超椭圆曲线

明文信息嵌入到超椭圆曲线HEC的除子，是该密码体制的一个重要的工作。

Plaintext imbedded into the divisors of a hyperelliptic curve is a key work in HEC C.

基于FPI的超椭圆曲线密码体制的研究

Research on Hyperelliptic Curve Cryptosystem Based on FPI

超椭圆曲线离散对数的WeilDescent代数攻击的分析

An analysis of Weil Descent algebraic attack on the hyperelliptic curves discrete logarithm

超椭圆曲线密码体制所基于的除子类群，又称Jacobian群，其结构与运算比有理点群要复杂得多。

The divisor class group , often called Jacobian group , based on which hyperelliptic curve cryptosystems are constructed , is much complicated than the elliptic curve rational point group .

本文基于代数方法阐述了HCC有关数学理论，给出关于一条超椭圆曲线的Jacobian求阶算法及其实例证明。

The maths theory of hyperelliptic curves cryptosystem ( HCC ) is expatiated in this article while the arithmetic of HCC Jacobian addition is also set forth , and its correctness is proved by examples .

但由于可以在一个很小的基域上构造具有较大素数因子阶的Jacobian群，且可应用于密码体制的超椭圆曲线比较丰富，这使得超椭圆曲线密码体制也逐渐受到人们的重视。

Since the order of a Jacobian group can be constructed to have a much large prime factor over a small base field , and there exist a lot of hyperelliptic curves suitable for cryptographical applications , hyperelliptic curve cryptosystems has gotten much attention more and more .

超椭圆曲线特性及其在曲面拟合中的应用

Characteristics of super-ellipse and survey for its applications in surface fitting

一类超椭圆曲线的整点个数

The Number of Integral Points on a Class of Hyperelliptic Curves

利用有效的求逆算法快速计算超椭圆曲线标量乘

Scalar multiplication of hyperelliptic curves with the efficient algorithm for inversion

超椭圆曲线可控代理签名方案的研究

The Study on Xiao 's Hyperelliptic Curve Limited Proxy Signature Scheme

在此基础上，综述目前国内外对超椭圆曲线在现代工业设计以及其发展上的应用。

Survey of its applications and development in industrial designed are presented .

除子标量乘是超椭圆曲线密码体制中的关键运算。

Divisor scalar multiplication is the key operation in hyperelliptic curve cryptosystem .

素数域上亏格为3的超椭圆曲线快速算法

Fast Arithmetic of Genus 3 Hyperelliptic Curves over Prime Fields

一种快速的明文信息嵌入超椭圆曲线除子的方法

A Method of High-speed Imbedding Plaintext into Divisor of a Hyperelliptic Curve

基于超椭圆曲线密码体制的门限签名方案

A Threshold Signature Scheme Based on Hyperelliptic Curve Cryptosystem

亏格为3的超椭圆曲线除子类群的计算公式

Formulae for Arithmetic on Genus 3 Hyperelliptic Curves

一个基于超椭圆曲线的单向数字签名

A Directed Digital Signature Based on HECC

在实现超椭圆曲线密码体制中起关键作用的运算是除子标量乘，一般采用的方法是二元法及其各种改进的二元法。

The general methods applied for computing divisor scalar multiplications are Binary method and its improved versions .

该文基于超椭圆曲线密码体制提出了一个单向签名方案，并分析了其安全性。

A directed digital signature based on hyper elliptic curve cryptosystems was proposed and the security was discussed .

介绍了椭圆曲线密码和超椭圆曲线密码算法中一个重要的模块&求逆模块。

Finite field inversion , an important module of elliptic curve cryptosystems and hyper-elliptic curve cryptosystems , is introduced .

关于椭圆型问题的多子域重叠型区域分解算法亏格为3的超椭圆曲线除子类群的计算公式

On the overlapping domain decomposition methods for elliptic problems in multi-subdomain case Formulae for Arithmetic on Genus 3 Hyperelliptic Curves

利用超椭圆曲线上的双线性对构造广播加密和解密算法，节省了广播通信传输带宽。

The bilinear paring on a super-elliptic curve was used to construct the broadcast encryption and decryption algorithms , which greatly saves the broadcasting communication transmission bandwidth .

结果表明，本文的工作使超椭圆曲线密码的执行效率和协议的安全性在一定程度上得到了提高。

The experiment shows that the efficiency and security of the hyperelliptic curve cryptography are improved in a certain extent because of the contribution of this paper .

超椭圆曲线密码体制是以超椭圆曲线离散对数问题的难解性为基础的，具有安全性高、操作数短等优点，相对于其他密码体制有明显的优势。

The hyperelliptic curve cryptosystem is based on the hyperelliptic curve discrete logarithm problem , and has the higher safety and the shorter operands compared to other cryptosystems .

建立有限域上安全超椭圆曲线密码体制的基础是构造有限域上安全的超椭圆曲线，因而应当首先选择适于建立密码体制的超椭圆曲线。

The basis of building secure hyperelliptic curve cryptosystems is constructing secure hyperelliptic curve over finite field , therefore firstly must select an hyperelliptic curve suitable to build cryptosystem .

利用查表法对基于特殊超椭圆曲线上有效自同态的标量乘算法进行了改进，分析了改进算法的时间与空间复杂度。

Using the look-up tables , the scalar multiplication algorithm based on efficient computable endomorphisms on special hyperelliptic curves is improved . Time and space complexity of improved algorithms are analyzed .

分析了现有公平离线电子现金方案的不足，提出了一类基于超椭圆曲线密码的可追踪公平离线电子现金方案；

Analyses are made on the security threats of present E-cash schemes , and a traceable faire E-cash scheme based on hyper-elliptic curves cryptosystem that can gain a wide application in computer and wireless communication network is presented .

基于椭圆曲线密码体制，通过对椭圆曲线上标量乘的分析，提出了在GF（2m）域上实现非超异椭圆曲线的标量乘的一种快速算法，并对参数m的选取进行了分析。

An algorithm is presented which speeds scalar multiplication on non-super singular elliptic curve defined over GF ( 2 m ) .

最后以密码学实践中常用到的超奇异椭圆曲线为例，构造了Weil对和Tate对的BDH参数生成器。

Finally , BDH parameter generators using Weil pairing and Tate pairing on supersingular elliptic curves were constructed . The generators could be widely applied to identity-based cryptography .

两类超奇异椭圆曲线的快速标量乘法

Fast Scalar Multiplication on Two Family of Supersingular Elliptic Curve