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Hardware Implementation of Efficient Modified Karatsuba Multiplier Used in Elliptic Curves
, 2009
"... The efficiency of the core Galois field arithmetic improves the performance of elliptic curve based public key cryptosystem implementation. This paper describes the design and implementation of a reconfigurable Galois field multiplier, which is implemented using field programmable gate arrays (FP ..."
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(FPGAs). The multiplier of Galois field based on Karatsuba’s divide and conquer algorithm allows for reasonable speedup of the toplevel public key algorithms. Binary Karatsuba multiplier is more efficient if it is truncated at nbit multiplicand level and use an efficient classic multiplier algorithm
An Efficient Elliptic Curve Scalar Multiplication using Karatsuba Multiplier
"... Abstract — In this era, network security is becoming a great concern.Cryptography offers high security for communication and networking. Elliptic Curve Cryptography is gaining attraction with their high level of security with low cost, small key size and smaller hardware realization. Elliptic curve ..."
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scalar multiplication is the most important operation in elliptic curve cryptosystems This paper develops a secure elliptic curve scalar multiplication using Karatsuba multiplier. Initially, three different finite field multipliers are simulated for the construction of an elliptic curve crypto processor
Volume 1 – No. 12 Cryptography by Karatsuba Multiplier with ASCII Codes
"... Abstract: In this paper we describe Cryptography by using Karatsuba multipliers and ASCII codes implementing through coordinate geometry for data encryption and decryption with its code in matlab. Elliptic curve cryptography is an asymmetric key cryptography. It includes (i) public key generation on ..."
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Abstract: In this paper we describe Cryptography by using Karatsuba multipliers and ASCII codes implementing through coordinate geometry for data encryption and decryption with its code in matlab. Elliptic curve cryptography is an asymmetric key cryptography. It includes (i) public key generation
Efficient Large Numbers KaratsubaOfman Multiplier Designs for Embedded Systems
"... Abstract—Long number multiplications (n ≥ 128bit) are a primitive in most cryptosystems. They can be performed better by using KaratsubaOfman technique. This algorithm is easy to parallelize on workstation network and on distributed memory, and it’s known as the practical method of choice. Multipl ..."
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. Multiplying long numbers using KaratsubaOfman algorithm is fast but is highly recursive. In this paper, we propose different designs of implementing KaratsubaOfman multiplier. A mixture of sequential and combinational system design techniques involving pipelining is applied to our proposed designs
Realtime visual tracking of complex structures
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... This paper presents a novel framework for threedimensional modelbased tracking. Graphical rendering technology is combined with constrained active contour tracking to create a robust wireframe tracking system. It operates in real time at video frame rate (25 Hz) on standard hardware. It is based ..."
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Cited by 226 (7 self)
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the motion computation problem into simple geometric terms so that tracking becomes a simple optimization problem solved by means of iterative reweighted least squares. A visual servoing system constructed using this framework is presented together with results showing the accuracy of the tracker. The system
IMPLEMENTATION OF KARATSUBA ALGORITHM USING POLYNOMIAL MULTIPLICATION
"... Efficiency in multiplication is very important in applications like signal processing, cryptosystems and coding theory. This paper presents the design of a fast multiplier using the Karatsuba algorithm to multiply two numbers using the technique of polynomial multiplication. The Karatsuba algorithm ..."
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Efficiency in multiplication is very important in applications like signal processing, cryptosystems and coding theory. This paper presents the design of a fast multiplier using the Karatsuba algorithm to multiply two numbers using the technique of polynomial multiplication. The Karatsuba algorithm
Lineartime dynamics using lagrange multipliers
 In SIGGRAPH 96 Conference Proceedings, Computer Graphics Proceedings, Annual Conference Series
, 1996
"... Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics ..."
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Cited by 139 (0 self)
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Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics
Five, Six, and SevenTerm KaratsubaLike Formulae
"... Abstract—The KaratsubaOfman algorithm starts with a way to multiply two 2term (i.e., linear) polynomials using three scalar multiplications. There is also a way to multiply two 3term (i.e., quadratic) polynomials using six scalar multiplications. These are used within recursive constructions to m ..."
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Abstract—The KaratsubaOfman algorithm starts with a way to multiply two 2term (i.e., linear) polynomials using three scalar multiplications. There is also a way to multiply two 3term (i.e., quadratic) polynomials using six scalar multiplications. These are used within recursive constructions
Partially Interleaved Modular KaratsubaOfman Multiplication, preprint
, 2011
"... Summary We describe a method of performing modular multiplication that has various applications in the field of modern cryptography and coding theory. The proposed algorithm, which combines the KaratsubaOfman multiplier and bipartite modular reduction, presents an interleaved processing on the upp ..."
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Summary We describe a method of performing modular multiplication that has various applications in the field of modern cryptography and coding theory. The proposed algorithm, which combines the KaratsubaOfman multiplier and bipartite modular reduction, presents an interleaved processing
KARATSUBA AND TOOMCOOK METHODS FOR MULTIVARIATE POLYNOMIALS
 ACTA UNIVERSITATIS APULENSIS
"... Karatsuba and ToomCook are wellknown methods used to efficiently multiply univariate polynomials and long integers. For multivariate polynomials, asymptotically good approaches like Kronecker’s trick combined with FFT become truly effective only when the degree is above some threshold. In this p ..."
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Karatsuba and ToomCook are wellknown methods used to efficiently multiply univariate polynomials and long integers. For multivariate polynomials, asymptotically good approaches like Kronecker’s trick combined with FFT become truly effective only when the degree is above some threshold
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