{"title":"A w-NNAF method for the efficient computation of scalar multiplication in elliptic curve cryptography","authors":"Yong Ding , Kwok-wo Wong , Yu-min Wang","doi":"10.1016/j.amc.2004.06.106","DOIUrl":null,"url":null,"abstract":"<div><p>Based on the non-adjacent form (NAF) expression, here we present a new method to express a large positive integer <em>k</em> with the base of any positive integer <em>w</em> other than 2. We call this method the <em>w</em>-NNAF method as the expression is near to the NAF one and with base <em>w</em><span>. This expression leads to the minimal Hamming weight of all the base </span><em>w</em> expressions. Based on the proposed expression and some existing methods, an algorithm is developed to compute <em>kP</em> efficiently.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"167 1","pages":"Pages 81-93"},"PeriodicalIF":3.4000,"publicationDate":"2005-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.amc.2004.06.106","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300304004758","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
Based on the non-adjacent form (NAF) expression, here we present a new method to express a large positive integer k with the base of any positive integer w other than 2. We call this method the w-NNAF method as the expression is near to the NAF one and with base w. This expression leads to the minimal Hamming weight of all the base w expressions. Based on the proposed expression and some existing methods, an algorithm is developed to compute kP efficiently.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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