28
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 geometric description o...
Geometric Group Law Computations on Jacobians of Hyperelliptic Curves
foundations Hyperelliptic curves group law Jacobian arithmetic genus 2
2011/7/25
We derive a new method of computing the composition step in Cantor's algorithm for group operations on Jacobians of hyperelliptic curves.
The Local Structure of Compactified Jacobians: Deformation Theory
Compactified Jacobian compactified Picard scheme nodal curve torsion-free sheaf
2011/9/16
Abstract: This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the completed local ri...
Computing $(\ell,\ell)$-isogenies in polynomial time on Jacobians of genus~$2$ curves
public-key cryptography / elliptic curve cryptosystem
2012/3/29
In this paper, we compute $\ell$-isogenies between abelian varieties over a field of characteristic different from $2$ in polynomial time in $\ell$, when $\ell$ is an odd prime which is coprime to the...
Short loop decompositions of surfaces and the geometry of Jacobians
Short loop decompositions the geometry of Jacobians
2010/11/19
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directi...
Families of explicitly isogenous Jacobians of variable-separated curves
Families of explicitly isogenous Jacobians variable-separated curves
2010/12/1
We construct six infinite series of families of pairs of curves (X, Y )of arbitrarily high genus, defined over number fields, together with an explicit isogeny JX ! JY splitting multiplication by 2, 3...
We study Esteves’s fine compactified Jacobians for nodal curves. We give a proof of the fact that, for a one-parameter regular local smoothing of a nodal curve X.
GENERATORS OF JACOBIANS OF GENUS TWO CURVES
Jacobians genus two curves Frobenius endomorphism
2009/6/2
We prove that in most cases relevant to cryptography, the Frobenius
endomorphism on the Jacobian of a genus two curve is represented
by a diagonal matrix with respect to an appropriate basis of the ...
NON-CYCLIC SUBGROUPS OF JACOBIANS OF GENUS TWO CURVES
Jacobians hyperelliptic genus two curves pairings
2009/6/2
Let E be an elliptic curve de ned over a nite eld. Balasubramanian
and Koblitz have proved that if the `th roots of unity ` is not contained
in the ground eld, then a eld extension of the groun...