{"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}
引用次数: 0
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.
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