Ł. Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka null, Martin Waldoch
{"title":"Cryptographic Systems Based on an Algebraic Structure","authors":"Ł. Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka null, Martin Waldoch","doi":"10.4208/eajam.240522.200822","DOIUrl":null,"url":null,"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","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/eajam.240522.200822","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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
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.