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
Les calculs d'appariement sur des courbes elliptiques avec des degrés premiers impairs sont rarement étudiés en raison de leur faible efficacité. Récemment, Clarisse, Duquesne et Sanders ont proposé deux nouvelles courbes avec des degrés de plongement premiers impairs : BW13-P310 et BW19-P286, qui conviennent à certains schémas cryptographiques spéciaux. Dans cet article, nous proposons des méthodes efficaces pour calculer l'appariement optimal sur ce type de courbes, instanciées par le BW13-P310 courbe. Nous étendons d’abord la technique de réduction paresseuse à l’arithmétique des corps finis. Ensuite, nous présentons une nouvelle méthode pour exécuter l'algorithme de Miller. Par rapport aux formules d'itération standard de Miller, les nouvelles offrent une implémentation logicielle plus efficace des calculs d'appariement. Enfin, nous donnons également une formule rapide pour effectuer l'exponentiation finale. Les résultats de notre implémentation indiquent qu'il peut être calculé efficacement, alors qu'il est plus lent que celui sur la courbe (BLS12-P446) au même niveau de sécurité.
Yu DAI
Sun Yat-sen University
Zijian ZHOU
National University of Defense Technology,Hunan Engineering Research Center of Commercial Cryptography Theory and Technology Innovation
Fangguo ZHANG
Sun Yat-sen University,Guangdong Key Laboratory of Information Security
Chang-An ZHAO
Sun Yat-sen University,Guangdong Key Laboratory of Information Security
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Yu DAI, Zijian ZHOU, Fangguo ZHANG, Chang-An ZHAO, "Software Implementation of Optimal Pairings on Elliptic Curves with Odd Prime Embedding Degrees" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 5, pp. 858-870, May 2022, doi: 10.1587/transfun.2021EAP1115.
Abstract: Pairing computations on elliptic curves with odd prime degrees are rarely studied as low efficiency. Recently, Clarisse, Duquesne and Sanders proposed two new curves with odd prime embedding degrees: BW13-P310 and BW19-P286, which are suitable for some special cryptographic schemes. In this paper, we propose efficient methods to compute the optimal ate pairing on this types of curves, instantiated by the BW13-P310 curve. We first extend the technique of lazy reduction into the finite field arithmetic. Then, we present a new method to execute Miller's algorithm. Compared with the standard Miller iteration formulas, the new ones provide a more efficient software implementation of pairing computations. At last, we also give a fast formula to perform the final exponentiation. Our implementation results indicate that it can be computed efficiently, while it is slower than that over the (BLS12-P446) curve at the same security level.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAP1115/_p
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@ARTICLE{e105-a_5_858,
author={Yu DAI, Zijian ZHOU, Fangguo ZHANG, Chang-An ZHAO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Software Implementation of Optimal Pairings on Elliptic Curves with Odd Prime Embedding Degrees},
year={2022},
volume={E105-A},
number={5},
pages={858-870},
abstract={Pairing computations on elliptic curves with odd prime degrees are rarely studied as low efficiency. Recently, Clarisse, Duquesne and Sanders proposed two new curves with odd prime embedding degrees: BW13-P310 and BW19-P286, which are suitable for some special cryptographic schemes. In this paper, we propose efficient methods to compute the optimal ate pairing on this types of curves, instantiated by the BW13-P310 curve. We first extend the technique of lazy reduction into the finite field arithmetic. Then, we present a new method to execute Miller's algorithm. Compared with the standard Miller iteration formulas, the new ones provide a more efficient software implementation of pairing computations. At last, we also give a fast formula to perform the final exponentiation. Our implementation results indicate that it can be computed efficiently, while it is slower than that over the (BLS12-P446) curve at the same security level.},
keywords={},
doi={10.1587/transfun.2021EAP1115},
ISSN={1745-1337},
month={May},}
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TY - JOUR
TI - Software Implementation of Optimal Pairings on Elliptic Curves with Odd Prime Embedding Degrees
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 858
EP - 870
AU - Yu DAI
AU - Zijian ZHOU
AU - Fangguo ZHANG
AU - Chang-An ZHAO
PY - 2022
DO - 10.1587/transfun.2021EAP1115
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2022
AB - Pairing computations on elliptic curves with odd prime degrees are rarely studied as low efficiency. Recently, Clarisse, Duquesne and Sanders proposed two new curves with odd prime embedding degrees: BW13-P310 and BW19-P286, which are suitable for some special cryptographic schemes. In this paper, we propose efficient methods to compute the optimal ate pairing on this types of curves, instantiated by the BW13-P310 curve. We first extend the technique of lazy reduction into the finite field arithmetic. Then, we present a new method to execute Miller's algorithm. Compared with the standard Miller iteration formulas, the new ones provide a more efficient software implementation of pairing computations. At last, we also give a fast formula to perform the final exponentiation. Our implementation results indicate that it can be computed efficiently, while it is slower than that over the (BLS12-P446) curve at the same security level.
ER -