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Volume 13, Issue 1
Cryptographic Systems Based on an Algebraic Structure

Łukasz Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka & Martin Waldoch

DOI: 10.4208/eajam.240522.200822

East Asian J. Appl. Math., 13 (2023), pp. 177-193.

Published online: 2023-01

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  • 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.

  • Keywords

Monoid, cryptography, Dedekind domain, Galois extension, factorization.

  • AMS Subject Headings

94A60, 11R32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-177, author = {Matysiak , ŁukaszChrzaniuk , MonikaDuda , MaximilianHanc , MartaKowalski , SebastianSkotnicka , Zoja and Waldoch , Martin}, title = {Cryptographic Systems Based on an Algebraic Structure}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {1}, pages = {177--193}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.240522.200822 }, url = {http://global-sci.org/intro/article_detail/eajam/21308.html} }
TY - JOUR T1 - Cryptographic Systems Based on an Algebraic Structure AU - Matysiak , Łukasz AU - Chrzaniuk , Monika AU - Duda , Maximilian AU - Hanc , Marta AU - Kowalski , Sebastian AU - Skotnicka , Zoja AU - Waldoch , Martin JO - East Asian Journal on Applied Mathematics VL - 1 SP - 177 EP - 193 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.240522.200822 UR - https://global-sci.org/intro/article_detail/eajam/21308.html KW - Monoid, cryptography, Dedekind domain, Galois extension, factorization. AB -

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.

Matysiak , ŁukaszChrzaniuk , MonikaDuda , MaximilianHanc , MartaKowalski , SebastianSkotnicka , Zoja and Waldoch , Martin. (2023). Cryptographic Systems Based on an Algebraic Structure. East Asian Journal on Applied Mathematics. 13 (1). 177-193. doi:10.4208/eajam.240522.200822
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