M. Joye, Oleksandra Lapiha, Ky Nguyen, D. Naccache
{"title":"第十一幂余数符号","authors":"M. Joye, Oleksandra Lapiha, Ky Nguyen, D. Naccache","doi":"10.1515/jmc-2020-0077","DOIUrl":null,"url":null,"abstract":"Abstract This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ(ζ11), $ \\mathbb{Q}\\left( {{\\zeta }_{11}} \\right), $where 11 is a primitive 11th root of unity. It extends an earlier algorithm due to Caranay and Scheidler (Int. J. Number Theory, 2010) for the 7th-power residue symbol. The new algorithm finds applications in the implementation of certain cryptographic schemes.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2020-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2020-0077","citationCount":"9","resultStr":"{\"title\":\"The Eleventh Power Residue Symbol\",\"authors\":\"M. Joye, Oleksandra Lapiha, Ky Nguyen, D. Naccache\",\"doi\":\"10.1515/jmc-2020-0077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ(ζ11), $ \\\\mathbb{Q}\\\\left( {{\\\\zeta }_{11}} \\\\right), $where 11 is a primitive 11th root of unity. It extends an earlier algorithm due to Caranay and Scheidler (Int. J. Number Theory, 2010) for the 7th-power residue symbol. The new algorithm finds applications in the implementation of certain cryptographic schemes.\",\"PeriodicalId\":43866,\"journal\":{\"name\":\"Journal of Mathematical Cryptology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/jmc-2020-0077\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Cryptology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/jmc-2020-0077\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/jmc-2020-0077","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Abstract This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ(ζ11), $ \mathbb{Q}\left( {{\zeta }_{11}} \right), $where 11 is a primitive 11th root of unity. It extends an earlier algorithm due to Caranay and Scheidler (Int. J. Number Theory, 2010) for the 7th-power residue symbol. The new algorithm finds applications in the implementation of certain cryptographic schemes.