In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type A1. We introduce a notion of root basis for these root systems, ...In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type A1. We introduce a notion of root basis for these root systems, and using a unique expression of the elements of the Weyl group with respect to a set of generators for the Weyl group, we calculate the length function with respect to a very specific root basis.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
利用W ey l群的性质及置换理论,讨论了Al型W ey l群作用下的子根系轨道生成的格.在同类型格中,研究了不同格之间的包含关系,给出了一个子根系是给定由μ生成的格L(μ)中一个元素的条件,最后讨论了按包含关系或反包含关系规定L(μ)的偏序...利用W ey l群的性质及置换理论,讨论了Al型W ey l群作用下的子根系轨道生成的格.在同类型格中,研究了不同格之间的包含关系,给出了一个子根系是给定由μ生成的格L(μ)中一个元素的条件,最后讨论了按包含关系或反包含关系规定L(μ)的偏序时,L(μ)是否为几何格.展开更多
Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of a...Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.展开更多
文摘In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type A1. We introduce a notion of root basis for these root systems, and using a unique expression of the elements of the Weyl group with respect to a set of generators for the Weyl group, we calculate the length function with respect to a very specific root basis.
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。
基金Project supported by the National Natural Science Foundation of China (No.19671079).
文摘Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.
