RSA Algorithm

Using RSA algorithm, what is the value of cipher text C, if the plain text M = 5 and p = 3, q = 11 & d = 7 ?
(A) 33
(B) 5
(C ) 25
(D )26

Ans:- D

Solution:-

Given p=3,q=11. n=(p X q) = (3 X 11)=33
   m=(p-1)X(q-1) = (2 X 10)=20
Find a small odd integer e, that is relatively prime to m.
If e=3, then GCD(3,20)=1. e should be small and prime and so we let e=3.
d is given, d=7.
Public key = (e,n). (Values of e and n are known).
To encrypt a message, we apply the public key to the function
E(s) = se(mod n),
where s is the given message and e and n represent the public key integer pair. In the above question, the plain text M = 5. Plain text needs to be encrypted using the above formula.
E(s) = s^e(mod n)
   =5³(mod 33)
   = 125 (mod 33)
   = 26
As a result, the encrypted message E(s) = 26. This is what gets transmitted.