Cryptographic Systems Based on an Algebraic Structure

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.4208/eajam.240522.200822

Ł. Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka null, Martin Waldoch

引用次数: 1

Abstract

. In this paper cryptographic systems based on the Dedekind and Galois structures are considered. We supplement the created cryptosystems based on the Dedekind structure with programs written in C ++ and discuss the inner structure of Galois in cryptography. It is well-known that such a structure is based on ﬁnite ﬁelds only. Our results reveals something more internal. The ﬁnal section contains additional information about square-free and radical factorizations in monoids consisting in searching for a minimal list of counterexamples. As an open problem, we leave creating a program that would generate such a list and how to use such a list to create a cryptosystem

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基于代数结构的密码系统

．本文研究了基于Dedekind和Galois结构的密码系统。我们用c++编写的程序对基于Dedekind结构创建的密码系统进行了补充，并讨论了密码学中伽罗瓦的内部结构。众所周知，这种结构仅基于有限域。我们的研究结果揭示了一些更为内在的东西。最后一节包含了关于一元群的无平方分解和根式分解的附加信息，包括查找反例的最小列表。作为一个开放的问题，我们留下了创建一个程序来生成这样一个列表，以及如何使用这样一个列表来创建一个密码系统

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.