{"title":"塑胶单关节部","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s021949882550080x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s021949882550080x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
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。
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.
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