Question

In a public-key system using RSA, you intercept the ciphertext C = 20 sent to a user whose public key is e = 13, n = 77. Calculate the plaintext M

Answer 1

Answer:

Answer:i know but i will not tell dont know anything do by yourself mad

Answer 2

Using RSA, We got the Plaintext M=48.

Explanation:

• RSA is an asymmetric cryptography algorithm that uses public and private keys.
• Here Given that n=77, so we can conclude that:

        p=7 and q=11

• Now, $\phi(n)\hspace{0.05cm}=(p-1)(q-1)$.

                  $\phi(n)\hspace{0.05cm}=(7-1)(11-1)$

                           $=60$

• Also given that public key e=13.

• Now we need to find private key d such as that $d.e = 1 mod \phi(n)$.
• So,

                $d=\frac{1+\phi(n).k}{e}$

• Now put k=0, 1, 2. . . . till we get the integer value of d.
• Here for k=8, we get d=37.
• Now, using private key d, the given cipher C=20 can be decrypted using the following formulae:

                $M=C^{d} mod \hspace{0.1cm}n$                   where M=Plaintext; C=Ciphertext

                $M=20^{37} mod \hspace{0.1cm}77$    

                $M=48$

Thus, Using the RSA algorithm, we got the Plaintext M=48.