# RSA encryption in the real world?

• geoffrey159
In summary, the problem statement is about RSA encryption and involves proving that a certain formula holds true under specific conditions. The RSA algorithm involves creating a public and private key to encrypt and decrypt messages between parties. However, it is unclear how this works in the real world. A simple, real world example of using RSA encryption would be two parties sending encrypted messages to each other using their respective public and private keys.
geoffrey159

## Homework Statement

It is about an exercise called "RSA encryption". The problem statement was :
Let p,q be distinct prime numbers so that ##n = pq##. If c,d are two integers so that the Euler totient function of n, ##\phi(n)##, divides ##cd - 1##, show that for any ##t\in\mathbb{Z}##, ##n## divides ##t^{cd} - t ##.

I have found the solution but I don't understand how it works in the real world although it is the most interesting part of the exercise. Can you give a simple, real world example ?

## The Attempt at a Solution

RSA is also known as public key cryptography. The RSA algorithm allows one to create a private key and a public key. These keys can be used to encrypt and decrypt messages between different parties.

The public and private keys are really just prime numbers produced by the algorithm; Although both of these numbers should be kept a secret by the creator and any associates.

geoffrey159
hmmm... but how does it work ? Say you want to send me the crypted message "Hello", how do we do ?

## 1. What is RSA encryption and how does it work?

RSA (Rivest–Shamir–Adleman) is a public-key encryption algorithm used for secure communication and digital signatures. It works by using two keys - a public key for encryption and a private key for decryption. The sender uses the recipient's public key to encrypt the message, and the recipient uses their private key to decrypt it.

## 2. How is RSA encryption used in the real world?

RSA encryption is widely used in the real world for secure communication over the internet, such as online banking, e-commerce transactions, and email communication. It is also used for digital signatures to ensure the authenticity and integrity of electronic documents.

## 3. Is RSA encryption vulnerable to attacks?

Although RSA encryption is considered to be secure, it can be vulnerable to attacks if the keys are not generated properly or if the key size is too small. It is important to use a strong key generation process and a sufficient key size to ensure the security of the encryption.

## 4. Can RSA encryption be cracked?

RSA encryption cannot be cracked if it is implemented correctly with a strong key generation process and a sufficient key size. However, if an attacker is able to obtain the private key, they can decrypt the messages encrypted with that key.

## 5. Are there any alternatives to RSA encryption?

Yes, there are other public-key encryption algorithms such as Elliptic Curve Cryptography (ECC) and Diffie-Hellman (DH) key exchange. These alternatives offer similar security but may have different features and performance advantages.

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