{"title":"椭圆曲线Selmer模型的快速配对计算","authors":"Emmanuel Fouotsa, Abdoul Aziz Ciss","doi":"10.1515/gcc-2016-0005","DOIUrl":null,"url":null,"abstract":"Abstract This paper revisits the computation of pairings on a model of elliptic curve called Selmer curves. We extend the work of Zhang, Wang, Wang and Ye [17] to the computation of other variants of the Tate pairing on this curve. Especially, we show that the Selmer model of an elliptic curve presents faster formulas for the computation of the Ate and optimal Ate pairings with respect to Weierstrass elliptic curves. We show how to parallelise the computation of these pairings and we obtained very fast results. We also present an example of optimal pairing on a pairing-friendly Selmer curve of embedding degree k = 12.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"48 1","pages":"55 - 67"},"PeriodicalIF":0.1000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Faster Ate pairing computation on Selmer's model of elliptic curves\",\"authors\":\"Emmanuel Fouotsa, Abdoul Aziz Ciss\",\"doi\":\"10.1515/gcc-2016-0005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract This paper revisits the computation of pairings on a model of elliptic curve called Selmer curves. We extend the work of Zhang, Wang, Wang and Ye [17] to the computation of other variants of the Tate pairing on this curve. Especially, we show that the Selmer model of an elliptic curve presents faster formulas for the computation of the Ate and optimal Ate pairings with respect to Weierstrass elliptic curves. We show how to parallelise the computation of these pairings and we obtained very fast results. We also present an example of optimal pairing on a pairing-friendly Selmer curve of embedding degree k = 12.\",\"PeriodicalId\":41862,\"journal\":{\"name\":\"Groups Complexity Cryptology\",\"volume\":\"48 1\",\"pages\":\"55 - 67\"},\"PeriodicalIF\":0.1000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Complexity Cryptology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/gcc-2016-0005\",\"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":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2016-0005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Faster Ate pairing computation on Selmer's model of elliptic curves
Abstract This paper revisits the computation of pairings on a model of elliptic curve called Selmer curves. We extend the work of Zhang, Wang, Wang and Ye [17] to the computation of other variants of the Tate pairing on this curve. Especially, we show that the Selmer model of an elliptic curve presents faster formulas for the computation of the Ate and optimal Ate pairings with respect to Weierstrass elliptic curves. We show how to parallelise the computation of these pairings and we obtained very fast results. We also present an example of optimal pairing on a pairing-friendly Selmer curve of embedding degree k = 12.
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