Lattice structure on some fuzzy algebraic systems

In this paper, we study the lattice structure of some fuzzy algebraic systems such as (G-)fuzzy groups, some fuzzy ordered algebras and fuzzy hyperstructures. We prove that under suitable conditions, these structures form a distributive or modular lattice. This research partially is supported by the “ Fuzzy Systems and its Applications Center of Excelence, Shahid Bahonar University of Kerman, Iran”.     

基于量子克隆的二面体群隐含子群问题量子算法的研究

基于最短向量问题的格公钥密码体制是典型的抗量子计算密码体制。格的唯一最短向量问题可转化为二面体群的隐含子群问题。有效地求解二面体群的隐含子群问题可攻破基于格的唯一最短向量问题的公钥密码体制。Kuperberg提出了二面体群隐含子群问题的半指数级量子算法。通过研究Kuperberg量子算法,利用概率量子克隆,文中提出了二面体群隐含子群问题的多项式时间量子算法。     

基于结构聚类的图像去噪

为了克服传统BM3D去噪算法的不足,根据图像局部结构相似性提出了基于结构聚类的图像去噪算法。首先根据均值进行粗聚类构成块群;其次利用鲁棒数据归一化构造结构相似子群;最后对子群进行去噪,如果子群容量大于1,运用BM3D对该子群进行去噪处理,反之,运用基于阈值的DCT去噪算法对该块进行去噪。实验结果表明,该算法保护了图像的结构信息,相对于传统BM3D算法提高了图像的视觉效果。     

基于优化GDH协商的高效安全群组密钥管理方案

针对GDH(group diffie-hellman)方案中节点可能成为系统的瓶颈以及计算复杂度、通信代价和存储复杂度远高于某些集中式方案等缺陷,提出并实现了一种基于优化GDH协商的高效安全的动态群组密钥管理方案,并对其安全性进行了证明。通过对计算量和通信量进行分析比较表明,优化GDH协商协议具有很大的优势,并且能够快速产生或更新组密钥,具有很强的实用性。     

A note on quantum related-key attacks

In a basic related-key attack against a block cipher, the adversary has access to encryptions under keys that differ from the target key by bit-flips. In this short note we show that for a quantum adversary such attacks are quite powerful: if the secret key is (i) uniquely determined by a small number of plaintext–ciphertext pairs, (ii) the block cipher can be evaluated efficiently, and (iii) a superposition of related keys can be queried, then the key can be extracted efficiently.     

Preferential normal fuzzy subgroups

In this paper we consider the notion of normality on preferential fuzzy subgroups of a finite group G and define the associated concept of a normal pinned-flag. We discuss the preferential equality of quotients and products of normal preferential fuzzy subgroups. Further normalizers of fuzzy subgroups under preferential equality are briefly dealt with. Examples are given to illustrate the structure of preferential normal fuzzy subgroups and normal pinned-flags.     

适于社会网络结构分析与可视化的布局算法

力导引布局算法是社会网络信息可视化领域的主流布局算法,但却在结构分析显示方面存在缺陷.产生的图像经常是节点聚集在屏幕中央,难以分辨结构信息.因此,提出了子群分析布局SAL(subgroup analysis layout)算法来解决这一问题.该算法通过角色分析和关键属性分析,对社会网络中的子群进行划分与分析,然后根据子群分析结果对力导引布局算法加以改进,包括2D和3D可视化.以对恐怖组织信息进行分析作为实例,也验证了SAL算法在社会网络结构分析与显示方面具有一定的优越性.     

Is Grover’s Algorithm a Quantum Hidden Subgroup Algorithm?

The arguments given in this paper suggest that Grover’s and Shor’s algorithms are more closely related than one might at first expect. Specifically, we show that Grover’s algorithm can be viewed as a quantum algorithm which solves a non-abelian hidden subgroup problem (HSP). But we then go on to show that the standard non-abelian quantum hidden subgroup (QHS) algorithm can not find a solution to this particular HSP. This leaves open the question as to whether or not there is some modification of the standard non-abelian QHS algorithm which is equivalent to Grover’s algorithm.      

基于椭圆曲线的KDM安全公钥加密方案

某些场合下敌手能够获取与私钥有关消息的密文,大多现有加密方案在上述情况下是不安全的。为抵抗这种攻击,给出一般子群不可区分困难假设的一个实例——椭圆曲线子群不可区分困难假设,并设计相应的归约算法。在此基础上,提出一个基于环 上椭圆曲线的公钥加密方案,并将该方案中的密文不可区分问题归约到椭圆曲线子群不可区分困难的假设上。分析结果证明,该方案在此假设下是安全的。     

基于多尺度并行免疫克隆优化聚类算法

针对无监督分类问题,提出一种多尺度并行免疫克隆优化聚类算法.算法中,进化在多个子群之间并行进行,不同子群的抗体根据子群适应度采用不同变异尺度.进化初期,利用大尺度变异子群实现全局最优解空间的快速定位,同时变异尺度随着适应值的提升逐渐降低;进化后期,利用小尺度变异子群完成局部解空间的精确搜索.将新算法与其他聚类算法进行比较,所得结果表明新算法具有较好的聚类性能和鲁棒性.