RSA Public-Key Encryption and Signature Lab - IT Assignment Help

Assignment Task

Introduction
RSA (RivestShamirAdleman) is one of the first public-key cryptosystems and is widely used for secure communication. The RSA algorithm first generates two large random prime numbers, and then use them to generate public and private key pairs, which can be used to do encryption, decryption, digital signature generation, and digital signature verification. The RSA algorithm is built upon number theories, and it can be quite easily implemented with the support of libraries.
The learning objective of this lab is for students to gain hands-on experiences on the RSA algorithm.

From lectures, students should have learned the theoretic part of the RSA algorithm, so they know mathematically how to generate public/private keys and how to perform encryption/decryption and signature generation/verification. This lab enhances student’s understanding of RSA by requiring them to go through every essential step of the RSA algorithm on actual numbers, so they can apply the theories learned from the class. Essentially, students will be implementing the RSA algorithm using the C program language. The lab covers the following security-related topics:
• Public-key cryptography
• The RSA algorithm and key generation
• Big number calculation
• Encryption and Decryption using RSA
• Digital signature
• X.509 certificate

Lab environment. This lab has been tested on our pre-built Ubuntu 12.04 VM and Ubuntu 16.04 VM, both of which can be downloaded from the SEED website. This lab requires the openssl library, which is already installed on the Ubuntu 16.04, but not on the Ubuntu 12.04 VM. If you use Ubuntu 12.04, please run the following two commands to install openssl:
$ sudo apt-get update
$ sudo apt-get install libssl-dev

Acknowledgment This lab was developed with the help of Shatadiya Saha, a graduate student in the Department of Electrical Engineering and Computer Science at Syracuse University.

Background
The RSA algorithm involves computations on large numbers. These computations cannot be directly conducted using simple arithmetic operators in programs, because those operators can only operate on primitive data types, such as 32-bit integer and 64-bit long integer types. The numbers involved in the RSA algorithms are typically more than 512 bits long. For example, to multiple two 32-bit integer numbers a and b, we just need to use a*b in our program. However, if they are big numbers, we cannot do that any more; instead, we need to use an algorithm (i.e., a function) to compute their products.
There are several libraries that can perform arithmetic operations on integers of arbitrary size. In this lab, we will use the Big Number library provided by openssl. To use this library, we will define each big number as a BIGNUM type, and then use the APIs provided by the library for various operations, such as addition, multiplication, exponentiation, modular operations, etc.

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