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1.
Algebraic properties of cryptosystem PGM 总被引:2,自引:0,他引:2
In the late 1970s Magliveras invented a private-key cryptographic system calledPermutation Group Mappings (PGM). PGM is based on the prolific existence of certain kinds of factorization sets, calledlogarithmic signatures, for finite permutation groups. PGM is an endomorphic system with message space ℤ|G| for a given finite permutation groupG. In this paper we prove several algebraic properties of PGM. We show that the set of PGM transformations ℐ
G
is not closed under functional composition and hence not a group. This set is 2-transitive on ℤ|G| if the underlying groupG is not hamiltonian and not abelian. Moreover, if the order ofG is not a power of 2, then the set of transformations contains an odd permutation. An important consequence of these results
is that the group generated by the set of transformations is nearly always the symmetric group ℒ|G|. Thus, allowing multiple encryption, any permutation of the message space is attainable. This property is one of the strongest
security conditions that can be offered by a private-key encryption system.
S. S. Magliveras was supported in part by NSF/NSA Grant Number MDA904-82-H0001, by U.S. West Communications, and by the Center
for Communication and Information Science of the University of Nebraska. 相似文献
2.
在Hilbert框架下借助于度量投影修正Mann迭代程序,证明了关于无限族非扩张映射的强收敛定理,并用于求解分裂可行性问题SFP.研究成果在很大程度上推广和改进了现有的结果. 相似文献
3.
设φ:Rn →Rn 是一个线性映射,对任意x∈Rn ,都存在与x有关的线性保控映射ψx ,使得φ(x)=ψx(x),则称φ是欧氏空间上的一个线性局部保控映射。线性保控映射是线性局部保控映射,其逆命题不成立。文中定义了两个与φ相关的Rn的子集Iφ和IIφ,如果任意Rn上的点都属于Iφ(或IIφ),那么这个线性局部保控映射φ是线性保控映射。 相似文献
4.
H. Iiduka 《Optimization methods & software》2016,31(5):931-951
This paper proposes an incremental subgradient method for solving the problem of minimizing the sum of nondifferentiable, convex objective functions over the intersection of fixed point sets of nonexpansive mappings in a real Hilbert space. The proposed algorithm can work in nonsmooth optimization over constraint sets onto which projections cannot be always implemented, whereas the conventional incremental subgradient method can be applied only when a constraint set is simple in the sense that the projection onto it can be easily implemented. We first study its convergence for a constant step size. The analysis indicates that there is a possibility that the algorithm with a small constant step size approximates a solution to the problem. Next, we study its convergence for a diminishing step size and show that there exists a subsequence of the sequence generated by the algorithm which weakly converges to a solution to the problem. Moreover, we show the whole sequence generated by the algorithm with a diminishing step size strongly converges to the solution to the problem under certain assumptions. We also give examples of real applied problems which satisfy the assumptions in the convergence theorems and numerical examples to support the convergence analyses. 相似文献
5.
Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk. 相似文献
6.
Continuity versus Discretization 总被引:1,自引:1,他引:0
The threefold interest in architecture, biology and mathematics motivated us to examine and justify new architectural forms.
We discuss some notions of rhythm: Euclidean, morphogenetic and morphologic. Contemporary relationships between structure
and form are based on the generation of shape by technological processes, thus the resulting objects are restricted to their
material expression. Here a phenomenological organisation of form and its continuity with the landscape arise out of the mathematical
and architectural creativity. The use of the computer is applied from outside to inside instead from inside to outside; this
means that we are dealing with the organisational processes via continuous methods instead of evolutionary processes given
by computer simulations, known as genetic algorithms, where the resulting configurations are reduced to a matter of routine. The role of design as an aesthetic component innovates
the theoretical framework of structural engineering to establish the architectural environments. 相似文献
7.
Weerayuth Nilsrakoo 《Computers & Mathematics with Applications》2011,62(12):4656-4666
In this paper, we note that the main convergence theorem in Zhang et al. (2011) [21] is incorrect and we prove a correction. We also modify Halpern’s iteration for finding a fixed point of a strongly relatively nonexpansive mapping in a Banach space. Consequently, two strong convergence theorems for a relatively nonexpansive mapping and for a mapping of firmly nonexpansive type are deduced. Using the concept of duality theorems, we obtain analogue results for strongly generalized nonexpansive mappings and for mappings of firmly generalized nonexpansive type. In addition, we study two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space. 相似文献
8.
9.
在Hilbert空间中,引入一种新的关于广义混合均衡问题的迭代方法,通过该迭代方法求得广义混合均衡问题的解集与非扩张映像的不动点集的公共解.并且在一定条件下,得到强收敛定理.所得结果改进和推广了这一领域内某些最新结果. 相似文献
10.
Some characteristic cases of formation of an ideal flow are described depending on preset values of controlling potential. Based on the modified G. Polozhii's method of summary mappings, the characteristic function of the flow is obtained. Examples of construction of a dynamic grid, field of velocities, and formation of different flows are given. Types of key problems of finding the values of controlling potential, which provide optimization of definite functionals are defined. An example of solution to one of them is presented. 相似文献