This study presents two new bit-parallel cellular multipliers based on an irreducible all one polynomial (AOP) over the finite field GF(2m). Using the property of the AOP, this work also presents an efficient algorithm of inner-product multiplication for computing AB2 multiplications is proposed, with a structure that can simplify the time and space complexity for hardware implementations. The first structure employs the new inner-product multiplication algorithm to construct the bit-parallel cellular architecture. The designed multiplier only requires the computational delays of (m+1)(TAND+TXOR). The second proposed structure is a modification of the first structure, and it requires (m+2) TXOR delays. Moreover, the proposed multipliers can perform A2iB2j computations by shuffling the coefficients to make i and j integers. For the computing multiplication in GF(2m), the novel multipliers turn out to be efficient as they simplify architecture and accelerate computation. The two novel architectures are highly regular, simpler, and have shorter computation delays than the conventional cellular multipliers.
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Chung-Hsin LIU, Nen-Fu HUANG, Chiou-Yng LEE, "Computation of AB2 Multiplier in GF(2m) Using an Efficient Low-Complexity Cellular Architecture" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 12, pp. 2657-2663, December 2000, doi: .
Abstract: This study presents two new bit-parallel cellular multipliers based on an irreducible all one polynomial (AOP) over the finite field GF(2m). Using the property of the AOP, this work also presents an efficient algorithm of inner-product multiplication for computing AB2 multiplications is proposed, with a structure that can simplify the time and space complexity for hardware implementations. The first structure employs the new inner-product multiplication algorithm to construct the bit-parallel cellular architecture. The designed multiplier only requires the computational delays of (m+1)(TAND+TXOR). The second proposed structure is a modification of the first structure, and it requires (m+2) TXOR delays. Moreover, the proposed multipliers can perform A2iB2j computations by shuffling the coefficients to make i and j integers. For the computing multiplication in GF(2m), the novel multipliers turn out to be efficient as they simplify architecture and accelerate computation. The two novel architectures are highly regular, simpler, and have shorter computation delays than the conventional cellular multipliers.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_12_2657/_p
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@ARTICLE{e83-a_12_2657,
author={Chung-Hsin LIU, Nen-Fu HUANG, Chiou-Yng LEE, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Computation of AB2 Multiplier in GF(2m) Using an Efficient Low-Complexity Cellular Architecture},
year={2000},
volume={E83-A},
number={12},
pages={2657-2663},
abstract={This study presents two new bit-parallel cellular multipliers based on an irreducible all one polynomial (AOP) over the finite field GF(2m). Using the property of the AOP, this work also presents an efficient algorithm of inner-product multiplication for computing AB2 multiplications is proposed, with a structure that can simplify the time and space complexity for hardware implementations. The first structure employs the new inner-product multiplication algorithm to construct the bit-parallel cellular architecture. The designed multiplier only requires the computational delays of (m+1)(TAND+TXOR). The second proposed structure is a modification of the first structure, and it requires (m+2) TXOR delays. Moreover, the proposed multipliers can perform A2iB2j computations by shuffling the coefficients to make i and j integers. For the computing multiplication in GF(2m), the novel multipliers turn out to be efficient as they simplify architecture and accelerate computation. The two novel architectures are highly regular, simpler, and have shorter computation delays than the conventional cellular multipliers.},
keywords={},
doi={},
ISSN={},
month={December},}
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TY - JOUR
TI - Computation of AB2 Multiplier in GF(2m) Using an Efficient Low-Complexity Cellular Architecture
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2657
EP - 2663
AU - Chung-Hsin LIU
AU - Nen-Fu HUANG
AU - Chiou-Yng LEE
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2000
AB - This study presents two new bit-parallel cellular multipliers based on an irreducible all one polynomial (AOP) over the finite field GF(2m). Using the property of the AOP, this work also presents an efficient algorithm of inner-product multiplication for computing AB2 multiplications is proposed, with a structure that can simplify the time and space complexity for hardware implementations. The first structure employs the new inner-product multiplication algorithm to construct the bit-parallel cellular architecture. The designed multiplier only requires the computational delays of (m+1)(TAND+TXOR). The second proposed structure is a modification of the first structure, and it requires (m+2) TXOR delays. Moreover, the proposed multipliers can perform A2iB2j computations by shuffling the coefficients to make i and j integers. For the computing multiplication in GF(2m), the novel multipliers turn out to be efficient as they simplify architecture and accelerate computation. The two novel architectures are highly regular, simpler, and have shorter computation delays than the conventional cellular multipliers.
ER -