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VLSI Implementation of Karatsuba Algorithm and Its Evaluation

by Syunji Yazaki, Kôki Abe
"... VLSI implementation of Karatsuba algorithm for multi-digit multiplication was investigated. We designed 32-bit recursive Karatsuba multiplier (RKM) and found that its critical path delay and area cost are 9.44ns and 0.228mm 2, respectively. Next we designed and evaluated RKM of larger bits. For bit ..."
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VLSI implementation of Karatsuba algorithm for multi-digit multiplication was investigated. We designed 32-bit recursive Karatsuba multiplier (RKM) and found that its critical path delay and area cost are 9.44ns and 0.228mm 2, respectively. Next we designed and evaluated RKM of larger bits. For bit

VLSI Design of Karatsuba Integer Multipliers and Its Evaluation

by Syunji Yazaki, Koki Abe
"... Multidigit multiplication is widely used for various applications in recent years, including numerical calcula-tion, chaos arithmetic, and primality testing. Systems with high performance and low energy consumption are de-manded, especially for image processing and communica-tions with cryptography ..."
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using chaos. Karatsuba algorithm with computational complexity of O(n1.58) has been em-ployed in software for multiplication of hundreds to thou-sands of bits, where n stands for bit-length of operands. In this paper, hardware design of multidigit integer multipli-cation based on Karatsuba algorithm

Index Terms-ECC, Double Point Multiplication, Karatsuba Multiplier and Systolic Multiplier

by Sunil Devidas Bobade , Vijay R Mankar
"... Abstract-Elliptic Curve Cryptography is one of the most preferred public key Cryptography algorithms known for its security strength and reduced key size. This makes ECC most suitable for implementing the hardware security chip for providing security services in portable embedded devices. This pape ..."
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reduction, new low footprint hybrid multiplier is integrated. This hybrid multiplier integrates traditional Karatsuba Multiplier with systolic multiplier. The proposed hybrid multiplier does the initial recursion using the systolic algorithm while final small sized multiplications are accomplished using

Efficient Large Numbers Karatsuba-Ofman Multiplier Designs for Embedded Systems

by M. Machhout, M. Zeghid, W. El Hadj Youssef, B. Bouallegue, A. Baganne, R. Tourki
"... Abstract—Long number multiplications (n ≥ 128-bit) are a primitive in most cryptosystems. They can be performed better by using Karatsuba-Ofman 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 Karatsuba-Ofman algorithm is fast but is highly recursive. In this paper, we propose different designs of implementing Karatsuba-Ofman multiplier. A mixture of sequential and combinational system design techniques involving pipelining is applied to our proposed designs

An Efficient Elliptic Curve Scalar Multiplication using Karatsuba Multiplier

by Christina Thomas, Gnana Sheela K, Saranya P Krishnan
"... 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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for high performance applications. It includes classical polynomial multiplier, recursive Karatsuba multiplier and hybrid Karatsuba multiplier. The simulation results show that hybrid Karatsuba multiplier consumes less area than the other two multipliers. The implementation of the elliptic curve point

A Less Recursive Variant of Karatsuba-Ofman Algorithm for Multiplying Operands of Size a Power of Two

by Serdar S. Erdem, Gebze Yüksek, Teknoloji Enstitüsü, Elektronik Mühendisli ˇgi Bölümü - Proc. 16th IEEE Symposium on Computer Arithmetic (Arith-16 2003 , 2003
"... We propose a new algorithm for fast multiplication of large integers having a precision of 2 k computer words, where k is an integer. The algorithm is derived from the Karatsuba-Ofman Algorithm and has the same asymptotic complexity. However, the running time of the new algorithm is slightly better, ..."
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We propose a new algorithm for fast multiplication of large integers having a precision of 2 k computer words, where k is an integer. The algorithm is derived from the Karatsuba-Ofman Algorithm and has the same asymptotic complexity. However, the running time of the new algorithm is slightly better

Five, Six, and Seven-Term Karatsuba-Like Formulae

by Peter L. Montgomery
"... Abstract—The Karatsuba-Ofman algorithm starts with a way to multiply two 2-term (i.e., linear) polynomials using three scalar multiplications. There is also a way to multiply two 3-term (i.e., quadratic) polynomials using six scalar multiplications. These are used within recursive constructions to m ..."
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Abstract—The Karatsuba-Ofman algorithm starts with a way to multiply two 2-term (i.e., linear) polynomials using three scalar multiplications. There is also a way to multiply two 3-term (i.e., quadratic) polynomials using six scalar multiplications. These are used within recursive constructions

Partially Interleaved Modular Karatsuba-Ofman Multiplication, preprint

by Gokay Saldamli , Yojin Baek , Levent Ertaul , 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 Karatsuba-Ofman 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 Karatsuba-Ofman multiplier and bipartite modular reduction, presents an interleaved processing

Design and implementation of long-digit Karatsuba’s multiplier using tensor product formulation

by Chin-bou Liu, Chua-huang Huang, Chin-laung Lei - In The Ninth Workshop on Compiler Techniques for HighPerformance Computing , 2003
"... Karatsuba’s multiplication algorithm uses three singledigit multiplications to perform one two-digit multiplication. If we apply Karatsuba’s multiplier recursively, it takes only 3 n single-digit multiplications to multiply a pair of 2 n-digit numbers. This is a significant improvement compared to 4 ..."
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Karatsuba’s multiplication algorithm uses three singledigit multiplications to perform one two-digit multiplication. If we apply Karatsuba’s multiplier recursively, it takes only 3 n single-digit multiplications to multiply a pair of 2 n-digit numbers. This is a significant improvement compared

International Journal of Electrical and Computer Engineering 4:9 2009 Efficient Large Numbers Karatsuba-Ofman Multiplier Designs for Embedded Systems

by M. Machhout, M. Zeghid, W. El Hadj Youssef, B. Bouallegue, A. Baganne, R. Tourki
"... Abstract—Long number multiplications (n ≥ 128-bit) are a primitive in most cryptosystems. They can be performed better by using Karatsuba-Ofman 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 Karatsuba-Ofman algorithm is fast but is highly recursive. In this paper, we propose different designs of implementing Karatsuba-Ofman multiplier. A mixture of sequential and combinational system design techniques involving pipelining is applied to our proposed designs
Results 1 - 10 of 42