The RSA encryption algorithm is one of the most widely used public key encryption algorithms invented in 1977. It uses two large prime numbers to generate a public key and a private key. The public key is used to encrypt messages while the private key is used to decrypt them. RSA works by: 1) Generating two large prime numbers and computing n as their product, 2) Finding a number e that is coprime to another number m, 3) Finding d such that d*e is congruent to 1 modulo m, 4) Publishing e and n as the public key and keeping d and n as the private key.

1. Data And Network Security
Name: Khawaja Rokham Tariq
Roll No: 25
Topic: The RSA encryption algorithm

2. The RSA encryption algorithm
Introduction
The RSA encryption algorithm is one of the most widely used
public key encryption algorithms that have ever been invented. It was
created by the three scientists Ronald Rivest, Adi Shamir, and Leonard
Adleman in 1977, and today it is increasingly being used in the network
area.

3. The RSA encryption algorithm
Working
To generate the keys for RSA encryption and decryption, two large prime
numbers p and q need to be found.
With those two primes, the RSA will output three numbers, e, d and n.
The user may choose either one of the first two number(e and d) as the
private key, and the other one would serve as the public key. n is a common
factor that needs to be combined with either one of e and d to form a key
pair, so that the key pairs may be used by encryption and decryption
procedures. For example, if the user choose e as the private
key, e and n form a private key pair, and d and n will form a public key
pair. Depending on the situation, the user may wish to use the either the
private key pair or the public key pair to perform encryption, and keep the
other key pair for decryption.

5. The RSA encryption algorithm
• The key generation:
• Generate two large prime numbers, p and q
• Let n = pq
• Let m = (p-1)(q-1)
• Choose a small number e, coprime to m
• Find d, such that d.e mod m = 1
• Publish e and n as the public key. Keep d and n as the secret key.

6. • RSA is a asymmetric key encryption technique and a standard for
encrypting data send over the internet. In this approach, the
encryption key differs from the decryption key which is kept private.
The asymmetry depends on the practical difficulty of factoring
the product of two large prime numbers.
• The strength of encryption increases exponentially with the increase
in key size, which is typically 1024 or 2048 bits long. While
implementing, RSA must be combined with some sort of padding
scheme so that no message results in insecure cipher texts

7. The RSA encryption algorithm