{"title":"The complexity of elliptic normal bases","authors":"Daniel Panario, Mohamadou Sall, Qiang Wang","doi":"arxiv-2401.11872","DOIUrl":null,"url":null,"abstract":"We study the complexity (that is, the weight of the multiplication table) of\nthe elliptic normal bases introduced by Couveignes and Lercier. We give an\nupper bound on the complexity of these elliptic normal bases, and we analyze\nthe weight of some special vectors related to the multiplication table of those\nbases. This analysis leads us to some perspectives on the search for low\ncomplexity normal bases from elliptic periods.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.11872","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
We study the complexity (that is, the weight of the multiplication table) of
the elliptic normal bases introduced by Couveignes and Lercier. We give an
upper bound on the complexity of these elliptic normal bases, and we analyze
the weight of some special vectors related to the multiplication table of those
bases. This analysis leads us to some perspectives on the search for low
complexity normal bases from elliptic periods.
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