搜索结果: 1-15 共查到“Jacobian”相关记录33条 . 查询时间(0.109 秒)
We construct a genus 2 curve inside the product of 2 elliptic curves. The formula for this construction has appeared in a previous paper. The current paper discusses how this formula arises naturally ...
Reduced Mumford divisors of a genus 2 curve through its jacobian function field
hyperelliptic Mumford arithmetic
2017/2/20
We explore the function field of the jacobian JH of a hyperelliptic curve H of genus 2 in order to find reduced coordinates to represent points of JH and do arithmetic. We show how this relates to the...
Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus 2 using base field operations
public-key cryptography hyperelliptic curves
2016/1/9
We present an efficient endomorphism for the Jacobian of a curve C of genus 2 for divisors having a Non
disjoint support. This extends the work of Costello in [12] who calculated explicit formul?for ...
This paper presents a new projective coordinate system and new explicit
algorithms which together boost the speed of arithmetic in the divisor class group of
genus 2 curves. The proposed formulas ge...
A New Method for Decomposition in the Jacobian of Small Genus Hyperelliptic Curves
Discrete Log Index calculus Hyperelliptic curve
2016/1/6
Decomposing a divisor over a suitable factor basis in the Jacobian of a hyperelliptic
curve is a crucial step in an index calculus algorithm for the discrete log problem in the
Jacobian. For small g...
Double-and-Add with Relative Jacobian Coordinates
elliptic curve relative Jacobian coordinates co-Z coordinates
2016/1/5
One of the most efficient ways to implement a scalar multiplication on elliptic
curves with precomputed points is to use mixed coordinates (affine and Jacobian).
We show how to relax these precondit...
AN EXPLICIT JACOBIAN OF DIMENSION 3 WITH MAXIMAL GALOIS ACTION
EXPLICIT JACOBIAN DIMENSION 3 MAXIMAL GALOIS ACTION
2015/8/26
We gives an explicit genus 3 curve over Q such that the Galois action on the torsion points of its Jacobian is a large as possible. That such curves exist is a consequence of a theorem of D. Zureick-B...
We give an algorithm for decomposing given element of Jacobian gruop into the sum of the decomposed factor, which consists of certain subset of the points of curve.
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation
2012/6/14
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation Ordinary Curves Pairing-Friendly Constructions Cocks-Pinch Method Brezing-Weng Method.
2012/3/22
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...
Genus 2 Hyperelliptic Curve Families with Explicit Jacobian Order Evaluation and Pairing-Friendly Constructions
public-key cryptography / Hyperelliptic Curves Genus 2 Order Computation Ordinary Curves Pairing-Friendly Constructions Cocks-Pinch Method Brezing-Weng Method.
2012/3/21
The use of (hyper)elliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test wheth...
Separation of Comprehensive Geometrical Errors of a 3-DoF Parallel Manipulator Based on Jacobian Matrix and its Sensitivity Analysis with Monte-Carlo Method
parallel kinematic machines (PKMs) limited-degree-of-freedom (limited-DoF) error separation
2011/8/4
Parallel kinematic machines (PKMs) have the advantages of a compact structure, high stiffness, a low moving inertia, and a high load/weight ratio. PKMs have been intensively studied since the 1980s, a...
Computing Discrete Logarithms in the Jacobian of High-Genus Hyperelliptic Curves over Even Characteristic Finite Fields
Computing Discrete Logarithms High-Genus Hyperelliptic Curves Characteristic Finite Fields
2011/3/10
We describe improved versions of index-calculus algorithms for
solving discrete logarithm problems in Jacobians of high-genus hyperelliptic
curves de ned over even characteristic elds. Our rst imp...
Computing Discrete Logarithms in the Jacobian of High-Genus Hyperelliptic Curves over Even Characteristic Finite Fields
foundations / hyperelliptic curves discrete logarithm problem sieving, Weil descent
2012/3/29
We describe improved versions of index-calculus algorithms for solving discrete logarithm problems in Jacobians of high-genus hyperelliptic curves defi ned over even characteristic fields. Our first i...
Separation of Comprehensive Geometrical Errors of a 3-DoF Parallel Manipulator Based on Jacobian Matrix and its Sensitivity Analysis with Monte-Carlo Method
parallel kinematic machines (PKMs) limited-degree-of-freedom (limited-DoF)
2011/8/4
Parallel kinematic machines (PKMs) have the advantages of a compact structure, high stiffness, a low moving inertia, and a high load/weight ratio. PKMs have been intensively studied since the 1980s, a...