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New Families of Hyperelliptic Curves with Efficient Gallant-Lambert-Vanstone Method

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Information Security and Cryptology – ICISC 2004 (ICISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3506))

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Abstract

The Gallant-Lambert-Vanstone method [14] (GLV method for short) is a scalar multiplication method for elliptic curve cryptography (ECC). In WAP WTLS[47], SEC 2[42], ANSI X9.62[1] and X9.63[2], several domain parameters for applications of the GLV method are described. Curves with those parameters have efficiently-computable endomorphisms. Recently the GLV method for hyperelliptic curve (HEC) Jacobians has also been studied.

In this paper, we discuss applications of the GLV method to curves with real multiplication (RM). It is the first time to use RM in cryptography. We describe the general algorithm for using such RM, and we show that some genus 2 curves with RM have enough effciency to be used in the GLV method as in the previous CM case.

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Authors and Affiliations

  1. Information Technology R&D Center, Mitsubishi Electric Corporation, 5-1-1, Ofuna, Kamakura, Kanagawa, 247-8501, Japan

    Katsuyuki Takashima

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  1. Katsuyuki Takashima
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Editors and Affiliations

  1. National Security Research Institute, 305-348, Daejeon, Korea

    Choon-sik Park

  2. National Security Research Institute (NSRI), 161 Gajeong-dong, Yuseong-gu, 305-350, Daejeon, Korea

    Seongtaek Chee

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Takashima, K. (2005). New Families of Hyperelliptic Curves with Efficient Gallant-Lambert-Vanstone Method. In: Park, Cs., Chee, S. (eds) Information Security and Cryptology – ICISC 2004. ICISC 2004. Lecture Notes in Computer Science, vol 3506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496618_21

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  • DOI: https://doi.org/10.1007/11496618_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26226-8

  • Online ISBN: 978-3-540-32083-8

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