$12.$ Alice creates an RSA public key pair. She chooses p$=37$ and q$=61$ as the two

prime numbers to generate the public key and $29$ as the other publicly$-$known value e$.$

i$)$ What is the value of the public key? Show your workings. $[2]$

ii$)$ What is the value of the private key? Show your workings. $[5]$

iii$)$ Bob wants to send the number $108$ to Alice. Work out the ciphertext by

applying the properties of modular arithmetic. Show your procedure of generating the

ciphertext. $[6]$

iv$)$ How should Alice decrypt the ciphertext? Give the formula $($you do not need

to show the procedure of working out plaintext from the ciphertext$).[2]$

iv$)$ Discuss the factors that can affect the security level of the RSA encryption

algorithm