双线性的

We describe the algebraic characteristic of the public-key cryptosystems based on algebraic structures such as elliptic curves,bilinear pairings,as well as braid group s,with the emphasis on the difficulties of constructing public-key cryptosystems based on non-commutative algebraic structures.

通过分析基于椭圆曲线、双线性对以及基于辫子群的公钥密码体制的代数学特征，着重讨论了构建基于非交换代数的公钥密码体制所面临的困难。

It belongs the kind of complex bridges because its liner changes usually and the weight condition is also complex, except bear moment and shearing force, there are larger torsion and doubled moment, as a result, crankle、warping and aberration would happen.

这种异形桥梁结构是受力很复杂的一种桥型，其线性变化多端，结构受力复杂，除承受弯距、剪力外，还有较大扭矩和翘曲双力矩的作用，即使外荷载的作用通过梁的剪切中心，也将发生弯扭组合变形，同时伴随有截面的翘曲和畸变。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

Bilinear quadrangular with reduced-dimension effect is used to simulate the real surface of the complex object, and a new hybrid basis function based on this quadrangular is presented.

采用具有降维效果的双线性四边形模型来模拟实际物体表面，提出了一种基于该四边形的混合域基函数，应用于金属物体的电磁散射特性的计算仿真中。

In this paper,we construct the transitive signature scheme based on bilinear pairings over elliptic curves or super elliptic curves,If one-more CDH problem is hard and standard signature scheme is unforgeable under adaptive chosen-message attack,our scheme is transitively unforgeable under adaptive chosen-message attack.

构造了基于椭圆曲线或超椭圆曲线上双线性对的可传递签名方案，并且证明了在one—more CDH问题是难的和标准签名方案是自适应选择信息攻击下不可伪造的条件下，该文的可传递签名是在自适应选择信息攻击下不可伪造的。

The main contributions are as follows:(1) The decoherence suppression of N level Markovian systems is investigatedby the optimal control in the coherence vector representation. The N level Markoviansystem can be described by the master equation, and possesses a standard bilinear formin the coherence vector representation.

本论文利用密度矩阵相干向量表示研究了退相干效应的抑制和相应的纠缠控制问题，论文主要工作包括：(1)在密度矩阵相干向量表示下，利用最优控制研究N能级Markov系统的退相干抑制问题。N能级Markov系统可以用主方程模型描述，在相干向量表示下具有标准的双线性形式。

At last ,this pater prove that the Coxeter mat rix of A has a composition of the fundamental reflections with the condition that Q has no oriented cycles.

然后利用A 的Cartan 矩阵和对称双线性型定义了A 的基本反射，并利用数学归纳法证明了在Q 无有向圈的条件下， A 的Coxeter 矩阵可分解为基本反射的乘积。

However, the situation has changed after Joux gave a simple tripartite one-round Diffie-Hellman key agreement protocol based on Weil pairing on supersingular curves.

然而，2000年Joux利用超奇异椭圆曲线上的Weil对构造了一个一轮三方密钥协商协议，这可以说是密钥协商协议中的重大突破之一。2001年Boneh等又利用双线性对设计出了实用的基于身份的加密方案和短签名方案。

If the doubly Horn formulas are dense, i. e. the average size of each clause is Θ, this algorithm runs in linear time.

若双Horn公式同时还是稠密的，即每个子句的平均长度为Θ，则该算法的时间复杂性是线性的。

On the basis of the ID-based signature schemes, this paper presents a proxy blind signature scheme using bilinear parings, which satisfies the security properties of both the proxy signature scheme and the blind signature.

文章结合两者的优点，利用椭圆曲线上的Weil对的双线性性，构造了一个基于身份的代理盲签名方案。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新