Radix-r non-adjacent form

Tsuyoshi Takagi, Sung Ming Yen, Bo Ching Wu

Research output: Chapter in Book/Report/Conference proceedingChapter

14 Citations (Scopus)

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 + l)/2 and its average density of non-zero digit is asymptotically (r - l)/(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. Keywords: Non-adjacent form, radix-r representation, signed window method, elliptic curve cryptosystem, pairing based cryptosystem

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsKan Zhang, Yuliang Zheng
PublisherSpringer Verlag
Pages99-110
Number of pages12
ISBN (Print)3540232087, 9783540232087
DOIs
Publication statusPublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3225
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Takagi, T., Yen, S. M., & Wu, B. C. (2004). Radix-r non-adjacent form. In K. Zhang, & Y. Zheng (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 99-110). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3225). Springer Verlag. https://doi.org/10.1007/978-3-540-30144-8_9