{"title":"用于信息加密保护的格鲁瓦域乘法算法分析","authors":"I. Zholubak","doi":"10.23939/sisn2023.13.338","DOIUrl":null,"url":null,"abstract":"The mathematical basis for processing a digital signature is elliptic curves. The processing of the points of an elliptic curve is based on the operations performed in the Galois fields GF(pm). Fields with a simple foundation are not well-studied and very interesting for research. In this paper, a comparison of the complexity of algorithms for the realization of the multiplication operation in Galois fields GF(pm) with different bases is carried out. Conducts a comparison of the 3 most common multiplication algorithms. Found that fields with a base greater than 2 will have greater complexity of the algorithm.","PeriodicalId":444399,"journal":{"name":"Vìsnik Nacìonalʹnogo unìversitetu \"Lʹvìvsʹka polìtehnìka\". Serìâ Ìnformacìjnì sistemi ta merežì","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of multiplication algorithms in Galuis fields for the cryptographic protection of information\",\"authors\":\"I. Zholubak\",\"doi\":\"10.23939/sisn2023.13.338\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The mathematical basis for processing a digital signature is elliptic curves. The processing of the points of an elliptic curve is based on the operations performed in the Galois fields GF(pm). Fields with a simple foundation are not well-studied and very interesting for research. In this paper, a comparison of the complexity of algorithms for the realization of the multiplication operation in Galois fields GF(pm) with different bases is carried out. Conducts a comparison of the 3 most common multiplication algorithms. Found that fields with a base greater than 2 will have greater complexity of the algorithm.\",\"PeriodicalId\":444399,\"journal\":{\"name\":\"Vìsnik Nacìonalʹnogo unìversitetu \\\"Lʹvìvsʹka polìtehnìka\\\". Serìâ Ìnformacìjnì sistemi ta merežì\",\"volume\":\"15 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vìsnik Nacìonalʹnogo unìversitetu \\\"Lʹvìvsʹka polìtehnìka\\\". Serìâ Ìnformacìjnì sistemi ta merežì\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23939/sisn2023.13.338\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vìsnik Nacìonalʹnogo unìversitetu \"Lʹvìvsʹka polìtehnìka\". Serìâ Ìnformacìjnì sistemi ta merežì","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23939/sisn2023.13.338","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analysis of multiplication algorithms in Galuis fields for the cryptographic protection of information
The mathematical basis for processing a digital signature is elliptic curves. The processing of the points of an elliptic curve is based on the operations performed in the Galois fields GF(pm). Fields with a simple foundation are not well-studied and very interesting for research. In this paper, a comparison of the complexity of algorithms for the realization of the multiplication operation in Galois fields GF(pm) with different bases is carried out. Conducts a comparison of the 3 most common multiplication algorithms. Found that fields with a base greater than 2 will have greater complexity of the algorithm.
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