{"title":"嵌入度为18的椭圆曲线上的塔楼施工技术","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":"{\"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}","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}
Tower Building Technique on Elliptic Curve with Embedding Degree 18
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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