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Radix-r Non-Adjacent Form

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Information Security (ISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3225))

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Abstract

Recently, the radix-3 representation of integers is used for the efficient implementation of pairing based cryptosystems. In this paper, we propose non-adjacent form of radix-r representation (rNAF) and efficient algorithms for generating rNAF. The number of non-trivial digits is (r–2)(r+1)/2 and its average density of non-zero digit is asymptotically (r–1)/(2r–1). For r=3, the non-trivial digits are { ± 2, ± 4} and the non-zero density is 0.4. We then investigate the width-w version of rNAF for the general radix-r representation, which is a natural extension of the width-w NAF. Finally we compare the proposed algorithms with the generalized NAF (gNAF) discussed by Joye and Yen. The proposed scheme requires a larger table but its non-zero density is smaller even for large radix. We explain that gNAF is a simple degeneration of rNAF — we can consider that rNAF is a canonical form for the radix-r representation. Therefore, rNAF is a good alternative to gNAF.

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Technische Universität Darmstadt, Hochschulstr.10, D-64283, Darmstadt, Germany

    Tsuyoshi Takagi

  2. Laboratory of Cryptography and Information Security (LCIS), Dept of Computer Science and Information Engineering, National Central University, Chung-Li, 320, Taiwan, R.O.C.

    Sung-Ming Yen & Bo-Ching Wu

Authors
  1. Tsuyoshi Takagi
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  2. Sung-Ming Yen
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  3. Bo-Ching Wu
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Editor information

Editors and Affiliations

  1. Institute of psychology, Chinese Academy of Sciences, 100101, Beijing, P.R. China

    Kan Zhang

  2. Department of Software & Information Systems, The University of North Carolina at Charlotte, 9201 University City Blvd, 28223-0001, Charlotte, NC, USA

    Yuliang Zheng

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© 2004 Springer-Verlag Berlin Heidelberg

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Takagi, T., Yen, SM., Wu, BC. (2004). Radix-r Non-Adjacent Form. In: Zhang, K., Zheng, Y. (eds) Information Security. ISC 2004. Lecture Notes in Computer Science, vol 3225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30144-8_9

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  • DOI: https://doi.org/10.1007/978-3-540-30144-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23208-7

  • Online ISBN: 978-3-540-30144-8

  • eBook Packages: Springer Book Archive

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