{"title":"椭圆曲线标量乘法运算:概览研究","authors":"Ayaat Waleed, Najlae Falah Hameed Al Saffar","doi":"10.31642/jokmc/2018/100226","DOIUrl":null,"url":null,"abstract":"Scalar multiplication is the fundamental operation in the elliptic curve cryptosystem. It involves calculating the integer multiple of a specific elliptic curve point. It involves three levels: field, point, and scalar arithmetic. Scalar multiplication will be significantly more efficient overall if the final level is improved. By reducing the hamming weight or the number of operations in the scalar representation, one can raise the level of scalar arithmetic. This paper reviews some of the algorithms and techniques that improve the elliptic curve scalar multiplication in terms of the third level.","PeriodicalId":499493,"journal":{"name":"Journal of Kufa for Mathematics and Computer","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Elliptic Curve Scalar Multiplication Operation: a Survey Study\",\"authors\":\"Ayaat Waleed, Najlae Falah Hameed Al Saffar\",\"doi\":\"10.31642/jokmc/2018/100226\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Scalar multiplication is the fundamental operation in the elliptic curve cryptosystem. It involves calculating the integer multiple of a specific elliptic curve point. It involves three levels: field, point, and scalar arithmetic. Scalar multiplication will be significantly more efficient overall if the final level is improved. By reducing the hamming weight or the number of operations in the scalar representation, one can raise the level of scalar arithmetic. This paper reviews some of the algorithms and techniques that improve the elliptic curve scalar multiplication in terms of the third level.\",\"PeriodicalId\":499493,\"journal\":{\"name\":\"Journal of Kufa for Mathematics and Computer\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Kufa for Mathematics and Computer\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31642/jokmc/2018/100226\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Kufa for Mathematics and Computer","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31642/jokmc/2018/100226","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Elliptic Curve Scalar Multiplication Operation: a Survey Study
Scalar multiplication is the fundamental operation in the elliptic curve cryptosystem. It involves calculating the integer multiple of a specific elliptic curve point. It involves three levels: field, point, and scalar arithmetic. Scalar multiplication will be significantly more efficient overall if the final level is improved. By reducing the hamming weight or the number of operations in the scalar representation, one can raise the level of scalar arithmetic. This paper reviews some of the algorithms and techniques that improve the elliptic curve scalar multiplication in terms of the third level.