Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm

Yasuyuki NOGAMI; Shigeru SHINONAGA; Yoshitaka MORIKAWA

doi:10.1093/ietfec/e88-a.5.1200

Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm

Yasuyuki NOGAMI, Shigeru SHINONAGA, Yoshitaka MORIKAWA

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This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF F_p⁵ is about 20% faster than those in OEF F_p⁵. Then, since CVMA is suitable for parallel processing, we show that TypeII AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.5 pp.1200-1208

Publication Date: 2005/05/01

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DOI: 10.1093/ietfec/e88-a.5.1200

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

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Yasuyuki NOGAMI, Shigeru SHINONAGA, Yoshitaka MORIKAWA, "Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 5, pp. 1200-1208, May 2005, doi: 10.1093/ietfec/e88-a.5.1200.
Abstract: This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF F_p⁵ is about 20% faster than those in OEF F_p⁵. Then, since CVMA is suitable for parallel processing, we show that TypeII AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.5.1200/_p

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@ARTICLE{e88-a_5_1200,
author={Yasuyuki NOGAMI, Shigeru SHINONAGA, Yoshitaka MORIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm},
year={2005},
volume={E88-A},
number={5},
pages={1200-1208},
abstract={This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF F_p⁵ is about 20% faster than those in OEF F_p⁵. Then, since CVMA is suitable for parallel processing, we show that TypeII AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.},
keywords={},
doi={10.1093/ietfec/e88-a.5.1200},
ISSN={},
month={May},}

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TY - JOUR
TI - Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1200
EP - 1208
AU - Yasuyuki NOGAMI
AU - Shigeru SHINONAGA
AU - Yoshitaka MORIKAWA
PY - 2005
DO - 10.1093/ietfec/e88-a.5.1200
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2005
AB - This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF F_p⁵ is about 20% faster than those in OEF F_p⁵. Then, since CVMA is suitable for parallel processing, we show that TypeII AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.
ER -