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VLSI Implementation of Karatsuba Algorithm and Its Evaluation
"... VLSI implementation of Karatsuba algorithm for multidigit multiplication was investigated. We designed 32bit 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 multidigit multiplication was investigated. We designed 32bit 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
"... Multidigit multiplication is widely used for various applications in recent years, including numerical calculation, chaos arithmetic, and primality testing. Systems with high performance and low energy consumption are demanded, especially for image processing and communications with cryptography ..."
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using chaos. Karatsuba algorithm with computational complexity of O(n1.58) has been employed in software for multiplication of hundreds to thousands of bits, where n stands for bitlength of operands. In this paper, hardware design of multidigit integer multiplication based on Karatsuba algorithm
Index TermsECC, Double Point Multiplication, Karatsuba Multiplier and Systolic Multiplier
"... AbstractElliptic 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 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
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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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 KaratsubaOfman Algorithm for Multiplying Operands of Size a Power of Two
 Proc. 16th IEEE Symposium on Computer Arithmetic (Arith16 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 KaratsubaOfman 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 KaratsubaOfman Algorithm and has the same asymptotic complexity. However, the running time of the new algorithm is slightly better
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
Design and implementation of longdigit Karatsuba’s multiplier using tensor product formulation
 In The Ninth Workshop on Compiler Techniques for HighPerformance Computing
, 2003
"... Karatsuba’s multiplication algorithm uses three singledigit multiplications to perform one twodigit multiplication. If we apply Karatsuba’s multiplier recursively, it takes only 3 n singledigit multiplications to multiply a pair of 2 ndigit numbers. This is a significant improvement compared to 4 ..."
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Cited by 6 (4 self)
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Karatsuba’s multiplication algorithm uses three singledigit multiplications to perform one twodigit multiplication. If we apply Karatsuba’s multiplier recursively, it takes only 3 n singledigit multiplications to multiply a pair of 2 ndigit numbers. This is a significant improvement compared
International Journal of Electrical and Computer Engineering 4:9 2009 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
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