RSA in extensions of the ring of integers

Abstract: The aim of this work is to create a variant of the RSA classical algorithm, through extensions from the ring of integers Z to two Euclidean domains:the domain of Gaussian integers, Z[i], and the domain generated by p2, Z[p2]. To achieve this purpose, the study of the theory behind both these sets becomes necessary, to ensure that all the properties are preserved when moving into extensions and so that the construction of the algorithm is possible. Moreover, a description of modular arithmetic is needed, to see how modules behave inside these new sets, since they are the most important ingredient for the algorithm.