$3.$ Alice wish to send a message M $=300400500$ to Bob using the RSA algorithm. Use the following parameters to obtain the RSA keys for Bob. Assume that Alice is able to obtain Bob$$s public keys.

Use p $=16381,$ q $=27449,$ obtain suitable values for Bob$$s private key d and public key e$.$

$($i$)$ What is ciphertext that Alice obtains by encrypting M using Bob$$s public key? Show how Bob would decrypt this ciphertext correctly using his private key.

Is the decrypted plaintext same as the message? $.(4$ marks$)$

If the message M $=500600700,$ can the message be decrypted correctly? Explain.

$(2$ marks$)$

$($ii$)$ Suppose Bob receive a ciphertext containing $4$ ASCII characters within the braces $\{4$BZR$\}$ encrypted using his public key e $=11,$ n $=449642069,$ what is the plaintext message. You need to convert $4$BZR into ASCII, concatenate them into a number, decrypt, and convert back to ASCII characters.