{"title":"有限阿贝尔群的根提取","authors":"Udvas Acharjee, M.S. Srinath","doi":"10.1016/j.jaca.2024.100017","DOIUrl":null,"url":null,"abstract":"<div><p>We formulate the <em>Root Extraction problem</em> in finite Abelian <em>p</em>-groups and then extend it to generic finite Abelian groups. We provide algorithms to solve them. We also give the bounds on the number of group operations required for these algorithms. We observe that once a basis is computed and the discrete logarithm relative to the basis is solved, root extraction takes relatively fewer “bookkeeping” steps. Thus, we conclude that root extraction in finite Abelian groups is <em>no harder</em> than solving discrete logarithms and computing basis.</p></div>","PeriodicalId":100767,"journal":{"name":"Journal of Computational Algebra","volume":"10 ","pages":"Article 100017"},"PeriodicalIF":0.0000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S277282772400007X/pdfft?md5=37c8cf927839f6d23b63dec45ccc0073&pid=1-s2.0-S277282772400007X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Root extraction in finite Abelian groups\",\"authors\":\"Udvas Acharjee, M.S. Srinath\",\"doi\":\"10.1016/j.jaca.2024.100017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We formulate the <em>Root Extraction problem</em> in finite Abelian <em>p</em>-groups and then extend it to generic finite Abelian groups. We provide algorithms to solve them. We also give the bounds on the number of group operations required for these algorithms. We observe that once a basis is computed and the discrete logarithm relative to the basis is solved, root extraction takes relatively fewer “bookkeeping” steps. Thus, we conclude that root extraction in finite Abelian groups is <em>no harder</em> than solving discrete logarithms and computing basis.</p></div>\",\"PeriodicalId\":100767,\"journal\":{\"name\":\"Journal of Computational Algebra\",\"volume\":\"10 \",\"pages\":\"Article 100017\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S277282772400007X/pdfft?md5=37c8cf927839f6d23b63dec45ccc0073&pid=1-s2.0-S277282772400007X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S277282772400007X\",\"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 Computational Algebra","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S277282772400007X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们提出了有限阿贝尔 p 群中的根提取问题，然后将其扩展到一般有限阿贝尔群。我们提供了解决这些问题的算法。我们还给出了这些算法所需的群运算次数的边界。我们发现，一旦计算出一个基，并求解出相对于基的离散对数，根提取所需的 "簿记 "步骤就会相对减少。因此，我们得出结论：有限阿贝尔群中的根提取并不比求解离散对数和计算基数难。
We formulate the Root Extraction problem in finite Abelian p-groups and then extend it to generic finite Abelian groups. We provide algorithms to solve them. We also give the bounds on the number of group operations required for these algorithms. We observe that once a basis is computed and the discrete logarithm relative to the basis is solved, root extraction takes relatively fewer “bookkeeping” steps. Thus, we conclude that root extraction in finite Abelian groups is no harder than solving discrete logarithms and computing basis.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
