SCA-Resistant and Fast Elliptic Scalar Multiplication Based on wNAF

Katsuyuki OKEYA  Tsuyoshi TAKAGI 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E87-A  No.1  pp.75-84
Publication Date: 2004/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Asymmetric Cipher
Keyword: 
elliptic curve cryptosystem,  side channel attacks,  width-w NAF,  smart card, 

Full Text: PDF(467.2KB)

Summary: 
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. Moller proposed an SPA-resistant window method based on 2w-ary window method, which replaces w-consecutive zeros to 1 plus w-consecutive 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. |00x|00x||00x|, 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 Moller's scheme for w = 2,3,4,5, which are relevant choices in the sense of efficiency for 160-bit ECC.