Comparison of the Minimum Bounding Rectangle and Minimum Circumscribed Ellipse of Rain Cells from TRMM

Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.

MIBS-64算法Rectangle与Boomerang攻击的改进

MIBS算法是Izadi等人于2009年提出的一种轻量级分组密码,包含MIBS-64和MIBS-80两个版本.2019年,Chen等人对MIBS-64开展了基于13轮Rectangle区分器的15轮密钥恢复攻击,时间、数据和存储复杂度为(T,D,M)=(2^(59),2^(45),2^(45)).本文进一步研究MIBS-64算法抵抗Rectangle与Boomerang攻击的能力.利用差分在轮函数线性层确定性传播的特点,改进了Chen等人的15轮Rectangle密钥恢复攻击,将时间复杂度从2^(59)降低至2^(47).引入Song等人提出的针对Boomerang攻击的新型密钥恢复算法,对MIBS-64开展了15、16轮的Boomerang密钥恢复攻击,所需的复杂度(T,D,M)为(238,2^(37),2^(36))和(2^(60),2^(60),2^(30)).给出了MIBS-64在Boomerang和Rectangle攻击下最新的安全性分析结果,首次成功开展16轮的密钥恢复攻击.

How Does Topology Help Solve the Inscribed Rectangle Problem by Proving that Every Jordan Curve Has 4 Vertices that Form a Rectangle?

When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably the most fascinating shape in the universe. A circle is defined as the set of all points equidistant from a given point, which, therefore, lies at the center of the circle. One of the various properties of circles is that it has infinite inscribed squares. This is because it is a continuous function, therefore if any point in the circle is transitioned by a specific factor, the other related points in the square would be shifted by the same factor. An ellipse is a similar shape with several inscribed squares. But does any closed curve have an inscribed square? This question was proposed by Otto Toeplitz in 1911 and to this day it is not answered. Another version of this problem is the inscribed rectangle problem which will be discussed in this paper.

对DES的Rectangle攻击和Boomerang攻击

作为加密标准,DES(data encryption standard)算法虽然已被AES(advanced encryption standard)算法所取代,但其仍有着不可忽视的重要作用.在一些领域,尤其是金融领域,DES和Triple DES仍被广泛使用着.而近年来又提出了一些新的密码分析方法,其中,Rectangle攻击和Boomerang攻击已被证明是非常强大而有效的.因此,有必要重新评估DES算法抵抗这些新分析方法的能力.研究了DES算法针对Rectangle攻击和Boomerang攻击的安全性.利用DES各轮最优差分路径及其概率,分别得到了对12轮DES的Rectangle攻击和对11轮DES的Boomerang攻击.攻击结果分别为:利用Rectangle攻击可以攻击到12轮DES,数据复杂度为2^(62)个选择明文,时间复杂度为2^(42)次12轮加密;利用Boomerang攻击可以攻击到11轮DES,数据复杂度为2^(58)个适应性选择明密文,时间复杂度为2^(38)次11轮加密.由于使用的都是DES各轮的最优差分路径,所以可以相信,该结果是Rectangle攻击和Boomerang攻击对DES所能达到的最好结果.

基于Dividing Rectangles的多模态医学图像配准算法

为了准确、可靠地配准多模态医学图像,提出了一种基于互信息的全局优化配准算法。该算法首先提取出目标物体的外轮廓面,再用迭代最近点方法初步对齐图像;然后用确定性的全局优化方法—Dividing Rectangles搜索归一化互信息的全局最优解。该算法利用图像的特征信息,为Dividing Rectangles方法提供了一个较好的初始配准位置,并充分利用了Dividing Rectangles方法在小范围内的高效搜索能力。实验结果表明,对于3维人体脑部数据,该算法配准精度高、速度快,而且有效地避免了配准过程中出现的局部极值。

轻量级分组密码RECTANGLE基于FELICS的实现与优化

随着物联网的普及以及RFID、传感器的广泛应用,轻量级密码算法受到人们越来越多的关注。对于一个轻量级密码算法,除了安全性之外,软件和硬件实现性能也非常重要。卢森堡大学的科研人员于2015年开发了一个开源框架——FELICS(Fair Evaluation of Lightweight Cryptographic Systems),旨在公平地测评轻量级密码算法在嵌入式设备上的软件性能。FELICS需要在两种应用场景下(一为通信协议,另一为认证协议),测试一个密码算法在三种嵌入式平台(8位AVR、16位MSP以及32位ARM)下运行所需的Flash、RAM和执行时间,再对结果取加权平均值,并据此对参赛的轻量级分组密码的软件性能进行综合排名。到目前为止,FELICS已经包含了18个轻量级分组密码。本文首先分析FELICS中已提交的分组密码的C语言及汇编语言代码,总结常用的优化方法。然后在三种嵌入式平台上实现了轻量级分组密码RECTANGLE。进一步地,我们对算法轮密钥加、列变换、行移位这三种操作进行了优化。优化后的结果如下:在ARM平台,优化后轮函数所需的Flash减少42.6%、同时时间减少36.8%;在AVR平台场景1下,优化后RECTANGLE-128的RAM减少了12.0%、同时时间减少了5.0%,RECTANGLE-80的RAM减少了10.9%、同时时间减少了2.8%。FELICS的最终结果显示,在18个轻量级分组密码算法中,RECTANGLE在两种应用场景下分别排名第4和第5位,这表明RECTANGLE在嵌入式平台上具有优秀的软件性能。

Local Bifurcation of a Thin Rectangle Plate with the Friction Support Boundary

The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.

对PICO和RECTANGLE的零相关线性分析

混合整数线性规划是一种解决优化问题的常用方法.2012年,Mouha等人首次将该方法应用于密码算法的安全性评估,成功实现了对活跃S盒数下界的求解.PICO和RECTANGLE均为SPN型结构的轻量级分组密码算法,目前对于这两种算法的零相关线性分析研究尚待完善.本文首先针对PICO算法的零相关线性逼近问题,建立基于混合整数线性规划的模型并进行路径搜索,找到大量7轮PICO算法的零相关线性逼近,优于设计者给出的4轮零相关线性逼近.进一步地,通过构造7轮多维零相关线性区分器,对含白化密钥的10轮PICO算法进行密钥恢复攻击.该攻击能够恢复共50比特轮子密钥,其时间复杂度为2^(68.7)次10轮PICO加密,数据复杂度为2^(63.3)个已知明文,存储复杂度为2^(42.3)字节.最后,本文针对RECTANGLE算法的零相关线性逼近问题,采用类似方法进行搜索,同时借助算法本身的传播性质,找到了208条8轮RECTANGLE的零相关线性逼近,并给出了11轮RECTANGLE的零相关线性攻击.该攻击可恢复共44比特轮子密钥,其数据复杂度为2^(63)个已知明文,时间复杂度为2^(107)次11轮RECTANGLE加密运算.

轻量级分组密码RECTANGLE在X86和X64平台的软件实现评估

轻量级密码是当前密码学研究的一个热门课题,设计硬件实现和软件实现性能均衡的轻量级密码算法已成为趋势.尽管在轻量级密码算法软件实现方面已经有一些理论和实际的研究,但是公平地比较不同算法的软件实现性能仍然很困难.切片实现是软件实现时模仿硬件实现的方式.本文给出RECTANGLE在X86和X64平台上切片实现以及速度测试结果.结果表明,RECTANGLE在中高端平台展现了非常优秀的软件实现性能.在2.9 GHz Intel(core)i5-4570s CPU平台RECTANGLE单块加解密速度分别为34.2和30.9 cyles/byte;使用SSE指令集,加解密速度分别为5.2和5.1 cycles/byte;使用AVX指令集,加解密速度分别为2.6和2.5 cycles/byte.

Effect of Rectangle Wave Pulse Current on Solidification Structure of ZA27 Alloy

The effect of rectangle wave pulse current on solidification structure of ZA27 alloy was studied. The restdts show that the wave pattern relies on the frequency range of harmonic wave and the energy of pulse current within the frequency range of pulse current. Imposed pulse current could induce the solidification system to oscillate. The frequency range and the relevant energy distribution of pulse current exert an influence on the amount of atoms involved for forming critical nucleus, the surface states of dusters in melt, the oscillating state of melt on the surface of dusters, the active energy of atom diffusion , the frequnce response of the resonance of bulk melt and the absorbability of the solidification system to the external work. Rectangle wave pulse current involves rich harmonic waves ; the amplitudes of high order of harmonic waves are higher and reduce slowly, so it has a better effect on inoculation and modification.

Searching for complete set of free resource rectangles on FPGA area based on CPTR

As a coprocessor, field-programmable gate array （FPGA） is the hardware computing processor accelerating the computing capacity of coraputers. To efficiently manage the hardware free resources for the placing of tasks on FPGA and take full advantage of the partially reconfigurable units, good utilization of chip resources is an important and necessary work. In this paper, a new method is proposed to find the complete set of maximal free resource rectangles based on the cross point of edge lines of running tasks on FPGA area, and the prove process is provided to make sure the correctness of this method.

19轮RECTANGLE-80的相关密钥差分分析

RECTANGLE是最近提出来基于bit-slice技术的可在多个平台快速实现的轻量级分组密码.它采用的是SPN结构,分组长度为64比特,密钥长度为80或128比特,迭代轮数为25轮.到目前为此,针对RECTANGLE算法的分析很少,其中包括算法设计者给出的18轮差分攻击.对于特定的输入、输出和轮子密钥差分,本文找出了所有活跃S盒个数为26-30的15轮相关密钥差分特征,总的差分概率为2-60.5.利用这些差分特征,我们将相应的差分区分器分别向前和向后扩展两轮,提出了19轮的相关密钥差分攻击,其中数据复杂度为262,时间复杂度为270,内存复杂度为272.数据和时间复杂度都低于设计者给出的18轮攻击.

Research on Algorithm for Generating Min-Area Rectangle Encasing Box for Closed Contour

In many engineering applications, it is necessary to calculate the min-area encasing box of a circumscription. In this paper, an algorithm for generating the min-area rectangle encasing box, based on revolving angle, is investigated and hence put forward. The algorithm computes the areas of the outer rectangular bounds of a closed contour in different revolving angles θ by dispersing approach where 0< θ < π/2 because of the axial symmetry. It is very simple, straight forward and highly efficient. The complexity of its computing time reaches O(n·k ). Practical applications suggest its usefulness and efficiency.

Numerical simulation of wrinkle phenomenon during multi-point forming process of shallow rectangle cup

In this paper, the principle of multi-point forming (MPF) technique is presented. One of the most serious defects, wrinkling, during the multi-point forming process of a shallow rectangle cup is discussed by means of numerical simulation on the shallow rectangle cup forming process. The effects of thickness, material of sheet metal and the pressure of the blank holder are investigated. Based on the simulation results, the reasons and control methods of wrinkling are pointed out. Moreover, the experiment on the multi-point die forming of the shallow rectangle cup by the MPF machine is done to validate the efficiency of the numerical simulation, and the result proves that the application of an elastic cushion in the forming can restrain wrinkling efficiently.

On Tilings of Quadrants and Rectangles and Rectangular Pattern

The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.

RECTANGLE-80的相关密钥差分分析

轻量级分组密码RECTANGLE采用SPN结构,分组长度是64比特,密钥长度是80或128比特,迭代轮数是25轮。其采用比特切片技术,在软硬件实现方面均有很好的性能。本文以Matsui和Moriai等人的自动化搜索算法为基础,采用包珍珍等人提出的2种优化策略,对RECTANGLE-80版本进行相关密钥差分分析。我们对最窄点处的密钥状态差分进行限制,使最窄点密钥状态差分的汉明重量取值范围分别属于区间[1,1],[1,2],[1,3],[1,4],[1,5]五种情况,目的是求得此五种情况下前9轮相关密钥差分最大概率及其对应的路径。我们获得了此5种情况前8轮的最大概率及其对应的路径,前2种情况9轮最大概率及其对应路径和后3种情况9轮最大概率的上界。以上5种情况的结果显示,当取值范围属于后三种情况时,前8轮的最大概率是相同的,由此说明随着取值范围的扩大,最大概率趋向稳定。当最窄点密钥状态差分的汉明重量取值范围属于[1,1]或[1,2]时,9轮的最大概率为2^-42。当取值范围分别是[1,3],[1,4]和[1,5]时,9轮最大概率的上界分别是2^-41,2^-37,2^-34。我们预测9轮最大概率的上界是2^-41,由此可以预测18轮的最大概率的上界是2^-82,从而RECTANGLE-80可以抵抗相关密钥差分分析。这是目前RECTANGLE抵抗相关密钥密码分析安全性评估最好结果。

Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval

In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.

Tiling Rectangles with Gaps by Ribbon Right Trominoes

We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the sides of the rectangle are of length at least 5, then the gap number is less than or equal to 3. We also show that for the family of rectangles that have nontrivial minimal number of gaps, with probability 1, the only obstructions to tiling appear from coloring invariants. This is in contrast to what happens for simply connected regions. For that class of regions Conway and Lagarias found a tiling invariant that does not follow from coloring.

Study on the transient radiation for apertures excited by rectangle pulse

The analytic representation of the transient radiation for an aperture excited by a rectangle pulse is obtained. It shows that the field duration and amplitude depend on the observation distance, the elevation angle, the pulse width of the rectangle pulse and the aperture size.

The Triangular Hermite Finite Element Complementing the Bogner-Fox-Schmit Rectangle

The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.