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
Nous présentons un algorithme de multiplication scalaire avec récupération du y-coordonner sur une courbe elliptique de forme Montgomery sur n'importe quel champ non binaire. Les algorithmes précédents de multiplication scalaire sur une forme de Montgomery ne considèrent pas comment récupérer le y-coordonner. Ainsi, bien qu'ils puissent être applicables à certains schémas restreints (ex. ECDH et ECDSA-S), certains schémas (ex. ECDSA-V et MQV) nécessitent une multiplication scalaire avec récupération du y-coordonner. Nous comparons notre algorithme de multiplication scalaire proposé avec les algorithmes de multiplication scalaire traditionnels (y compris les méthodes Window sur la forme de Weierstrass), et discutons de la forme de Montgomery par rapport à la forme de Weierstrass dans la performance de la mise en œuvre avec plusieurs techniques de cryptosystèmes à courbe elliptique (y compris ECES, ECDSA). , et ECMQV). Nos résultats clarifient l'avantage de l'utilisation cryptographique de la courbe elliptique de forme Montgomery dans des environnements contraints tels que les appareils mobiles et les cartes à puce.
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Katsuyuki OKEYA, Kouichi SAKURAI, "A Scalar Multiplication Algorithm with Recovery of the y-Coordinate on the Montgomery Form and Analysis of Efficiency for Elliptic Curve Cryptosystems" in IEICE TRANSACTIONS on Fundamentals,
vol. E85-A, no. 1, pp. 84-93, January 2002, doi: .
Abstract: We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve over any non-binary field. The previous algorithms for scalar multiplication on a Montgomery form do not consider how to recover the y-coordinate. So although they can be applicable to certain restricted schemes (e.g. ECDH and ECDSA-S), some schemes (e.g. ECDSA-V and MQV) require scalar multiplication with recovery of the y-coordinate. We compare our proposed scalar multiplication algorithm with the traditional scalar multiplication algorithms (including Window-methods on the Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementation with several techniques of elliptic curve cryptosystems (including ECES, ECDSA, and ECMQV). Our results clarify the advantage of the cryptographic usage of Montgomery-form elliptic curve in constrained environments such as mobile devices and smart cards.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e85-a_1_84/_p
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@ARTICLE{e85-a_1_84,
author={Katsuyuki OKEYA, Kouichi SAKURAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Scalar Multiplication Algorithm with Recovery of the y-Coordinate on the Montgomery Form and Analysis of Efficiency for Elliptic Curve Cryptosystems},
year={2002},
volume={E85-A},
number={1},
pages={84-93},
abstract={We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve over any non-binary field. The previous algorithms for scalar multiplication on a Montgomery form do not consider how to recover the y-coordinate. So although they can be applicable to certain restricted schemes (e.g. ECDH and ECDSA-S), some schemes (e.g. ECDSA-V and MQV) require scalar multiplication with recovery of the y-coordinate. We compare our proposed scalar multiplication algorithm with the traditional scalar multiplication algorithms (including Window-methods on the Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementation with several techniques of elliptic curve cryptosystems (including ECES, ECDSA, and ECMQV). Our results clarify the advantage of the cryptographic usage of Montgomery-form elliptic curve in constrained environments such as mobile devices and smart cards.},
keywords={},
doi={},
ISSN={},
month={January},}
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TY - JOUR
TI - A Scalar Multiplication Algorithm with Recovery of the y-Coordinate on the Montgomery Form and Analysis of Efficiency for Elliptic Curve Cryptosystems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 84
EP - 93
AU - Katsuyuki OKEYA
AU - Kouichi SAKURAI
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E85-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2002
AB - We present a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve over any non-binary field. The previous algorithms for scalar multiplication on a Montgomery form do not consider how to recover the y-coordinate. So although they can be applicable to certain restricted schemes (e.g. ECDH and ECDSA-S), some schemes (e.g. ECDSA-V and MQV) require scalar multiplication with recovery of the y-coordinate. We compare our proposed scalar multiplication algorithm with the traditional scalar multiplication algorithms (including Window-methods on the Weierstrass form), and discuss the Montgomery form versus the Weierstrass form in the performance of implementation with several techniques of elliptic curve cryptosystems (including ECES, ECDSA, and ECMQV). Our results clarify the advantage of the cryptographic usage of Montgomery-form elliptic curve in constrained environments such as mobile devices and smart cards.
ER -