RSA—概率公钥密码体制

提出一种新的公钥体制：ＴＳＡ－概率公钥密码体制，新体制克服了Ｇｏｌｄｗａｓｅｒ的概率加密体制可被系统内主动窃听者破译和不具备数字签名的弱点，使概率加密体制更加完善。     

RSA－概率公钥密码体制

提出一种新的公钥体制：ＲＳＡ－概率公钥密码体制。新体制克服了Ｇｏｌｄｗａｓｓｅｒ的概率加密体制可被系统内主动窃听者破译和不具备数字签名的弱点，使概率加密体制更加完善。     

椭圆曲线密码体制安全性研究

分析了椭圆曲线密码体制的安全性基础以及常见的攻击方法。考虑到目前还没有有效的方法可以求解有限域上阶中含有大素因子的非超奇异椭圆曲线的离散对数问题,指出高安全性的椭圆曲线密码体制可以靠选择有限域上高安全性的椭圆曲线来获得。给出了适于构建密码体制的椭圆曲线的构造方法,利用这种方法构造出来的椭圆曲线是安全的,可以抵御现有的各种攻击方法。     

基于二次剩余的密钥体制的构造

为了避免确定性的公钥密码体制容易遭受选择明文攻击的问题,文中以大数因数分解的困难性和模Blum数的二次剩余求平方根的不易性为理论基础,引入随机数,构造了一种以二次剩余为基础的多项式加密密钥体制.该密码体制的密码强度不低于RSA公钥密码体制的密码强度,可以有效地抵挡来自选择明文的攻击,安全性较高.它的密文膨胀率不高于Bl...     

RSA密码体制安全性分析

对RSA公钥套码体制进行了分析，在指出其安全漏洞的同时，对RSA实现的协议进行了分析，而且克服了它们潜在的破译问题，这对增强RSA密码体制安全性有着十分重要的意义．     

关于二次剩余与原根的关系

设P为奇素数,主要研究了模P的任一二次剩余和二次非剩余与模P原根之间的相互关系,得出了一个非常有趣的结论：即模P的任何一个二次剩余都可以表示成模P的两个原根之积;任何一个二次非剩余都可以表示成模P的三个原根之积。     

RSA公开密钥密码体制的密钥生成研究

介绍了密钥生成的一般方法,即确定性素数产生和概率性素数产生方法,并给出了利用ＭｉｌｌｅｒＲａｂｉｎ测试和Ｐｏｃｋｌｉｎｇｔｏｎ定理生成强伪素数的算法实现。     

关于密码体制的完善保密性

在密码体制和完善保密性定义的基础上,利用概率统计与信息论等工具,从不同的视角,给出并证明了一般密码体制完善保密性的3个充分条件和1个充要条件.其结果将有助于推广保密系统的通信理论及密码体制的设计和应用.     

关于二次剩余与原根的关系

设P为奇素数 ,主要研究了模P的任一二次剩余和二次非剩余与模P原根之间的相互关系 ,得出了一个非常有趣的结论 :即模P的任何一个二次剩余都可以表示成模P的两个原根之积 ;任何一个二次非剩余都可以表示成模P的三个原根之积     

背包密码体制中求解逆元的探讨

背包密码体制是基于组合学中的背包问题所设计的密码系统,属于公开密钥密码体制。它是将一个超递增序列转换为一个一般序列,这个一般序列作为加密密钥给予公开,任何人都可以使用它对明文进行加密,超递增序列作为保密的解密密钥,只有接收者知道,接收者利用解密密钥很容易地将密文还原成明文。然而．由一般序列转换为超递增序列的转换过程是严加保密的,对非正当接收者来说其转换过程是相当困难的。转换过程中的关键是求解逆元,也就是背包体制的保密性所在。本文就是对求解逆元中的问题进行探讨,使得更容易求解。     

Threshold signature scheme based on discrete logarithm and quadratic residue

Digital signature scheme is a very important research field in computer security and modern cryptography. A(k,n) threshold digital signature scheme is proposed by integrating digital signature scheme with Shamir secret sharing scheme. It can realize group-oriented digital signature, and its security is based on the difficulty in computing discrete logarithm and quadratic residue on some special conditions. In this scheme, effective digital signature can not he generatedby any h 1 or fewer legal users, or only by signature executive. In addition, this scheme can identify any legal user who presents incorrect partial digital signature to disrupt correct signature, or any illegal user who forges digital signature. A method of extending this scheme to an Abelian group such as elliptical curve group is also discussed. The extended scheme can provide rapider computing speed and stronger security in the case of using shorter key.     

Distribution of Random Session Key Based on Key-insulated Public-Key Cryptosystems

Based on the characteristic of key-insulated puhtic-key cryptosystem, we propose a distributed random session keys distribution protocol without a key distribution center. The session key is generated by different user and only used one time. So the key is one-time key. In addition, the user who generates the next one-time key, is random selected by the current session key. In the protocol of this paper, thecharacteristic of time in the key-insulated public-key, a dis-tributed protocol, translates into the characteristic of space which every point has different secret key in the different period. At the same time, the system is fit for key management in Ad Hoc, and is a new scheme of key management in Ad Hoc.     

Identity-based ring signature scheme based on quadratic residues

Identity-based (ID-based) ring signature has drawn great concerns in recent years and many ID-based ring signature schemes have been proposed until now. Unfortunately, all of these ID-based ring signatures are constructed from bilinear pairings, a powerful but computationally expensive primitive. Hence, ID-based ring signature without pairing is of great interest in the field of cryptography. In this paper, the authors firstly propose an ID-based ring signature scheme based on quadratic residues. The proposed scheme is proved to be existentially unforgeable against adaptive chosen message-and-identity attack under the random oracle model, assuming the hardness of factoring. The proposed scheme is more efficient than those which are constructed from bilinear pairings.     

带有二次约束二次规划问题的全局最优化

根据带有二次约束二次规划模型的特殊结构,利用乘积的凸包络和凹包络,给出带有二次约束二次规划问题的松弛线性规划问题,以确定全局最优值的下界,使用超矩形缩减技术以加快分支定界算法的收敛速度,从而提出一个求解带有二次约束二次规划问题的全局最优化算法,证明该算法的收敛性,这个新算法实际上是把分支定界方法与外逼近方法有机地结合起来.数值算例表明所提出的算法是可行的.     

2次奇摄动Robin问题的不动点原理解法

文章利用不同量级的伸长变量,对2次奇摄动Robin问题构造了形式上的m阶渐近解及齐次边界条件,在该条件下,证明了双射条件和利普希茨条件,从而利用不动点原理证明了Robin问题解的存在性与惟一性,在运用不动点定理验证解的存在性时,对边界条件构造齐次边界时运用了2次变换.     

带有二次约束的二次规划问题的一个收缩分枝定界算法

通过解线性规划问题,寻找包含原问题可行域的超矩形,利用剖分技术对这个超矩形进行分枝和收缩以减少算法的迭代次数,从而用线性规划松弛方法来确定原问题在每个小超矩形上的最优值的下界,提出一种新的带有二次约束的二次规划问题的收缩分枝定界算法,并证明了该算法是收敛的．     

Cycling attacks against homomorphic cryptosystems

We study security of some homomorphic cryptosysterns with similar algebraic structure. It is found out that those cryptosystems have special common properties. Based on these properties, we pose two cycling attacks and point out some parameters under which the attacks are efficient. It is verified that randomly selected parameters almost impossibly submit to such attacks. Anyhow, two effective methods are given to construct weak parameters for certain homomorphic cryptosystems, and two moduli over 1 024 bits computed by them are shown to be vulnerable to our cycling attacks. It is concluded that strong primes should be used to avert weak parameters.     

基于最优扩域上的椭圆曲线密码系统的基点选取

本文讨论了重模二次剩余的定义、性质，完整地设计出选取最优扩域上的椭圆曲线密码系统的基点的算法，并给出了选取成功的概率和相关数学证明．     

Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem

The homogeneous quadratic Riemann boundary value problem (1) with Hoelder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained.