搜索结果: 1-15 共查到“密码学 Jacobian”相关记录16条 . 查询时间(0.015 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...
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...
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...
Co-Z Divisor Addition Formulae in Jacobian of Genius 2 Hyperelliptic Curves over Prime Fields
hyperelliptic curve divisor Jacobian addition formulae exponentiation projective representation
2010/9/29
In this paper we proposed a new approach to divisor scalar multiplication in Jacobian of genus 2 hyperelliptic curves over fields with odd characteristic, without field inversion. It based on improved...
Improvement of Th´eriault Algorithm of Index Calculus for Jacobian of Hyperelliptic Curves of Small Genus
calculus attack Jacobian Hyperelliptic curve
2009/3/27
Gaudry present a variation of index calculus attack for solving the
DLP in the Jacobian of hyperelliptic curves. Harley and Th´erialut
improve these kind of algorithm. Here, we will present a ...
ON THE SECURITY OF GENERALIZED JACOBIAN CRYPTOSYSTEMS
semi-abelian varieties elliptic curves pairing-friendly curve
2008/12/19
Generalized Jacobians are natural candidates to use in discrete
logarithm (DL) based cryptography since they include the multiplicative group
of …nite …elds, algebraic tori, elliptic curve...