Paper Abstract and Keywords |
Presentation |
2011-11-15 14:50
On Definition Fields of Pairing Friendly Curves With Embedding Degree 4, 6, 8 Masaaki Shirase (FUN) ISEC2011-58 LOIS2011-52 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The BN prime $p$, which is required for constructing the BN curve, is given by $p=36z^4+36z^3+24z^2+6z+1$. By the way, the $p$ has a representation as $p=(6z^2+3z+1)^2+3z^2$ and then a primary resolution of $p$ is given as $p=-(6z^2+4z+1)-2z\omega \ (\mbox{if }z \equiv 0 \Pmod{3}$), $p=2z-(6z^2+2z+1)\omega \ (\mbox{if }z \equiv 1 \Pmod{3}$),or $p=6z^2+2z+1+(6z^2+4z+1)\omega \ (\mbox{if }z \equiv 2 \Pmod{3}$), where $\omega$ satisfies $\omega^3=1$, $\omega \ne 1$. It is known that these results help for efficiently constructing the extension field ${\mathbb F}_{p^{12}}$ and deciding a coefficient of the BN curve. This paper considers similar representations and primary resolutions for primes which define pairing-friendly curves with the embedding degree $k=4,6,8$. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
pairing-friendly curve / primary / 4th residue / embedding degree / CM discriminant / / / |
Reference Info. |
IEICE Tech. Rep., vol. 111, no. 285, ISEC2011-58, pp. 163-170, Nov. 2011. |
Paper # |
ISEC2011-58 |
Date of Issue |
2011-11-07 (ISEC, LOIS) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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ISEC2011-58 LOIS2011-52 |
Conference Information |
Committee |
ISEC LOIS |
Conference Date |
2011-11-14 - 2011-11-15 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Osaka Electro-Communication University |
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Paper Information |
Registration To |
ISEC |
Conference Code |
2011-11-ISEC-LOIS |
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Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
On Definition Fields of Pairing Friendly Curves With Embedding Degree 4, 6, 8 |
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pairing-friendly curve |
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primary |
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4th residue |
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embedding degree |
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CM discriminant |
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Masaaki Shirase |
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Future University Hakodate (FUN) |
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Speaker |
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Date Time |
2011-11-15 14:50:00 |
Presentation Time |
25 minutes |
Registration for |
ISEC |
Paper # |
ISEC2011-58, LOIS2011-52 |
Volume (vol) |
vol.111 |
Number (no) |
no.285(ISEC), no.286(LOIS) |
Page |
pp.163-170 |
#Pages |
8 |
Date of Issue |
2011-11-07 (ISEC, LOIS) |
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