Separable reversible data hiding in encrypted image based on pixel value ordering and additive homomorphism

This work proposes a separable reversible data hiding scheme in encrypted images based on pixel value ordering (PVO). After the original image is encrypted using homomorphism encryption by the content owner, the data hider embeds the secret data in encrypted domain. The PVO strategy realizes hiding data in each block. Additive homomorphism guarantees the performance of PVO in encrypted domain is close to that in plain domain. Besides, the homomorphism encryption does not cause data expansion, and the payload can be further improved. With the watermarked encrypted image, if the receiver has only the data hiding key, he can extract the additional data. If the receiver has only the encryption key, he can obtain a decrypted image similar to the original one. If the receiver has both the data hiding key and the encryption key, he can extract the additional data without any error and recover the original image losslessly.     

SF6断路器气体泄漏红外图像中散斑噪声的抑制算法

SF6断路器是电力系统中常见的电气设备,针对SF6断路器气体泄漏红外图像中广泛存在的激光散斑噪声,提出一种抑制散斑噪声的新算法.将同态均值滤波与小波变换结合,并应用贝叶斯软阈值,对红外图像进行去噪处理.研究中,将该算法与同态均值滤波、同态均值滤波与传统周定小波阈值结合滤波等算法作了比较,结果表明,在图像标准偏差、信噪比和散斑指数等常用性能指标上所提算法优于其他算法.     

Generalized lower and upper approximations in a ring

In this paper, the concepts of set-valued homomorphism and strong set-valued homomorphism of a ring are introduced, and related properties are investigated. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximation of a ring, are provided. We also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by Davvaz [B. Davvaz, Roughness in rings, Information Science 164 (2004) 147-163] in a ring and discuss some significant properties of them.     

群作用轨道及其应用

运用群作用与同态刻划了群作用之轨道，轨道数与群阶数之间的关系，群与它可迁作用正规子群共轭子群之关系及其作用。     

基于隐私同态数据融合的完整性验证协议

在无线传感器网络中的安全数据融合能够有效防止隐私泄露和数据篡改等问题,并实现高效的数据传输。由此提出一种基于隐私同态数据融合的完整性验证协议IV-PHDA。该协议采用同态加密保证数据隐私性;利用随机检测节点对节点聚合结果的完整性进行检测,以验证聚合节点是否忠实地传输每个数据分组。通过理论分析和仿真对比,对其算法的性能进行验证,结果表明,该协议能够在网络传输的过程中检测数据的完整性,并且实现较好的隐私保护和较高的数据精确度。     

面向数据库加密的秘密同态算法的研究

在Domingo提出的秘密同态加密算法的理论基础上,给出了一种将浮点数转换为整数的同态运算,基于复合同态的数学理论基础,提出了类复合同态的概念并扩展应用到了实现浮点型数据的同态加密机制中。最后利用中国剩余定理实现了字符串数据的加密。     

标准模型下抗CPA与抗CCA2的RSA型加密方案

RSA型加密系统（RSA加密系统及其改进系统的统称）至今仍然被广泛应用于许多注重电子数据安全的电子商务系统中.然而对现有的RSA型加密方案分析发现：（1）只有在随机谕言机模型下抗CCA2攻击的RSA型加密方案,还没有在标准模型下实现IND-CCA2安全的RSA型概率加密方案;（2）没有在标准模型下实现抗CPA且保持乘法同态性的RSA型同态加密方案,而同态性是实现安全多方计算和云计算安全服务的重要性质之一;（3）在实现密文不可区分方面,这些方案除HD-RSA外都是通过一个带hash的Feistel网络引入随机因子的,从而导致这些方案只能在随机谕言机模型下实现IND-CCA2安全.针对以上问题,本文在RSA加密系统的基础上,通过增加少量的有限域上的模指数运算,设计了一个标准模型下具有IND-CPA安全的RSA型概率同态加密方案和一个具有IND-CCA2安全的RSA型概率加密方案.这两个方案在实现密文不可区分时,都不再通过明文填充引入随机因子.此外,本文还提出一个RSA问题的变形问题（称作RSA判定性问题）.     

超半环中的理想

为了研究超半环的结构,在超半环中引入了理想的概念,并研究了理想关于同态与同构的定理.     

Soft polygroups

Soft set theory, introduced by Molodtsov, has been considered as an effective mathematical tool for modeling uncertainties. In this paper, we initiate the study of algebraic hyperstructures of soft sets. The concepts of soft polygroups, normal soft polygroups, soft subpolygroups and normal soft subpolygroups are introduced, and some related properties are investigated. Furthermore, we propose the homomorphism and isomorphism of soft polygroups, and establish three isomorphism theorems for soft polygroups.     

Soft groups and normalistic soft groups

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Akta? and Çag˜man [H. Akta?, N. Çag˜man, Soft sets and soft groups, Inf. Sci. 177 (2007) 2726-2735]. Moreover, we introduce the concepts of normalistic soft group and normalistic soft group homomorphism, study their several related properties, and investigate some structures that are preserved under normalistic soft group homomorphisms.