Intended Ciphered Message in Rsa Crypto-System

Since the first introduction of technologies into my life, I have always had a fascination, and interest in how can technologies such as smartphones transfer data from one person to another without the need to travel to do it; their existence has created a huge dependency for us toward the use of technology devices as they can simply help us to do what seems impossible into possible. This fascination and interest have brought me to wonder how safe it is to transmit data using technologies.

I did a little research on what actually happens when data is being transmitted from one device to another. During those research, I came across the term cryptography. So I did further research and came across information about the existence of a modern security system called the crypto-system. Crypto-system is essential to the prevailing era as they help to secure and control data during transmission. The RSA system is one of the most well-known and the most used crypto-system in the world, used by many technology companies to base their data transmission security on. RSA stands for its creators, who are: Rivest, Shamir, and Adleman. The existence of RSA has helped us to maintain the integrity and security of data transmission, which can be applied to an online bank transfer, virtual money account, or even our personal message and data within the server.

Aim

The aim of this investigation is to understand the use of mathematics functions within the RSA crypto-system, explore each of the formulas involved manually by experimenting with my own intended ciphered message, and ensure the accuracy of the RSA crypto-system. I will be using some calculator websites that can assist me in the process of counting using the large value of numbers.

Exploration

How RSA Crypto-System works?

RSA Crypto-system is the most widely used asymmetrical encryption that uses two types of a key in order to decrypt and encrypt a message, unlike simple ciphers, which use only one key and are shared together among the recipient and the sender. RSA Crypto is much safer and more advanced in terms of providing security.

So RSA Crypto-system uses two types of a key which are the public key and the private key. A user can publish his or her public key to others, and others can send the user an encrypted message using the user’s public key. Only the publisher of the public key is used to encrypt the message, and those who have the private key can decrypt the message.

The use of Mathematics in the RSA Crypto-System

RSA is a cryptographic algorithm that uses a large prime number that is hard to be factorized and is considered to be out of reach. Therefore the involvement of the number theory will be very much needed in the process of the RSA Crypto-System investigation. The number theory includes Euler’s Totient Function and Euclidean Algorithm. The use of Modulus Arithmetic will also be needed in RSA Crypto-System to create a connection or modulus inversion between the public and private keys.

The formula used in RSA Crypto-system

In RSA Crypto-System, we have two key which has a different formula used to either Encrypt or Decrypt a message.

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