The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second comm...The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.展开更多
Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this pape...Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.展开更多
近些年,无线医疗传感器网络(Wireless Medicine Sensor Networks,WMSNs)得到了广泛的应用。WMSNs提高了患者护理质量,但同时也存在许多安全隐患。为了保护患者数据的隐私安全,Yi等人提出了一个基于Paillier密码系统的分布式ElGamal密码...近些年,无线医疗传感器网络(Wireless Medicine Sensor Networks,WMSNs)得到了广泛的应用。WMSNs提高了患者护理质量,但同时也存在许多安全隐患。为了保护患者数据的隐私安全,Yi等人提出了一个基于Paillier密码系统的分布式ElGamal密码系统。然而,Rao分析了他们的方案并展示了一种可行的攻击,该攻击允许攻击者获取密钥。因此,是否可以将具有加法同态性质的密码系统修改为安全的分布式解密系统,以实现更简单的分布式密钥生成和更高效的分布式解密仍然是一个挑战。针对上述挑战,该文提出了一种基于Castagnos和Laguillaumie(CL)加密的改进分布式解密系统,并对未知阶群G上的离散对数关系给出了有效的零知识证明。与其他分布式解密系统相比,基于CL加密的改进分布式系统具有良好的性能、更可靠的设置、更高的安全级别。展开更多
文摘The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.
基金Yibin University Pre-research Project,Research on the coupling and coordinated development ofmanufacturing and logistics industry under the background of intelligentmanufacturing,(2022YY001)Sichuan ProvincialDepartment of EducationWater Transport EconomicResearch Center,Research on the Development Path and Countermeasures of the Advanced Manufacturing Industry in the Sanjiang New District of Yibin under a“dual circulation”development pattern(SYJJ2020A06).
文摘Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.
文摘近些年,无线医疗传感器网络(Wireless Medicine Sensor Networks,WMSNs)得到了广泛的应用。WMSNs提高了患者护理质量,但同时也存在许多安全隐患。为了保护患者数据的隐私安全,Yi等人提出了一个基于Paillier密码系统的分布式ElGamal密码系统。然而,Rao分析了他们的方案并展示了一种可行的攻击,该攻击允许攻击者获取密钥。因此,是否可以将具有加法同态性质的密码系统修改为安全的分布式解密系统,以实现更简单的分布式密钥生成和更高效的分布式解密仍然是一个挑战。针对上述挑战,该文提出了一种基于Castagnos和Laguillaumie(CL)加密的改进分布式解密系统,并对未知阶群G上的离散对数关系给出了有效的零知识证明。与其他分布式解密系统相比,基于CL加密的改进分布式系统具有良好的性能、更可靠的设置、更高的安全级别。
