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 - <p style="text-align: justify;">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.</p>