Question

Perform encryption using the RSA algorithm. Given p=5, q=11, e=3, M=9, determine the following:

modulus n =  , t =  , private key d =  , ciphertext c =

(Note: Choose the smallest value "d" that works)

If M is changed to M=40, the new ciphertext value becomes c =

Answer 1

In RSA,

n = p x q = 5 x 11 = 55

It is given that e = 3

We have to choose private key d such that

Here d is the multiplicative inverse of e

d = 27 satisfies the condition

So d = 27

Now the public key is (e,n) = (3,55)

Private key is (d,n) = (27,55)

Now M = 9

c = M^e mod n = 9³ mod 55 = 14

So c = 14

Now if M = 40

c = M^e mod n = 40³ mod 55 = 35

So c = 35