Computer network network security

Question

Please explain theorem in simplest way and solve example with explanation.

Using RSA algorithm what is the value of cipher test c if the plain text m=5 and P=3, q=11 & d = 7 ( if d not given how to find d ).

Answer 1

Given Plain text (m)=5, P=3, Q=11

where P and Q are two prime integer

n=P*Q

n=3*11=33

Z=(P-1)*(Q-1)

Z=(3-1)*(11-1)=20

Now selecting the public key(i.e encryption key) E such that it is not a factor of (P-1) and (Q-1)

say E=3 

Now selecting the private key (i.e the decryption key) D such that the following equation is true:

(D*E) mod Z =1

Say D=7

(7*3) mod 20 =1

For encryption calculating the cipher text (CT) from the plain text (PT) is as follows:

CT = (PT)^E mod n

CT = 5^3 mod 33

Cipher Text =26

Now Sender will send this cipher text (26)  to the receiver

For decryption calculating the plain text PT from the cipher text CT as follows:

PT = (CT)^D mod n

      = (26^7) mod 33

      = 5