SCA-Resistant and Fast Elliptic Scalar Multiplication Based on wNAF

Katsuyuki Okeya, Tsuyoshi Takagi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 1̄ 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⋯0x|0⋯0x|0⋯0x|, where x 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-w 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
Pages (from-to)75-84
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - Jan 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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