TWO FAST ALGORITHMS FOR COMPUTING POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES

The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Muller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces the corresponding multiplier by modulo Υk-1 +…+Υ+ 1 and improves the above algorithms. Implementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free, Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over

SPEED UP RATIONAL POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES BY FROBENIUS EQUATIONS

Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.

Embedded Programmable Single Point Multiple Output Intelligent Data Acquisition and Transmission System

To effectively solve the problems of inconsistent communication protocols in automatic monitoring equipment,and limited data acquisition transmission and monitoring equipment,this paper developed programmable single point multiple output intelligent data acquisition and transmission system. It made an in-depth elaboration of the data acquisition and transmission system from hardware design,software architecture and principle,main functions and technical parameters. Finally,it came up with four innovation points:(i) intelligent(automatic)matching a variety of communication protocols for environmental monitoring equipment,(ii) realizing multi-protocol and multi-target parallel data transmission,(iii) realizing remote dynamic input of control instructions through wired or wireless network,and(iv) supporting configuration(process) simulation of field equipment DCS operating conditions.

RATE OF CONVERGENCE FOR MULTIPLE CHANGEPOINTS ESTIMATION OF MOVING-AVERAGE PROCESSES

In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions.

NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

FPGA Implementation of Elliptic-Curve Diffie Hellman Protocol

This paper presents an efficient crypto processor architecture for key agreement using ECDH(Elliptic-curve Diffie Hellman)protocol over GF2163.The composition of our key-agreement architecture is expressed in consisting of the following:(i)Elliptic-curve Point Multiplication architecture for public key generation(DESIGN-I)and(ii)integration of DESIGN-I with two additional routing multiplexers and a controller for shared key generation(DESIGN-II).The arithmetic operators used in DESIGN-I and DESIGNII contain an adder,squarer,a multiplier and inversion.A simple shift and add multiplication method is employed to retain lower hardware resources.Moreover,an essential inversion operation is operated using the Itoh-Tsujii algorithm with similar hardware resources of used squarer and multiplier units.The proposed architecture is implemented in a Verilog HDL.The implementation results are given on a Xilinx Virtex-7 FPGA(field-programmable gate array)device.For DESIGN-I and DESIGN-II over GF2163,(i)the utilized Slices are 3983 and 4037,(ii)the time to compute one public key and a shared secret is 553.7μs and 1170.7μs and(iii)the consumed power is 29μW and 57μW.Consequently,the achieved area optimized and power reduced results show that the proposed ECDH architecture is a suitable alternative(to generate a shared secret)for the applications that require low hardware resources and power consumption.

Non-parametric machine learning methods for interpolation of spatially varying non-stationary and non-Gaussian geotechnical properties

Spatial interpolation has been frequently encountered in earth sciences and engineering.A reasonable appraisal of subsurface heterogeneity plays a significant role in planning,risk assessment and decision making for geotechnical practice.Geostatistics is commonly used to interpolate spatially varying properties at un-sampled locations from scatter measurements.However,successful application of classic geostatistical models requires prior characterization of spatial auto-correlation structures,which poses a great challenge for unexperienced engineers,particularly when only limited measurements are available.Data-driven machine learning methods,such as radial basis function network(RBFN),require minimal human intervention and provide effective alternatives for spatial interpolation of non-stationary and non-Gaussian data,particularly when measurements are sparse.Conventional RBFN,however,is direction independent(i.e.isotropic)and cannot quantify prediction uncertainty in spatial interpolation.In this study,an ensemble RBFN method is proposed that not only allows geotechnical anisotropy to be properly incorporated,but also quantifies uncertainty in spatial interpolation.The proposed method is illustrated using numerical examples of cone penetration test(CPT)data,which involve interpolation of a 2D CPT cross-section from limited continuous 1D CPT soundings in the vertical direction.In addition,a comparative study is performed to benchmark the proposed ensemble RBFN with two other non-parametric data-driven approaches,namely,Multiple Point Statistics(MPS)and Bayesian Compressive Sensing(BCS).The results reveal that the proposed ensemble RBFN provides a better estimation of spatial patterns and associated prediction uncertainty at un-sampled locations when a reasonable amount of data is available as input.Moreover,the prediction accuracy of all the three methods improves as the number of measurements increases,and vice versa.It is also found that BCS prediction is less sensitive to the number of measurement data and outperforms RBFN and MPS when only limited point observations are available.

Identification of proteins associated with Fusarium crown rot resistance in wheat using label-free quantification analysis

Fusarium crown rot(FCR),typically caused by Fusarium pseudograminearum,is a severe soil-borne disease that,in recent years,has become an emerging threat to Chinese wheat crops.For the first time in this study,we investigated and compared the proteomic characteristics of two Chinese wheat varieties(04 Zhong 36 and Xinmai 26)at 24,48,and 72 h post-inoculation using label-free quantitative proteomic analysis.A total of 9234 proteins were successfully quantified,of which 783 were differentially expressed after inoculation.These proteins were mainly involved in metabolic,single-organism,and cellular processes.Thirty-three proteins associated with defense,cell wall formation,photosynthesis,etc.,showed consistently different expression between the two genotypes at multiple time points.In particular,chitinase,which degrades chitin in the fungal cell wall and limits fungal growth,was exclusively and consistently upregulated in 04 Zhong 36 across the three time points.Other proteins such as flavonoid O-methyltransferase,glycosyltransferase,and peroxidase were only upregulated in 04 Zhong 36,and proteins,including the berberine bridge enzyme and rubisco large subunit-binding protein,were specifically downregulated in Xinmai 26.The expression of transcripts encoding eight selected proteins through qRT-PCR analysis supported the proteomic profiles.Overall,the results of this study allow us to understand FCR resistance in wheat at the protein level.Some proteins and their corresponding genes may be useful resources for the genetic improvement of FCR resistance in wheat.

Simultaneously Designing and Targeting for Networks with Multiple Resources of Different Qualities

This paper presents a new design procedure for the networks with multiple resources, such as hydrogen and water, of different qualities. The minimum consumption targets of the resources and pinch-causing sources can be identified as well during design. The objective of this work is to reduce the consumption of the resources with higher quality due to their higher cost. A few examples are investigated to show the proposed method. For a net-work of single resource with single contaminant, there is often only one pinch point for the resource. On the other hand, for a network of multiple resources with single contaminant, there might be a few different pinch points. Each resource might have its own pinch point, if its amount is sufficient. The contaminant concentration of the pinch-causing source for a resource with lower concentration will be below that of the higher-concentration resource(s).

Two-Codebook-Based Cooperative Precoding for TDD-CoMP in 5G Ultra-Dense Networks

In ultra-dense networks （UDN）, the local precoding scheme for time-division duplex coordinated multiple point transmission （TDD-CoMP） can have a good performance with no feedback by using reciprocity between uplink and dovallink. However, if channel is time-varying, the channel difference would cause codeword mismatch between transmitter and receiver, which leads to performance degradation. In this paper, a linear interpolation method is proposed for TDD-CoMP system to estimate the uplink channel at the receiver, which would reduce the channel difference caused by time delay and decrease the probability of codeword mismatch between both sides. Moreover, to mitigate severe inter-cell interference and increase the coverage and throughput of celledge users in UDN, a two-codebook scheme is used to strengthen cooperation between base stations （BSs）, which can outperform the global precoding scheme with less overhead. Simulations show that the proposed scheme can significantly improve the link performance compared to the global precoding scheme.

Extended tanh-function Method for Solving Traveling Wave Solutions of Nonlinear Kundu Equation

In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.

Some Polar Sets for the Generalized Brownian Sheet

Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.

Reliance or Defiance： Writing out of Her Mother in Maxine Hong Kingston＇s The Woman Warrior

This paper is to illustrate that form develops meaning in Maxine Hong Kingston＇s The Woman Warrior （1989）. Her writing is permeated with the dual forces stretching to diverse directions, and equips readers with the mimic world to be pushed and pulled to experience all the paradoxes in narrator＇s life. This enigmatic writing style is the mimesis of the push-pull dynamics existent in the mother-daughter relationship in the book, and also through this kind of writing does the writer finally succeed in breaking away from the suffocating mother-daughter relationship and in claiming her own unique identity.

Multiplicities of fixed points of holomorphic maps in several complex variables

Let Δυ be the unit ball in ?υ with center 0 (the origin of υ) and let F:Δυ→?υbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF i =F°?°F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally.

A Complete Set of Addition Laws for Twisted Jacobi Intersection Curves

A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to compute P1＋P2. This paper proposes a complete set of the addition laws for arbitrary twisted Jacobi intersection curve.

Crack status analysis for concrete dams based on measured entropy

The integrity and safety of concrete darns are seriously affected by the existing cracks in dam bodies, and some serious cracks may cause dam failure or disaster. The propagation of cracks in concrete dams is accompanied by changes in energy distribution, which can be represented by changes in the structure＇s system entropy. Therefore, the entropy theory can be used in analyzing the behavior of dam cracks. Due to the randomness and locality of crack propagation, it is difficult to predict the loca- tion of cracks by traditional monitoring methods. To solve this problem, the influence of spatial positions of monitoring points on inspection zones is represented by a weight index, and the weight index is determined by the distance measure method proposed in this paper. Through the weighted linear fusion method, the entropy of multiple monitoring points is obtained for analyzing the behavior of dam cracks in the selected zones. Meanwhile, the catastrophe theory is used as the variation criterion of an entropy sequence in order to predict the instability time of dam cracks. Case studies are put forward on a high arch darn, and the fusion entropy is calculated according to the monitoring data from strain gauges. Results show that the proposed method can effectively predict the occurrence time and location of dam cracks regardless of the layout of monitoring instruments, and it is a new way to analyze the occurrence and propagation of dam cracks.

DYNAMICAL BEHAVIORS FOR A THREE－DIMENSIONAL DIFFERENTIAL EQUATION IN CHEMICAL SYSTEM

In this paper, a mathematical model of chemical system is investigated, the conditions of existence and local stability and bifurcation for the steady-states are obtained, the periodic solutions of the Hopf type are considered, the multiple Hopf bifurcation points exist if one parameter varies, and a technique for studying the Hopf biforcation value is given here.

Multi-recurrence and van der Waerden systems

We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.

Multiple Solutions for a Quasilinear Second Order Differential Equation Depending on a Parameter

The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.