A Multiplication Algorithm in Fpm Such That p>m with a Special Class of Gauss Period Normal Bases
Summary :
In this paper, a multiplication algorithm in extension field Fpm is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic p and extension degree m only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p>m, 4p does not divide m(p-1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree m is small.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.1 pp.173-181
- Publication Date
- 2009/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.173
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
- Mathematics
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Hidehiro KATO, Yasuyuki NOGAMI, Tomoki YOSHIDA, Yoshitaka MORIKAWA, "A Multiplication Algorithm in Fpm Such That p>m with a Special Class of Gauss Period Normal Bases" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 1, pp. 173-181, January 2009, doi: 10.1587/transfun.E92.A.173.
Abstract: In this paper, a multiplication algorithm in extension field Fpm is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic p and extension degree m only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p>m, 4p does not divide m(p-1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree m is small.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.173/_p
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@ARTICLE{e92-a_1_173,
author={Hidehiro KATO, Yasuyuki NOGAMI, Tomoki YOSHIDA, Yoshitaka MORIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Multiplication Algorithm in Fpm Such That p>m with a Special Class of Gauss Period Normal Bases},
year={2009},
volume={E92-A},
number={1},
pages={173-181},
abstract={In this paper, a multiplication algorithm in extension field Fpm is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic p and extension degree m only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p>m, 4p does not divide m(p-1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree m is small.},
keywords={},
doi={10.1587/transfun.E92.A.173},
ISSN={1745-1337},
month={January},}
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TY - JOUR
TI - A Multiplication Algorithm in Fpm Such That p>m with a Special Class of Gauss Period Normal Bases
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 173
EP - 181
AU - Hidehiro KATO
AU - Yasuyuki NOGAMI
AU - Tomoki YOSHIDA
AU - Yoshitaka MORIKAWA
PY - 2009
DO - 10.1587/transfun.E92.A.173
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2009
AB - In this paper, a multiplication algorithm in extension field Fpm is proposed. Different from the previous works, the proposed algorithm can be applied for an arbitrary pair of characteristic p and extension degree m only except for the case when 4p divides m(p-1) and m is an even number. As written in the title, when p>m, 4p does not divide m(p-1). The proposed algorithm is derived by modifying cyclic vector multiplication algorithm (CVMA). We adopt a special class of Gauss period normal bases. At first in this paper, it is formulated as an algorithm and the calculation cost of the modified algorithm is evaluated. Then, compared to those of the previous works, some experimental results are shown. Finally, it is shown that the proposed algorithm is sufficient practical when extension degree m is small.
ER -
English
