{"title":"Division in the Plactic Monoid","authors":"Chris Monico","doi":"10.1142/s021949882550080x","DOIUrl":null,"url":null,"abstract":"In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol. 17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements [Formula: see text] in the plactic monoid, the problem is to find [Formula: see text] for which [Formula: see text], given that such a [Formula: see text] exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s021949882550080x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol. 17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements [Formula: see text] in the plactic monoid, the problem is to find [Formula: see text] for which [Formula: see text], given that such a [Formula: see text] exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.
在[D。R. L. Brown, Plactic key agreement (insecure?)， J. Math。Cryptol. 17(1)(2023) 20220010]，基于求解plactic单群中除法问题的明显困难，提出了一种新的加密密钥交换技术。具体地说，给定plactic monooid中的元素[Formula: see text]，问题是找到[Formula: see text]的[Formula: see text]，假设存在这样一个[Formula: see text]。在本文中，我们引入了一个关于plactic monooid的度量，并利用它给出了一个求解该问题的概率算法，该算法对于参数值在感兴趣的范围内是快速的。
期刊介绍：
The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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