TY - JOUR T1 - Cryptographic Systems Based on an Algebraic Structure AU - Matysiak , Ɓukasz 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.