Results 1  10
of
95
KARATSUBA ALGORITHM
, 2005
"... The Karatsuba algorithm (KA) for multiplying two polynomials was introduced in 1962 [3]. It saves coefficient multiplications at the cost of extra additions compared to the schoolbook or ordinary multiplication method. The basic KA is performed as follows. Consider two degree1 polynomials A(x) and ..."
Abstract
 Add to MetaCart
The Karatsuba algorithm (KA) for multiplying two polynomials was introduced in 1962 [3]. It saves coefficient multiplications at the cost of extra additions compared to the schoolbook or ordinary multiplication method. The basic KA is performed as follows. Consider two degree1 polynomials A
Generalizations of the Karatsuba Algorithm for Efficient Implementations
 Department of
, 2006
"... In this work we generalize the classical Karatsuba Algorithm (KA) for polynomial multiplication to (i) polynomials of arbitrary degree and (ii) recursive use. We determine exact complexity expressions for the KA and focus on how to use it with the least number of operations. We develop a rule for th ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
In this work we generalize the classical Karatsuba Algorithm (KA) for polynomial multiplication to (i) polynomials of arbitrary degree and (ii) recursive use. We determine exact complexity expressions for the KA and focus on how to use it with the least number of operations. We develop a rule
Generalizations of the Karatsuba Algorithm for Polynomial Multiplication
"... In this work we generalize the classical Karatsuba Algorithm (KA) for polynomial multiplication to (i) polynomials of arbitrary degree and (ii) recursive use. We determine exact complexity expressions for the KA and focus on how to use it with the least number of operations. We develop a rule for th ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
In this work we generalize the classical Karatsuba Algorithm (KA) for polynomial multiplication to (i) polynomials of arbitrary degree and (ii) recursive use. We determine exact complexity expressions for the KA and focus on how to use it with the least number of operations. We develop a rule
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 ..."
Abstract
 Add to MetaCart
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
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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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
Using the Parallel Karatsuba Algorithm for Long Integer Multiplication and Division
 In European Conference on Parallel Processing
, 1997
"... . We experiment with sequential and parallel versions of the Karatsuba multiplication algorithm implemented under the paclib computer algebra system on a Sequent Symmetry sharedmemory architecture. In comparison with the classical multiplication algorithm, the sequential version gives a speedup of ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
. We experiment with sequential and parallel versions of the Karatsuba multiplication algorithm implemented under the paclib computer algebra system on a Sequent Symmetry sharedmemory architecture. In comparison with the classical multiplication algorithm, the sequential version gives a speed
Reversible Karatsuba’s Algorithm
"... Abstract: Karatsuba discovered the first algorithm that accomplishes multiprecision integer multiplication with complexity below that of the gradeschool method. This algorithm is implemented nowadays in computer algebra systems using irreversible logic. In this paper we describe reversible circuits ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract: Karatsuba discovered the first algorithm that accomplishes multiprecision integer multiplication with complexity below that of the gradeschool method. This algorithm is implemented nowadays in computer algebra systems using irreversible logic. In this paper we describe reversible
Comments on “five, Six, and SevenTerm KaratsubaLike Formulae
 IEEE Transactions on Computers
, 2007
"... We show that multiplication complexities of nterm KaratsubaLike formulae of GF (2)[x] (7 < n < 19) presented in the above paper can be further improved using the Chinese Remainder Theorem and the construction multiplication modulo (x − ∞) w. Index Terms Karatsuba algorithm, polynomial multip ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
We show that multiplication complexities of nterm KaratsubaLike formulae of GF (2)[x] (7 < n < 19) presented in the above paper can be further improved using the Chinese Remainder Theorem and the construction multiplication modulo (x − ∞) w. Index Terms Karatsuba algorithm, polynomial
Comments on Montgomery’s “Five, Six, and SevenTerm KaratsubaLike Formulae”
"... We show that multiplication complexities of nterm KaratsubaLike formulae (7 < n < 19) in the above paper can be further improved using the Chinese Remainder Theorem and the construction multiplication modulo (x − ∞) w. Index Terms Karatsuba algorithm, polynomial multiplication, finite field. ..."
Abstract
 Add to MetaCart
We show that multiplication complexities of nterm KaratsubaLike formulae (7 < n < 19) in the above paper can be further improved using the Chinese Remainder Theorem and the construction multiplication modulo (x − ∞) w. Index Terms Karatsuba algorithm, polynomial multiplication, finite field.
Practical Integer Division with Karatsuba Complexity
 Proc. ISSAC'97, 339341
, 1997
"... Combining Karatsuba multiplication with a technique developed by Krandick for computing the highorder part of the quotient, we obtain an integer division algorithm which is only two times slower, on average, than Karatsuba multiplication. The main idea is to delay part of the dividend update until ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
Combining Karatsuba multiplication with a technique developed by Krandick for computing the highorder part of the quotient, we obtain an integer division algorithm which is only two times slower, on average, than Karatsuba multiplication. The main idea is to delay part of the dividend update until
Results 1  10
of
95