IEICE TRANSACTIONS on Fundamentals
Fast Implementation of Extension Fields with TypeII ONB and Cyclic Vector Multiplication Algorithm
Summary :
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 Fp5 is about 20% faster than those in OEF Fp5. 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
- Publicized
- Online ISSN
- DOI
- 10.1093/ietfec/e88-a.5.1200
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
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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 Fp5 is about 20% faster than those in OEF Fp5. 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://global.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 Fp5 is about 20% faster than those in OEF Fp5. 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 Fp5 is about 20% faster than those in OEF Fp5. 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 -
English
