The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Pour le niveau de sécurité AES 128, il existe plusieurs choix naturels pour des courbes elliptiques faciles à appairer. En particulier, comme nous l'expliquerons, on pourrait choisir des courbes avec k=9 ou courbes avec k=12. L'affaire k=9 n’a pas été étudié dans la littérature, et il n’est donc pas clair avec quelle efficacité les appariements peuvent être calculés dans ce cas. Dans cet article, nous présentons des méthodes efficaces pour k=9 cas, incluant la génération de courbes elliptiques avec la boucle de Miller la plus courte, l'élimination du dénominateur et l'accélération de l'exponentiation finale. Nous comparons ensuite les performances de ces choix. De l'analyse, nous concluons que pour la cryptographie basée sur l'appariement au niveau de sécurité AES 128, les courbes de Barreto-Naehrig sont le choix le plus efficace, et les performances du cas k=9 est comparable aux courbes de Barreto-Naehrig.
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Xibin LIN, Chang-An ZHAO, Fangguo ZHANG, Yanming WANG, "Computing the Ate Pairing on Elliptic Curves with Embedding Degree k=9" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 9, pp. 2387-2393, September 2008, doi: 10.1093/ietfec/e91-a.9.2387.
Abstract: For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k=9 or curves with k=12. The case k=9 has not been studied in the literature, and so it is not clear how efficiently pairings can be computed in that case. In this paper, we present efficient methods for the k=9 case, including generation of elliptic curves with the shorter Miller loop, the denominator elimination and speed up of the final exponentiation. Then we compare the performance of these choices. From the analysis, we conclude that for pairing-based cryptography at the AES 128 security level, the Barreto-Naehrig curves are the most efficient choice, and the performance of the case k=9 is comparable to the Barreto-Naehrig curves.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.9.2387/_p
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@ARTICLE{e91-a_9_2387,
author={Xibin LIN, Chang-An ZHAO, Fangguo ZHANG, Yanming WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Computing the Ate Pairing on Elliptic Curves with Embedding Degree k=9},
year={2008},
volume={E91-A},
number={9},
pages={2387-2393},
abstract={For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k=9 or curves with k=12. The case k=9 has not been studied in the literature, and so it is not clear how efficiently pairings can be computed in that case. In this paper, we present efficient methods for the k=9 case, including generation of elliptic curves with the shorter Miller loop, the denominator elimination and speed up of the final exponentiation. Then we compare the performance of these choices. From the analysis, we conclude that for pairing-based cryptography at the AES 128 security level, the Barreto-Naehrig curves are the most efficient choice, and the performance of the case k=9 is comparable to the Barreto-Naehrig curves.},
keywords={},
doi={10.1093/ietfec/e91-a.9.2387},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - Computing the Ate Pairing on Elliptic Curves with Embedding Degree k=9
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2387
EP - 2393
AU - Xibin LIN
AU - Chang-An ZHAO
AU - Fangguo ZHANG
AU - Yanming WANG
PY - 2008
DO - 10.1093/ietfec/e91-a.9.2387
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2008
AB - For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k=9 or curves with k=12. The case k=9 has not been studied in the literature, and so it is not clear how efficiently pairings can be computed in that case. In this paper, we present efficient methods for the k=9 case, including generation of elliptic curves with the shorter Miller loop, the denominator elimination and speed up of the final exponentiation. Then we compare the performance of these choices. From the analysis, we conclude that for pairing-based cryptography at the AES 128 security level, the Barreto-Naehrig curves are the most efficient choice, and the performance of the case k=9 is comparable to the Barreto-Naehrig curves.
ER -