**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1820

# Search results for: point multiplication.

##### 1820 A Design of Elliptic Curve Cryptography Processor Based on SM2 over GF(p)

**Authors:**
Shiji Hu,
Lei Li,
Wanting Zhou,
Daohong Yang

**Abstract:**

The data encryption is the foundation of today’s communication. On this basis, to improve the speed of data encryption and decryption is always an important goal for high-speed applications. This paper proposed an elliptic curve crypto processor architecture based on SM2 prime field. Regarding hardware implementation, we optimized the algorithms in different stages of the structure. For modulo operation on finite field, we proposed an optimized improvement of the Karatsuba-Ofman multiplication algorithm and shortened the critical path through the pipeline structure in the algorithm implementation. Based on SM2 recommended prime field, a fast modular reduction algorithm is used to reduce 512-bit data obtained from the multiplication unit. The radix-4 extended Euclidean algorithm was used to realize the conversion between the affine coordinate system and the Jacobi projective coordinate system. In the parallel scheduling point operations on elliptic curves, we proposed a three-level parallel structure of point addition and point double based on the Jacobian projective coordinate system. Combined with the scalar multiplication algorithm, we added mutual pre-operation to the point addition and double point operation to improve the efficiency of the scalar point multiplication. The proposed ECC hardware architecture was verified and implemented on Xilinx Virtex-7 and ZYNQ-7 platforms, and each 256-bit scalar multiplication operation took 0.275ms. The performance for handling scalar multiplication is 32 times that of CPU (dual-core ARM Cortex-A9).

**Keywords:**
Elliptic curve cryptosystems,
SM2,
modular
multiplication,
point multiplication.

##### 1819 A Reduced-Bit Multiplication Algorithm for Digital Arithmetic

**Authors:**
Harpreet Singh Dhillon,
Abhijit Mitra

**Abstract:**

A reduced-bit multiplication algorithm based on the ancient Vedic multiplication formulae is proposed in this paper. Both the Vedic multiplication formulae, Urdhva tiryakbhyam and Nikhilam, are first discussed in detail. Urdhva tiryakbhyam, being a general multiplication formula, is equally applicable to all cases of multiplication. It is applied to the digital arithmetic and is shown to yield a multiplier architecture which is very similar to the popular array multiplier. Due to its structure, it leads to a high carry propagation delay in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in the multiplication of large numbers as it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and is further optimized by use of some general arithmetic operations such as expansion and bit-shifting to take advantage of bit-reduction in multiplication. We illustrate the proposed algorithm by reducing a general 4x4-bit multiplication to a single 2 x 2-bit multiplication operation.

**Keywords:**
Multiplication,
algorithm,
Vedic mathematics,
digital
arithmetic,
reduced-bit.

##### 1818 Efficient Hardware Implementation of an Elliptic Curve Cryptographic Processor Over GF (2 163)

**Authors:**
Massoud Masoumi,
Hosseyn Mahdizadeh

**Abstract:**

A new and highly efficient architecture for elliptic curve scalar point multiplication which is optimized for a binary field recommended by NIST and is well-suited for elliptic curve cryptographic (ECC) applications is presented. To achieve the maximum architectural and timing improvements we have reorganized and reordered the critical path of the Lopez-Dahab scalar point multiplication architecture such that logic structures are implemented in parallel and operations in the critical path are diverted to noncritical paths. With G=41, the proposed design is capable of performing a field multiplication over the extension field with degree 163 in 11.92 s with the maximum achievable frequency of 251 MHz on Xilinx Virtex-4 (XC4VLX200) while 22% of the chip area is occupied, where G is the digit size of the underlying digit-serial finite field multiplier.

**Keywords:**
Elliptic curve cryptography,
FPGA implementation,
scalar point multiplication.

##### 1817 The Fallacy around Inserting Brackets to Evaluate Expressions Involving Multiplication and Division

**Authors:**
Manduth Ramchander

**Abstract:**

Evaluating expressions involving multiplication and division can give rise to the fallacy that brackets can be arbitrarily inserted into expressions involving multiplication and division. The aim of this article was to draw upon mathematical theory to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division and in particular in expressions where division precedes multiplication. In doing so, it demonstrates that the notion that two different answers are possible, when evaluating expressions involving multiplication and division, is indeed a false one. Searches conducted in a number of scholarly databases unearthed the rules to be applied when removing brackets from expressions, which revealed that consideration needs to be given to sign changes when brackets are removed. The rule pertaining to expressions involving multiplication and division was then extended upon, in its reverse format, to prove that brackets cannot be arbitrarily inserted into expressions involving multiplication and division. The application of the rule demonstrates that an expression involving multiplication and division can have only one correct answer. It is recommended that both the rule and its reverse be included in the curriculum, preferably at the juncture when manipulation with brackets is introduced.

**Keywords:**
Brackets,
multiplication,
division,
operations,
order.

##### 1816 Novel Method for Elliptic Curve Multi-Scalar Multiplication

**Authors:**
Raveen R. Goundar,
Ken-ichi Shiota,
Masahiko Toyonaga

**Abstract:**

**Keywords:**
elliptic curve cryptosystems,
multi-scalar multiplication,
addition chains,
Fibonacci sequence.

##### 1815 Modified Montgomery for RSA Cryptosystem

**Authors:**
Rupali Verma,
Maitreyee Dutta,
Renu Vig

**Abstract:**

Encryption and decryption in RSA are done by modular exponentiation which is achieved by repeated modular multiplication. Hence efficiency of modular multiplication directly determines the efficiency of RSA cryptosystem. This paper designs a Modified Montgomery Modular Multiplication in which addition of operands is computed by 4:2 compressor. The basic logic operations in addition are partitioned over two iterations such that parallel computations are performed. This reduces the critical path delay of proposed Montgomery design. The proposed design and RSA are implemented on Virtex 2 and Virtex 5 FPGAs. The two factors partitioning and parallelism have improved the frequency and throughput of proposed design.

**Keywords:**
RSA,
Montgomery modular multiplication,
4:2 compressor,
FPGA.

##### 1814 An Efficient Architecture for Interleaved Modular Multiplication

**Authors:**
Ahmad M. Abdel Fattah,
Ayman M. Bahaa El-Din,
Hossam M.A. Fahmy

**Abstract:**

**Keywords:**
Montgomery multiplication,
modular multiplication,
efficient architecture,
FPGA,
RSA

##### 1813 A High-Speed Multiplication Algorithm Using Modified Partial Product Reduction Tree

**Authors:**
P. Asadee

**Abstract:**

**Keywords:**
adder,
CMOS,
counter,
Dadda tree,
encoder.

##### 1812 Efficient Semi-Systolic Finite Field Multiplier Using Redundant Basis

**Authors:**
Hyun-Ho Lee,
Kee-Won Kim

**Abstract:**

**Keywords:**
Finite field,
Montgomery multiplication,
systolic array,
cryptography.

##### 1811 Some Characteristics of Systolic Arrays

**Authors:**
Halil Snopce,
Ilir Spahiu

**Abstract:**

**Keywords:**
Data dependences,
matrix multiplication,
systolicarray,
transformation matrix.

##### 1810 Very Large Scale Integration Architecture of Finite Impulse Response Filter Implementation Using Retiming Technique

**Authors:**
S. Jalaja,
A. M. Vijaya Prakash

**Abstract:**

**Keywords:**
Carry save adder Karatsuba multiplication,
mid-range Karatsuba multiplication,
modified FFA,
transposed filter,
retiming.

##### 1809 The Impact of Video Games in Children-s Learning of Mathematics

**Authors:**
Muhammad Ridhuan Tony Lim Abdullah,
Zulqarnain Abu Bakar,
Razol Mahari Ali,
Ibrahima Faye,
Hilmi Hasan

**Abstract:**

This paper describes a research project on Year 3 primary school students in Malaysia in their use of computer-based video game to enhance learning of multiplication facts (tables) in the Mathematics subject. This study attempts to investigate whether video games could actually contribute to positive effect on children-s learning or otherwise. In conducting this study, the researchers assume a neutral stand in the investigation as an unbiased outcome of the study would render reliable response to the impact of video games in education which would contribute to the literature of technology-based education as well as impact to the pedagogical aspect of formal education. In order to conduct the study, a subject (Mathematics) with a specific topic area in the subject (multiplication facts) is chosen. The study adopts a causal-comparative research to investigate the impact of the inclusion of a computer-based video game designed to teach multiplication facts to primary level students. Sample size is 100 students divided into two i.e., A: conventional group and B conventional group aided by video games. The conventional group (A) would be taught multiplication facts (timetables) and skills conventionally. The other group (B) underwent the same lessons but with supplementary activity: a computer-based video game on multiplication which is called Timez-Attack. Analysis of marks accrued from pre-test will be compared to post- test using comparisons of means, t tests, and ANOVA tests to investigate the impact of computer games as an added learning activity. The findings revealed that video games as a supplementary activity to classroom learning brings significant and positive effect on students- retention and mastery of multiplication tables as compared to students who rely only upon formal classroom instructions.

**Keywords:**
Technology for education,
Gaming for education,
Computer-based video games,
Cognitive learning

##### 1808 A Novel Recursive Multiplierless Algorithm for 2-D DCT

**Authors:**
V.K.Ananthashayana,
Geetha.K.S

**Abstract:**

**Keywords:**
DCT,
Multilplerless,
Ramanujan Number,
Recursive.

##### 1807 New Scheme in Determining nth Order Diagrams for Cross Multiplication Method via Combinatorial Approach

**Authors:**
Sharmila Karim,
Haslinda Ibrahim,
Zurni Omar

**Abstract:**

In this paper, a new recursive strategy is proposed for determining $\frac{(n-1)!}{2}$ of $n$th order diagrams. The generalization of $n$th diagram for cross multiplication method were proposed by Pavlovic and Bankier but the specific rule of determining $\frac{(n-1)!}{2}$ of the $n$th order diagrams for square matrix is yet to be discovered. Thus using combinatorial approach, $\frac{(n-1)!}{2}$ of the $n$th order diagrams will be presented as $\frac{(n-1)!}{2}$ starter sets. These starter sets will be generated based on exchanging one element. The advantages of this new strategy are the discarding process was eliminated and the sign of starter set is alternated to each others.

**Keywords:**
starter sets,
permutation,
exchanging one element,
determinant

##### 1806 Performance Analysis and Optimization for Diagonal Sparse Matrix-Vector Multiplication on Machine Learning Unit

**Authors:**
Qiuyu Dai,
Haochong Zhang,
Xiangrong Liu

**Abstract:**

Efficient matrix-vector multiplication with diagonal sparse matrices is pivotal in a multitude of computational domains, ranging from scientific simulations to machine learning workloads. When encoded in the conventional Diagonal (DIA) format, these matrices often induce computational overheads due to extensive zero-padding and non-linear memory accesses, which can hamper the computational throughput, and elevate the usage of precious compute and memory resources beyond necessity. The ’DIA-Adaptive’ approach, a methodological enhancement introduced in this paper, confronts these challenges head-on by leveraging the advanced parallel instruction sets embedded within Machine Learning Units (MLUs). This research presents a thorough analysis of the DIA-Adaptive scheme’s efficacy in optimizing Sparse Matrix-Vector Multiplication (SpMV) operations. The scope of the evaluation extends to a variety of hardware architectures, examining the repercussions of distinct thread allocation strategies and cluster configurations across multiple storage formats. A dedicated computational kernel, intrinsic to the DIA-Adaptive approach, has been meticulously developed to synchronize with the nuanced performance characteristics of MLUs. Empirical results, derived from rigorous experimentation, reveal that the DIA-Adaptive methodology not only diminishes the performance bottlenecks associated with the DIA format but also exhibits pronounced enhancements in execution speed and resource utilization. The analysis delineates a marked improvement in parallelism, showcasing the DIA-Adaptive scheme’s ability to adeptly manage the interplay between storage formats, hardware capabilities, and algorithmic design. The findings suggest that this approach could set a precedent for accelerating SpMV tasks, thereby contributing significantly to the broader domain of high-performance computing and data-intensive applications.

**Keywords:**
Adaptive method,
DIA,
diagonal sparse matrices,
MLU,
sparse matrix-vector multiplication.

##### 1805 Callusing in Stevia rebaudiana (Natural Sweetener) for Steviol Glycoside Production

**Authors:**
Pratibha Gupta,
Satyawati Sharma,
Sanjay Saxena

**Abstract:**

**Keywords:**
2,
4-D,
Callusing,
NAA,
Stevia,
Steviol glycosides

##### 1804 Solving 94-bit ECDLP with 70 Computers in Parallel

**Authors:**
Shunsuke Miyoshi,
Yasuyuki Nogami,
Takuya Kusaka,
Nariyoshi Yamai

**Abstract:**

**Keywords:**
Pollard’s rho method,
BN curve,
Montgomery
multiplication.

##### 1803 Influence of Cyperus rotundus Active Principles Inhibit Viral Multiplication and Stimulate Immune System in Indian White Shrimp Fenneropenaeus indicus against White Spot Syndrome Virus Infection

**Authors:**
T. Citarasu,
M. Michaelbabu V. N. Vakharia

**Abstract:**

The rhizome of Java grass, Cyperus rotundus was extracted different organic polar and non-polar solvents and performed the in vitro antiviral and immunostimulant activities against White Spot Syndrome Virus (WSSV) and Vibrio harveyi respectively. Based on the initial screening the ethyl acetate extract of C. rotundus was strong activities and further it was purified through silica column chromatography and the fractions were screened again for antiviral and immunostimulant activity. Among the different fractions screened against the WSSV and V. harveyi, the fractions, FIII to FV had strong activities. In order to study the in vivo influence of C. rotundus, the fractions (F-III to FV) were pooled and delivered to the F. indicus through artificial feed for 30 days. After the feeding trail the experimental and control diet fed F. indicus were challenged with virulent WSSV and studied the survival, molecular diagnosis, biochemical, haematological, and immunological parameters. Surprisingly, the pooled fractions (F-IV to FVI) incorporated diets helped to significantly (P<0.01) suppressed viral multiplication, showed significant (P<0.01) differences in protein and glucose levels, improved total haemocyte count (THC), coagulase activity, significantly increased (P <= 0.001) prophenol oxidase and intracellular superoxide anion production compared to the control shrimps. Based on the results, C. rotundus extracts effectively suppressed WSSV multiplication and improve the immune system in F. indicus against WSSV infection and this knowledge will helps to develop novel drugs from C. rotundus against WSSV.

**Keywords:**
Antiviral drugs,
Cyperus rotundus,
Fenneropenaeus
indicus,
WSSV.

##### 1802 A Finite Point Method Based on Directional Derivatives for Diffusion Equation

**Authors:**
Guixia Lv,
Longjun Shen

**Abstract:**

**Keywords:**
Finite point method,
directional derivatives,
diffusionequation,
method for selecting neighbor point set.

##### 1801 On Finite Wordlength Properties of Block-Floating-Point Arithmetic

**Authors:**
Abhijit Mitra

**Abstract:**

**Keywords:**
Block floating point,
Roundoff error,
Block exponent dis-tribution fuction,
Signal factor.

##### 1800 Simulation Tools for Fixed Point DSP Algorithms and Architectures

**Authors:**
K. B. Cullen,
G. C. M. Silvestre,
N. J. Hurley

**Abstract:**

This paper presents software tools that convert the C/Cµ floating point source code for a DSP algorithm into a fixedpoint simulation model that can be used to evaluate the numericalperformance of the algorithm on several different fixed pointplatforms including microprocessors, DSPs and FPGAs. The tools use a novel system for maintaining binary point informationso that the conversion from floating point to fixed point isautomated and the resulting fixed point algorithm achieves maximum possible precision. A configurable architecture is used during the simulation phase so that the algorithm can produce a bit-exact output for several different target devices.

**Keywords:**
DSP devices,
DSP algorithm,
simulation model,
software

##### 1799 Efficient Large Numbers Karatsuba-Ofman Multiplier Designs for Embedded Systems

**Authors:**
M.Machhout,
M.Zeghid,
W.El hadj youssef,
B.Bouallegue,
A.Baganne,
R.Tourki

**Abstract:**

**Keywords:**
finite field,
Karatsuba-Ofman,
long numbers,
multiplication,
mathematical model,
recursivity.

##### 1798 Effective Security Method for Wireless LAN using Life-Cycle of Wireless Access Point

**Authors:**
Soon-Tai Park,
Haeryong Park,
Myoung-sun Noh,
Yoo-Jae Won

**Abstract:**

**Keywords:**
Wireless LAN Security,
Wi-Fi Security,
Wireless Access Point,
Product Life-Cycle

##### 1797 PointNetLK-OBB: A Point Cloud Registration Algorithm with High Accuracy

**Authors:**
Wenhao Lan,
Ning Li,
Qiang Tong

**Abstract:**

To improve the registration accuracy of a source point cloud and template point cloud when the initial relative deflection angle is too large, a PointNetLK algorithm combined with an oriented bounding box (PointNetLK-OBB) is proposed. In this algorithm, the OBB of a 3D point cloud is used to represent the macro feature of source and template point clouds. Under the guidance of the iterative closest point algorithm, the OBB of the source and template point clouds is aligned, and a mirror symmetry effect is produced between them. According to the fitting degree of the source and template point clouds, the mirror symmetry plane is detected, and the optimal rotation and translation of the source point cloud is obtained to complete the 3D point cloud registration task. To verify the effectiveness of the proposed algorithm, a comparative experiment was performed using the publicly available ModelNet40 dataset. The experimental results demonstrate that, compared with PointNetLK, PointNetLK-OBB improves the registration accuracy of the source and template point clouds when the initial relative deflection angle is too large, and the sensitivity of the initial relative position between the source point cloud and template point cloud is reduced. The primary contribution of this paper is the use of PointNetLK to avoid the non-convex problem of traditional point cloud registration and leveraging the regularity of the OBB to avoid the local optimization problem in the PointNetLK context.

**Keywords:**
Mirror symmetry,
oriented bounding box,
point cloud registration,
PointNetLK-OBB.

##### 1796 Balancing of Quad Tree using Point Pattern Analysis

**Authors:**
Amitava Chakraborty,
Sudip Kumar De,
Ranjan Dasgupta

**Abstract:**

**Keywords:**
Algorithm,
Height balanced tree,
Point patternanalysis,
Point quad tree.

##### 1795 Image Rotation Using an Augmented 2-Step Shear Transform

**Authors:**
Hee-Choul Kwon,
Heeyong Kwon

**Abstract:**

**Keywords:**
High speed rotation operation,
image rotation,
transform matrix,
image processing,
pattern recognition.

##### 1794 Single Spectrum End Point Predict of BOF with SVM

**Authors:**
Ling-fei Xu,
Qi Zhao,
Yan-ru Chen,
Mu-chun Zhou,
Meng Zhang,
Shi-xue Xu

**Abstract:**

SVM ( Support Vector Machine ) is a new method in the artificial neural network ( ANN ). In the steel making, how to use computer to predict the end point of BOF accuracy is a great problem. A lot of method and theory have been claimed, but most of the results is not satisfied. Now the hot topic in the BOF end point predicting is to use optical way the predict the end point in the BOF. And we found that there exist some regular in the characteristic curve of the flame from the mouse of pudding. And we can use SVM to predict end point of the BOF, just single spectrum intensity should be required as the input parameter. Moreover, its compatibility for the input space is better than the BP network.

**Keywords:**
SVM,
predict,
BOF,
single spectrum intensity.

##### 1793 Scalable Systolic Multiplier over Binary Extension Fields Based on Two-Level Karatsuba Decomposition

**Authors:**
Chiou-Yng Lee,
Wen-Yo Lee,
Chieh-Tsai Wu,
Cheng-Chen Yang

**Abstract:**

Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit level and digi -level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba schemes, and used that to derive a novel scalable multiplier architecture. Analytical results show that the proposed multiplier provides a trade-off between space and time complexities. Our proposed multiplier is modular, regular, and suitable for very large scale integration (VLSI) implementations. It involves less area complexity compared to the multipliers based on traditional decomposition methods. It is therefore, more suitable for efficient hardware implementation of pairing based cryptography and elliptic curve cryptography (ECC) in constraint driven applications.

**Keywords:**
Digit-serial systolic multiplier,
elliptic curve
cryptography (ECC),
Karatsuba algorithm (KA),
shifted polynomial
basis (SPB),
pairing computation.

##### 1792 MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's

**Authors:**
J. Sulaiman,
M. Othman,
M. K. Hasan

**Abstract:**

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

**Keywords:**
MEG iteration,
second-order finite difference,
weighted parameter.

##### 1791 Dimension Free Rigid Point Set Registration in Linear Time

**Authors:**
Jianqin Qu

**Abstract:**

**Keywords:**
Covariant point,
point matching,
dimension free,
rigid
registration.