论线性系统在可加可幂半环上的解

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-18 DOI:10.3390/math12182904

Álvaro Otero Sánchez, Daniel Camazón Portela, Juan Antonio López-Ramos

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引用次数: 0

摘要

本文的目的是求解系统 XA=Y，其中 A=(ai,j)∈Mn×m(S)，Y∈Sm，X 是一个大小为 n 的未知向量，S 是一个可加可幂半iring。如果系统有解，那么我们就能完全描述其最大解，而在 S 是广义热带配线的特殊情况下，我们就能提供其解的完整描述，以及与其计算相关的计算成本的明确约束。最后，我们展示了如何应用这种方法对分别为有限情况和热带配子定义的两种不同密钥交换协议进行加密分析。

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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On the Solutions of Linear Systems over Additively Idempotent Semirings

The aim of this article is to solve the system XA=Y, where A=(ai,j)∈Mn×m(S), Y∈Sm and X is an unknown vector of a size n, with S being an additively idempotent semiring. If the system has solutions, then we completely characterize its maximal one, and in the particular case where S is a generalized tropical semiring, a complete characterization of its solutions is provided as well as an explicit bound of the computational cost associated with its computation. Finally, we show how to apply this method to cryptanalyze two different key exchange protocols defined for a finite case and the tropical semiring, respectively.

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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.