RSA is an **Internet Encryption and Authentication System** that uses an algorithm developed by Ron Rivest, Adi Shamir, and Leonard Adleman.

RSA Encryption is widely used and is one of the **defacto Ecncryption standard**.

It uses **Modular Arithmetic** and **Elementary Number** Theories to perform computations using two large prime numbers

## RSA Algorithm Encryption

We let y = E(x) be the encryption function where x is an interger and y is the encrypted from of x

y = x^e mod n

## RSA Algorithm Decryption

We let X = D(y) be the decryption function where y is an encryted integer and X is the decrypted from of y

X = y^d mod n

### Example

1, We start by selecting primes p = 3 and q =11.

2. n = pq = 33

m = (p-1)(q-1) = (2)(10) = 20

3. Try e = 3

ged(3.20) = 1

=> e is co-prime to n

4. Find d such that 1= de mod m

=> 1 = Km + de

Using the extended Euclid Algorithm we see that 1 = –1 (20) + 7(3)

=> d = 7

5. Now let’s say that we want to encrypt the number x = 9:

We use the Encryption function y = x^e mod n

y = 9^3 mod 33

y = 729 mod 33 = 3

=> y = 3

6. To decrypt y we use the function X =y^d mod n

X = 3^7 mod 33

X = 2187 mod 33 = 9

=> X = 9 = x

=> It Works!

**Also Read:** How to hack wifi using kali linux

### PassWord Cracking

Passwords aren’t generally stored in plaintext form. A file containing all the passwords in plain text form would be far too attractive a target, so instead, a one-way hash function is used. The best-known of these functions is based on DES and is called crypt.

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