INTRODUCTION

RSA was first published in 1977 and since then, it has been the cryptosystem that has been most widely used for encryption and decryption of data. In Don Boneh's paper entitled "Twenty Years of Attacks on the RSA Cryptosystem", he pointed out several attacks that have been mounted against this cryptosystem. And the conclusion that he made at the end of his paper was that there has not yet been any devastating attack, and the attacks that have been mounted so far are against the implementation of the cryptosystem.

In this term paper, we would like to explore further the various attacks that are mentioned in Boneh's paper. We have divided our paper into 4 parts, based on that 4 categories of attacks mentioned by Boneh:

1) Elementary attacks

2) Low Private Exponent attacks

3) Low Public Exponent attacks

4) Implementation attacks

We will approach each attack by describing the idea behind each attack, the implementation of the attacks and the steps that we can take to prevent such attacks.

Elementary Attacks

First of all, we will explain the first category, which is the elementary attack. Although there are many attacks that can be categorized into this category, we will only explain the common modulus and blinding attack. We will describe the attacks, and how the each attack is carried out. Then we will try to simulate each attack by using magma. Finally, we will give some ways to avoid the attack.

Low Private Exponent Attacks

The second category of attacks that we will explain is low private exponent attack. We will explain why such attack can happen. Then we will describe the attack. Finally we will explain some techniques that can be implemented to avoid this attack. For every technique, we will explain how the technique can...