How to Choose Secret Parameters for RSA-Type Cryptosystems over Elliptic Curves

Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA-type cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curve-based analogues, the length of the RSA-modulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSA-type cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSA-type systems over elliptic curves if a fixed point is found.     

On the Strong McShane Integral of Functions with Values in a Banach Space

The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions.     

具有一个细焦点和一个粗焦点的二次系统极限环的个数

Abstract. It is proved that the quadratic system with a weak focus and a strong focus has atmost one limit cycle around the strong focus, and as the weak focus is a 2nd -order (or 3rd-order ) weak focus the quadratic system has at most two (one) limit cycles which have (1,1)-distribution ((0,1)-distribution).     

BANACH空间中具无限时滞泛函微分方程的初值问题

考虑了如下具无限时滞泛函微分方程：“u′（t）=f（t,u(t),ut),uσ=ψ（σ≤t≤α）”,利用锥的强极小性质,获得了上述方程的初值问题的某些有解的充分条件。     

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωP_g respectively. In the case of ω_e⋙ω_g, the PEMFs are manifested as the EM wave beams with frequency ω_e and a standing EM wave with ω_g. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ω_g⋙ω_e, all PEMFs are expressed as the standing EM waves with frequency ω_g. The resonant response occurs in two cases of ω_e = 1/2 ω_g andω_e, = ω_g only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10^-33 - 10^-35 and λ_g = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.     

△(G)=4的Halin-图的邻强边染色

图G(V,E)的一正常k-边染色f称为G(V,E)的一k-邻强边染色(简称k-ASEC)当且仅当任意uv∈E(G)满足f[u]≠f[v],其中f[u]={f(uw)|uw∈E(G)},并称Xas(G)=min{k|存在G的一k-ASEC}为G的邻强边色数.本文研究了△(G)=4的Halin-图的邻强边染色,得到了如下结果对△(G)=4的Halin-图有△(G)=4≤Xas(G)≤△(G)+1=5.     

再论循环空间中全脐子流形

本文在作者前文工作的基础上继续考查 C循环空间子流形的全脐子流形特征 .给出了一个充分必要条件即定理 1 .从而结合已有文献我们推广并改进了 Olszak文中的相应结果 .     

Multiple Scattering Solution of Millimeter Wave Propagation in Strong Sandstorm

As the operating frequencies of communication systems more higher into the millimeter wave range, and the density of particles in medium is more denser, the effects of multiple scattering in sandstorm become more significant. This paper treats the problems of electromagnetic multiple scattering in strong sandstorm by the Monte Carlo method. Based on the analytical theory of multiple scattering, the millimeter wave propagation and scattering in discrete random media are investigated by means of the particle-tracking technique. The millimeter wave is regarded as a Markov chain of wave particle collisions in a medium in which it is scattered and absorbed. Considering the effect of multiple scattering, millimeter wave attenuation induced by strong sandstorm is simulated numerically. The values of theoretical calculation are in good agreement with the measured results of simulated experiment at 34 and 93 GHz.     

BTCF上离子引起的束流不稳定性研究

对所设计的北京τ-粲工厂(BTCF)高亮度对撞模式下电子环中的离子引起的束流不稳定性做了研究.计算了不同束团填充空隙下的离子俘获比,然后用自编的模拟程序对BTCF上快束流–离子不稳定性做了模拟跟踪,得到的快束流–离子不稳定性的增长时间和理论解析计算值基本一致.     

n-Strongly Gorenstein Projective,Injective and Flat Modules

In this article, we study the relation between m-strongly Gorenstein projective (resp., injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever m ≠ n, and the homological behavior of n-strongly Gorenstein projective (resp., injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Gorenstein flat modules, and the relation between these modules and n-strongly Gorenstein projective (resp., injective) modules.