# Public Key Cryptography: An Overview of RSA Encryption

Public key cryptography is a method of securing communication that relies on a pair of keys – public and private keys – to encrypt and decrypt data. Unlike symmetric encryption, where the same key is used for both encryption and decryption, public key cryptography uses different keys for encryption and decryption, providing a more secure method of communication over public networks. In this article, we will focus on the RSA algorithm, one of the most widely used public key encryption algorithms.

## RSA Encryption: An Overview

RSA encryption is a public key encryption algorithm that was first proposed by Ron Rivest, Adi Shamir, and Leonard Adleman in 1978. RSA encryption works by using a pair of keys – public and private keys – to encrypt and decrypt data. The public key is used to encrypt data, while the private key is used to decrypt data.

RSA encryption is based on the mathematical properties of large prime numbers. The algorithm works by generating two large prime numbers, p and q, and computing their product, n=pq. The next step is to select a number e that is relatively prime to (p-1)(q-1), which means that e and (p-1)*(q-1) have no common factors other than 1. This number e is used as the public key. The private key is then calculated using a mathematical function known as the Extended Euclidean Algorithm.

To encrypt a message, the sender uses the recipient’s public key to encrypt the message, which can then only be decrypted using the recipient’s private key. This provides a secure method of communication over public networks, as anyone can use the public key to encrypt a message, but only the recipient can decrypt it using their private key.

## RSA Encryption: Key Properties

RSA encryption has several key properties that make it a popular choice for secure communication:

• Security: RSA encryption is considered to be a secure method of communication, as the private key is required to decrypt the data.
• Scalability: RSA encryption can be used for both small and large messages, making it a scalable method of communication.
• Compatibility: RSA encryption is widely supported by software and hardware, making it a compatible method of communication.
• Flexibility RSA encryption can be used in a variety of applications, including secure email, file transfer, and online transactions.

## How public and private keys are used in the RSA encryption algorithm:

RSA Encryption Diagram

The diagram above shows the process of using public and private keys in RSA encryption. Here are the steps:

• Key generation: The first step is to generate a public-private key pair. The public key is shared with anyone who wants to send a message to the owner of the private key, while the private key is kept secret by the owner.
• Message encryption: To send a message, the sender uses the recipient’s public key to encrypt the message. The encrypted message can only be decrypted by the recipient using their private key.
• Message decryption: When the recipient receives the encrypted message, they use their private key to decrypt it and read the original message.
• Signature generation: The owner of the private key can also use it to generate a digital signature for a message. The digital signature is a unique value that can be used to verify the authenticity of the message and the identity of the sender.
• Signature verification: To verify the digital signature, the recipient uses the sender’s public key to decrypt the signature and compare it to the original message. If the two values match, the message is considered authentic and the sender is verified.