{"title":"Tower Building Technique on Elliptic Curve with Embedding Degree 18","authors":"Ismail Assoujaa, Siham Ezzouak, H. Mouanis","doi":"10.37394/23205.2022.21.39","DOIUrl":null,"url":null,"abstract":"Abstract Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally effcient, we choose to work with extension finite field of the form 𝔽pk with k ≥ 12. In this paper, we focus on the case of curves with embedding degree 18. We use the tower building technique, and study the case of degree 2 or 3 twist to carry out most arithmetics operations in 𝔽p2 , 𝔽p3, 𝔽p6, 𝔽p9 and 𝔽p18, thus we speed up the computation in optimal ate pairing.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"83 1","pages":"103 - 118"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tatra Mountains Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23205.2022.21.39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally effcient, we choose to work with extension finite field of the form 𝔽pk with k ≥ 12. In this paper, we focus on the case of curves with embedding degree 18. We use the tower building technique, and study the case of degree 2 or 3 twist to carry out most arithmetics operations in 𝔽p2 , 𝔽p3, 𝔽p6, 𝔽p9 and 𝔽p18, thus we speed up the computation in optimal ate pairing.
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