RSA encryption

     

Scenario:

Create a RSA public/private key for parties to communicate securely.

Solution:

Example: If Ram and Shyam wants to share messages securely they would use below algorithm RSA

1. Generate Keys




--It uses 3 numbers. 

-p: which is a large prime number

-q: which is a large prime number. 

-e: An exponent, which is small, odd and coprime (1<e<(p-1)*(q-1)).

Steps:

1. N = p * q. This is half public key
2. e = 1 <e <(p-1)*(q-1). It could be 3. This is other half of public key
3. d (mod inverse) = (d * e) % N = 1. The d is the private key.
4. The receiver will distribute, #1 and #2 and keep 3 secret.


Ex: Ram will select p and q to start with.

p = 11
q = 17

N = p * q = 11 * 17 = 187.

e = 1 < e < (11-1) * (17-1) = 170 = 3

d = 321 = 1(160) = 107

Public Key = (3, 187) - This is shared with Shyam.

Private Key = (107,187) - This is stored secretly by Ram.