The width-w NAF method provides small memory and fast elliptic scalar multiplications secure against side channel attacks

Katsuyuki Okeya, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingChapter

58 Citations (Scopus)

Abstract

The side channel attack (SCA) is a serious attack on wearable devices that have scarce computational resources. Cryptographic algorithms on them should be efficient using small memory - we have to make efforts to optimize the trade-off between efficiency and memory. In this paper we present efficient SCA-resistant scalar multiplications based on window method. Möller proposed an SPA-resistant window method based on 2w-ary window method, which replaces w-consecutive zeros to 1 plus w-consecutive 1 and it requires 2w points of table (or 2w-1 + 1 points if the signed 2w-ary is used). The most efficient window method with small memory is the width-w NAF, which requires 2w-2 points of table. In this paper we convert the width-w NAF to an SPA-resistant addition chain. Indeed we generate a scalar sequence with the fixed pattern, e.g. |0..0cursive Greek chi|0..0cursive Greek chi|...|0..0cursive Greek chi|, where cursive Greek chi is positive odd points < 2w. Thus the size of the table is 2w-1, which is optimal in the construction of the SPA-resistant chain based on width-2 NAF. The table sizes of the proposed scheme are 6% to 50% smaller than those of Möller's scheme for w = 2,3,4,5, which are relevant choices in the sense of efficiency for 160-bit ECC.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsMarc Joye
PublisherSpringer Verlag
Pages328-342
Number of pages15
ISBN (Print)3540008470, 9783540008477
DOIs
Publication statusPublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2612
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Okeya, K., & Takagi, T. (2003). The width-w NAF method provides small memory and fast elliptic scalar multiplications secure against side channel attacks. In M. Joye (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 328-342). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2612). Springer Verlag. https://doi.org/10.1007/3-540-36563-x_23