{"title":"基于连分式展开的模乘除算法","authors":"Mourad Gouicem","doi":"10.1109/ARITH.2015.21","DOIUrl":null,"url":null,"abstract":"In this paper, we provide new methods to generate a class of algorithms computing modular multiplication and division. All these algorithms rely on sequences derived from the Euclidean algorithm for a well chosen input. We then use these sequences as number scales of the Ostrowski number system to construct the result of either the modular multiplication or division.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"1 1","pages":"137-143"},"PeriodicalIF":0.0000,"publicationDate":"2013-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Modular Multiplication and Division Algorithms Based on Continued Fraction Expansion\",\"authors\":\"Mourad Gouicem\",\"doi\":\"10.1109/ARITH.2015.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we provide new methods to generate a class of algorithms computing modular multiplication and division. All these algorithms rely on sequences derived from the Euclidean algorithm for a well chosen input. We then use these sequences as number scales of the Ostrowski number system to construct the result of either the modular multiplication or division.\",\"PeriodicalId\":6526,\"journal\":{\"name\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"volume\":\"1 1\",\"pages\":\"137-143\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.2015.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE 22nd Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.2015.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Modular Multiplication and Division Algorithms Based on Continued Fraction Expansion
In this paper, we provide new methods to generate a class of algorithms computing modular multiplication and division. All these algorithms rely on sequences derived from the Euclidean algorithm for a well chosen input. We then use these sequences as number scales of the Ostrowski number system to construct the result of either the modular multiplication or division.
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