ON THE ARITHMETIC OF ENDOMORPHISM RING End$(\mathbb{Z}_{p^2} \times \mathbb{Z}_{p})$ AND ITS RSA VARIANTS
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 53
DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.04
Author :
Ning Jauharotul Farida (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha No 10, Bandung, Jawa Barat, 40132, INDO)
Irawati (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha No 10, Bandung, Jawa Barat, 40132, INDO)
Abstract
Bergman (1974) found that for any prime number $p$, the endomorphism ring End$(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})$ is a semilocal ring which has $p^5$ elements and can not be embedded in matrices over any commutative ring. Later on, Climent et al. (2011) found that each element of endomorphism ring End$(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})$ can be identified as a two by two matrix of $E_p$ where the first and the second row entries belong to $\mathbb{Z}_{p}$ and $\mathbb{Z}_{p^2}$ respectively. By this characterization, Long D.T., Thu D. T., and Thuc D. N. constructed a new RSA variant based on End$(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})$ (2013). In this paper, we state the characteristic of the endomorphism ring End $(\mathbb{Z}_{p^2} \times \mathbb{Z}_{p})$ and the RSA analogue cryptosystem based on it.
Keywords and Phrases
Endomorphism ring, RSA, monoid, cryptosystem, noncommutative ring.
A.M.S. subject classification
16S50.
.....
![](img/pdf_file_icon_32x32.png)