Cryptographic Systems Based on an Algebraic Structure

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Ł. Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka null, Martin Waldoch
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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
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
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来源期刊
CiteScore
2.60
自引率
8.30%
发文量
48
期刊介绍: The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.
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