Hardware Architecture for RSA Cryptography Based on Residue Number System

A parallel architecture for efficient hardware implementation of Rivest Shamir Adleman(RSA) cryptography is proposed.Residue number system(RNS) is introduced to realize high parallelism,thus all the elements under the same base are independent of each other and can be computed in parallel.Moreover,a simple and fast base transformation is used to achieve RNS Montgomery modular multiplication algorithm,which facilitates hardware implementation.Based on transport triggered architecture(TTA),the proposed architecture is designed to evaluate the performance and feasibility of the algorithm.With these optimizations,a decryption rate of 106 kbps can be achieved for 1 024-b RSA at the frequency of 100 MHz.

FAULT-TOLERANT PERFORMANCE OF DATA TRANSMISSION MODELS BASED ON REDUNDANT RESIDUE NUMBER SYSTEM

Fault-tolerant data transmission models based on the redundant residue number system are proposed in this paper; they can transmit data correctly between two ends unless the residue errors exceed the error-correction capability. The expressions for the probability of error are presented when the channel noise is additive Gaussian noise and each branch is M-ary orthogonal signaling modulation. The expressions of the probabilities of undetected and uncorrected error are also obtained when the redundant residue number system are single error-checking and single error-correcting model, respectively.

Extensions of the Constructivist Real Number System

The paper reviews the most consequential defects and rectification of traditional mathematics and its foundations. While this work is only the tip of the iceberg, so to speak, it gives us a totally different picture of mathematics from what we have known for a long time. This journey started with two teasers posted in SciMath in 1997: 1) The equation 1 = 0.99… does not make sense. 2) The concept ?does not exist. The first statement sparked a debate that raged over a decade. Both statements generated a series of publications that continues to grow to this day. Among the new findings are: 3) There does not exist nondenumerable set. 4) There does not exist non-measurable set. 5) Cantor’s diagonal method is flawed. 6) The real numbers are discrete and countable. 7) Formal logic does not apply to mathematics. The unfinished debate between logicism, intuitionism-constructivism and formalism is resolved. The resolution is the constructivist foundations of mathematics with a summary of all the rectification undertaken in 2015, 2016 and in this paper. The extensions of the constructivist real number system include the complex vector plane and transcendental functions. Two important results in the 2015 are noted: The solution and resolution of Hilbert’s 23 problems that includes the resolution of Fermat’s last theorem and proof Goldbach’s conjecture.

Dividing Process in Base-10 Number System Reversed Dividing Process for 1/X

A new set of steps for dividing process, the Reversed Dividing Process, is introduced, in which the position based number representation digits for the value of l/X are reversely output one by one compared with digit output order of the normal dividing process.

Killing Imaginary Numbers? From Today’s Asymmetric Number System to a Symmetric System

In this paper, we point out an interesting asymmetry in the rules of fundamental mathematics between positive and negative numbers. Further, we show an alternative numerical system identical to today’s system, but where positive numbers dominate over negative numbers. This is like a mirror symmetry of the existing number system. The asymmetry in both systems leads to imaginary and complex numbers. We also suggest an alternative number system with perfectly symmetrical rules—that is, where there is no dominance of negative numbers over positive numbers or vice versa, and where imaginary and complex numbers are no longer needed. This number system seems to be superior to other numerical systems, as it brings simplicity and logic back to areas that complex rules have dominated for much of the history of mathematics. Finally, we also briefly discuss how the Riemann hypothesis may be linked to the asymmetry in the current number system. The foundation rules of a number system can, in general, not be proven incorrect or correct inside the number system itself. However, the ultimate goal of a number system is, in our view, to describe nature accurately. The optimal number system should therefore be developed with feedback from nature. If nature, at a very fundamental level, is ruled by symmetry, then a symmetric number system should make it easier to understand nature than an asymmetric number system would. We hypothesize that a symmetric number system may thus be better suited to describing nature. Further, such a number system should eliminate imaginary numbers in space-time and quantum mechanics, for example, two areas of physics that are clouded in mystery to this day.

The Constructivist Real Number System

The paper summarizes the contributions of the three philosophies of mathematics—logicism, intuitionism-constructivism (constructivism for short) and formalism and their rectification—which constitute the new foundations of mathematics. The critique of the traditional foundations of mathematics reveals a number of errors including inconsistency (contradiction or paradox) and undefined and vacuous concepts which fall under ambiguity. Critique of the real and complex number systems reveals similar defects all of which are responsible not only for the unsolved long standing problems of foundations but also of traditional mathematics such as the 379-year-old Fermat’s last theorem (FLT) and 274-year-old Goldbach’s conjecture. These two problems require rectification of these defects before they can be resolved. One of the major defects is the inconsistency of the field axioms of the real number system with the construction of a counterexample to the trichotomy axiom that proved it and the real number system false and at the same time not linearly ordered. Indeed, the rectification yields the new foundations of mathematics, constructivist real number system and complex vector plane the last mathematical space being the rectification of the complex real number system. FLT is resolved by a counterexample that proves it false and the Goldbach’s conjecture has been proved both in the constructivist real number system and the new real number system. The latter gives to two mathematical structures or tools—generalized integral and generalized physical fractal. The rectification of foundations yields the resolution of problem 1 and the solution of problem 6 of Hilbert’s 23 problems.

Design of fuzzy number recognition based on embedded system platform

A system of number recognition with a graphic user interface （GUI） is implemented on the embedded development platform by using the fuzzy pattern recognition method. An application interface （API） of uC/ OS-Ⅱ is used to implement the features of multi-task concurrency and the communications among tasks. Handwriting function is implemented by the improvement of the interface provided by the platform. Fuzzy pattern recognition technology based on fuzzy theory is used to analyze the input of handwriting. A primary system for testing is implemented. It can receive and analyze user inputs from both keyboard and touch-screen. The experimental results show that the embedded fuzzy recognition system which uses the technology which integrates two ways of fuzzy recognition can retain a high recognition rate and reduce hardware requirements.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

ON NUMBER OF LIMIT CYCLES FOR THE QUADRATIC SYSTEMS WITH A WEAK FOCUS AND A STRONG FOCUS

It is proved that the quadratic system with a weak focus and a strong focus has at most 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).

An Improved Semi-Orthogonal User Selection Algorithm Based on Condition Number for Multiuser MIMO Systems

In Multiple-Input Multiple-Out （MIMO） systems, the user selection algorithm plays an important role in the realization of multiplexing gain. In this paper, an improved Semi-orthogonal User Selection algorithm based on condition number is proposed. Besides, a new MIMO pre- coding scheme is designed. The proposed SUS- CN （SUS with condition number） algorithm outperforms the SUS algorithm for the selection of users with better matrix inversion property, thus a higher information rate for selected user pair is achieved. The designed MIMO precoding matrix brings benefits of the power equality at transmitted terminals, the limited dynamic range of the power over time, and a better power efficiency. The simulation results give the key insights into the im- pact of the different condition number value and users on the sum-rate capacity.

Number Entities Recognition in Multiple Rounds of Dialogue Systems

As a representative technique in natural language processing(NLP),named entity recognition is used in many tasks,such as dialogue systems,machine translation and information extraction.In dialogue systems,there is a common case for named entity recognition,where a lot of entities are composed of numbers,and are segmented to be located in different places.For example,in multiple rounds of dialogue systems,a phone number is likely to be divided into several parts,because the phone number is usually long and is emphasized.In this paper,the entity consisting of numbers is named as number entity.The discontinuous positions of number entities result from many reasons.We find two reasons from real-world dialogue systems.The first reason is the repetitive confirmation of different components of a number entity,and the second reason is the interception of mood words.The extraction of number entities is quite useful in many tasks,such as user information completion and service requests correction.However,the existing entity extraction methods cannot extract entities consisting of discontinuous entity blocks.To address these problems,in this paper,we propose a comprehensive method for number entity recognition,which is capable of extracting number entities in multiple rounds of dialogues systems.We conduct extensive experiments on a real-world dataset,and the experimental results demonstrate the high performance of our method.

Combinatory Spread－Spectrum Multiple－Access Based on Residue Number System：System and Performance

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Genome-wide investigation to assess copy number variants in the Italian local chicken population

Background Copy number variants(CNV)hold significant functional and evolutionary importance.Numerous ongoing CNV studies aim to elucidate the etiology of human diseases and gain insights into the population structure of livestock.High-density chips have enabled the detection of CNV with increased resolution,leading to the identification of even small CNV.This study aimed to identify CNV in local Italian chicken breeds and investigate their distribution across the genome.Results Copy number variants were mainly distributed across the first six chromosomes and primarily associated with loss type CNV.The majority of CNV in the investigated breeds were of types 0 and 1,and the minimum length of CNV was significantly larger than that reported in previous studies.Interestingly,a high proportion of the length of chromosome 16 was covered by copy number variation regions(CNVR),with the major histocompatibility complex being the likely cause.Among the genes identified within CNVR,only those present in at least five animals across breeds(n=95)were discussed to reduce the focus on redundant CNV.Some of these genes have been associated to functional traits in chickens.Notably,several CNVR on different chromosomes harbor genes related to muscle development,tissue-specific biological processes,heat stress resistance,and immune response.Quantitative trait loci(QTL)were also analyzed to investigate potential overlapping with the identified CNVR:54 out of the 95 gene-containing regions overlapped with 428 QTL associated to body weight and size,carcass characteristics,egg production,egg components,fat deposition,and feed intake.Conclusions The genomic phenomena reported in this study that can cause changes in the distribution of CNV within the genome over time and the comparison of these differences in CNVR of the local chicken breeds could help in preserving these genetic resources.

The first factor affecting dryland winter wheat grain yield under various mulching measures: Spike number

Water is the key factor limiting dryland wheat grain yield.Mulching affects crop yield and yield components by affecting soil moisture.Further research is needed to determine the relationships between yield components and soil moisture with yield,and to identify the most important factor affecting grain yield under various mulching measures.A long-term 9-yearifeld experiment in the Loess Plateau of Northwest China was carried out with three treatments:no mulch (CK),plastic mulch (M_(P)) and straw mulch (M_(S)).Yield factors and soil moisture were measured,and the relationships between them were explored by correlation analysis,structural equation modeling and significance analysis.The results showed that compared with CK,the average grain yields of M_(P) and M_(S) increased by 13.0and 10.6%,respectively.The average annual grain yield of the M_(P) treatment was 134 kg ha^(–1) higher than the M_(S) treatment.There were no significant differences in yield components among the three treatments (P<0.05).Soil water storage of the M_(S) treatment was greater than the M_(P) treatment,although the differences were not statistically signifiant.Soil water storage during the summer fallow period (SWSSF) and soil water storage before sowing (SWSS) of M_(S) were significantly higher than in CK,which increased by 38.5 and 13.6%,respectively.The relationship between M_(P) and CK was not statistically significant for SWSSF,but the SWSS in M_(P) was significantly higher than in CK.In terms of soil water storage after harvest (SWSH) and water consumption in the growth period(ET),there were no signi?cant differences among the three treatments.Based on the three analysis methods,we found that spike number and ET were positively correlated with grain yield.However,the relative importance of spike number to yield was the greatest in the M_(P )and M_(S) treatments,while that of ET was the greatest in CK.Suifcient SWSSF could indirectly increase spike number and ET in the three treatments.Based on these results,mulch can improve yield and soil water storage.The most important factor affecting the grain yield of dryland wheat was spike number under mulching,and ET with CK.These findings may help us to understand the main factors influencing dryland wheat grain yield under mulching conditions compared to CK.

Analysis of Helical Gear System Dynamic Response Based on Fuzzy Numbers

A non-linear dynamic model with the single degree of freedom of a helical gear pair introducing frzzy numbers is developed. In this proposed model, time-variant mesh stiffness, which is a non-linear parameter, mesh damping and composite error of a pair of meshing tooth of the gear pair are all included. Mesh stiffness is calculated by expressing Bo (r) as a Fourier series. Ⅱshape function is introduced as the membership function to characterize the fuzziness of the error. Fuzzy displacement dynamic response of the geared system at A- level, which is a closed interval, is ohtained by removing the fuzziness of the fuzzy differential equations and using Runge-Kutta numerical method. In fact, the fuzzy dynamic response and dynamic loading factor are aH the interval functions related λ. The result obtained here can be used to the fuzzy dynamic optimization design course of the helical gear system. The main advantage of this method is to introduce the concept of fuzzy number for the first time to the analysis of the gear system dynamics.

Quantum phase distribution and the number-phase Wigner function of the generalized squeezed vacuum states associated with solvable quantum systems

The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.

On the Solutions of Difference Equation Systems with Padovan Numbers

In this study, we investigate the form of the solutions of the following rational difference equation systems? , , such that their solutions are associated with Padovan numbers.

Coupling-matrix approach to the Chern number calculation in disordered systems

The Chern number is often used to distinguish different topological phases of matter in two-dimensional electron systems. A fast and efficient coupling-matrix method is designed to calculate the Chern number in finite crystalline and disordered systems. To show its effectiveness, we apply the approach to the Haldane model and the lattice Hofstadter model, and obtain the correct quantized Chern numbers. The disorder-induced topological phase transition is well reproduced, when the disorder strength is increased beyond the critical value. We expect the method to be widely applicable to the study of topological quantum numbers.

The limit of the Boussinesq system of Rayleigh-Bénard convection as the Prandtl number approaches infinity

Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.