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Mastrovito Multiplier for All Trinomials
 IEEE Trans. Computers
, 1999
"... An e cient algorithm for the multiplication in GF (2m)was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x m + x +1was given as m 2, 1 XOR and m 2 AND gates. In this paper, we describe an architecture based on a new formulation of the multip ..."
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Cited by 46 (3 self)
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of the multiplication matrix, and show that the Mastrovito multiplier for the generating trinomial x m + x n +1, where m 6 = 2n, also requires m 2, 1 XOR and m 2 AND gates. However, m 2, m=2 XOR gates are su cient when the generating trinomial is of the form x m + x m=2 +1 for an even m. We also calculate the time
Brief Contributions________________________________________________________________________________ Mastrovito Multiplier for
"... AbstractÐAn efficient algorithm for the multiplication in GF …2 m † was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x m ‡ x ‡ 1 was given as m 2 � 1 XOR and m 2 AND gates. In this paper, we describe an architecture based on a new formulat ..."
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formulation of the multiplication matrix and show that the Mastrovito multiplier for the generating trinomial x m ‡ x n ‡ 1, where m 6 ˆ 2n, also requires m 2 � 1 XOR and m 2 AND gates. However, m 2 � m=2 XOR gates are sufficient when the generating trinomial is of the form x m ‡ x m=2 ‡ 1 for an even m. We
Brief Contributions________________________________________________________________________________ Mastrovito Multiplier for General Irreducible Polynomials
"... AbstractÐWe present a new formulation of the Mastrovito multiplication matrix for the field GF…2 m † generated by an arbitrary irreducible polynomial. We study in detail several specific types of irreducible polynomials, e.g., trinomials, allonepolynomials, and equallyspacedpolynomials, and obtai ..."
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AbstractÐWe present a new formulation of the Mastrovito multiplication matrix for the field GF…2 m † generated by an arbitrary irreducible polynomial. We study in detail several specific types of irreducible polynomials, e.g., trinomials, allonepolynomials, and equally
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 ..."
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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
Abstract On fully parallel Karatsuba Multipliers for ¢¡¤£¦¥¨§�©
"... In this paper we present a new approach that generalizes the classic Karatsuba multiplier technique. In contrast with versions of this algorithm previously discussed [1, 2], in our approach we do not use composite fields to perform the ground field arithmetic. The most attractive feature of the new ..."
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In this paper we present a new approach that generalizes the classic Karatsuba multiplier technique. In contrast with versions of this algorithm previously discussed [1, 2], in our approach we do not use composite fields to perform the ground field arithmetic. The most attractive feature of the new
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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Cited by 1 (0 self)
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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
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 ..."
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Cited by 26 (0 self)
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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
Hardware Accelerator for the Tate Pairing in Characteristic Three Based on KaratsubaOfman Multipliers
 CHES 2009
, 2009
"... This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller’s loop based on a pipelined KaratsubaOfman multiplier. Thanks to a careful sel ..."
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Cited by 3 (2 self)
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This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller’s loop based on a pipelined KaratsubaOfman multiplier. Thanks to a careful
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 ..."
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Cited by 4 (1 self)
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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
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
Results 1  10
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