Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An RSA Cryptosystem over a Halidon Group Ring of a Dihedral Group

A. Telveenus

TL;DR

The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group to construct a cryptosystem using a halidon group ring of a dihedral group.

Abstract

The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used to develop a decryption programme was also quite complex.

An RSA Cryptosystem over a Halidon Group Ring of a Dihedral Group

TL;DR

The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group to construct a cryptosystem using a halidon group ring of a dihedral group.

Abstract

The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used to develop a decryption programme was also quite complex.

Paper Structure

This paper contains 4 sections, 4 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. Preliminary results
  3. An RSA Cryptosystem over a halidon ring of a dihedral group
  4. Conclusion

Key Result

Theorem 1

pjdat$RD_{m} \cong V$ , as $R$ -algebras, where $V$ is a subalgebra of the algebra of matrices, $Mat_{2m} (R)$, of order $2m$ over $R$ and therefore $U(RD_{2m}) \cong U(V)$.

Theorems & Definitions (6)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Proposition 4
  • Remark 1
  • Example 1