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A VLSI algorithm for division in GF(2^{m}) with the canonical basis representation is proposed. It is based on the extended Binary GCD algorithm for GF(2^{m}), and performs division through iteration of simple operations, such as shifts and bitwise exclusive-OR operations. A divider in GF(2^{m}) based on the algorithm has a linear array structure with a bit-slice feature and carries out division in 2*m* clock cycles. The amount of hardware of the divider is proportional to *m* and the depth is a constant independent of *m*.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.5 pp.994-999

- Publication Date
- 2002/05/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

- Category

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Yasuaki WATANABE, Naofumi TAKAGI, Kazuyoshi TAKAGI, "A VLSI Algorithm for Division in GF(2m) Based on Extended Binary GCD Algorithm" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 5, pp. 994-999, May 2002, doi: .

Abstract: A VLSI algorithm for division in GF(2^{m}) with the canonical basis representation is proposed. It is based on the extended Binary GCD algorithm for GF(2^{m}), and performs division through iteration of simple operations, such as shifts and bitwise exclusive-OR operations. A divider in GF(2^{m}) based on the algorithm has a linear array structure with a bit-slice feature and carries out division in 2*m* clock cycles. The amount of hardware of the divider is proportional to *m* and the depth is a constant independent of *m*.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_5_994/_p

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@ARTICLE{e85-a_5_994,

author={Yasuaki WATANABE, Naofumi TAKAGI, Kazuyoshi TAKAGI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A VLSI Algorithm for Division in GF(2m) Based on Extended Binary GCD Algorithm},

year={2002},

volume={E85-A},

number={5},

pages={994-999},

abstract={A VLSI algorithm for division in GF(2^{m}) with the canonical basis representation is proposed. It is based on the extended Binary GCD algorithm for GF(2^{m}), and performs division through iteration of simple operations, such as shifts and bitwise exclusive-OR operations. A divider in GF(2^{m}) based on the algorithm has a linear array structure with a bit-slice feature and carries out division in 2*m* clock cycles. The amount of hardware of the divider is proportional to *m* and the depth is a constant independent of *m*.},

keywords={},

doi={},

ISSN={},

month={May},}

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TY - JOUR

TI - A VLSI Algorithm for Division in GF(2m) Based on Extended Binary GCD Algorithm

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 994

EP - 999

AU - Yasuaki WATANABE

AU - Naofumi TAKAGI

AU - Kazuyoshi TAKAGI

PY - 2002

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E85-A

IS - 5

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - May 2002

AB - A VLSI algorithm for division in GF(2^{m}) with the canonical basis representation is proposed. It is based on the extended Binary GCD algorithm for GF(2^{m}), and performs division through iteration of simple operations, such as shifts and bitwise exclusive-OR operations. A divider in GF(2^{m}) based on the algorithm has a linear array structure with a bit-slice feature and carries out division in 2*m* clock cycles. The amount of hardware of the divider is proportional to *m* and the depth is a constant independent of *m*.

ER -