Division in the Plactic Monoid

Pub Date : 2023-11-01 DOI:10.1142/s021949882550080x
Chris Monico
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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.
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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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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