$3)$ The question involves encoding$/$decoding using an RSA algorithm.

A B C D E F G H I J K L M

$65666768697071727374757677$

N O P Q R S T U V W X Y Z

$78798081828384858687888990$

ASCII Table

Our problem

Consider the following plaintext message:

$$BAHRAINPOLYTECHNIC$$

Present a step$-$by$-$step encryption and decryption process of the above$-$mentioned message with the help of ASCII table and the following values:

p $=29,$ q $=41$

a$)$ Choose the appropriate value of $$e$$ for public key.

b$)$ Compute the private key d using extended Euclidean algorithm.

c$)$ Encrypt the message using the above derived public key and then decrypt the message again using the above derived private key.

Explain each step how you work while ciphering and deciphering the above given message.