Part $2$: Breaking $8-$bit RSA $(10$ pts$)$

For this part of the assignment, you will attempt to break $8-$bit RSA. You overhear some RSA

encrypted exchange between Alice and Bob. Alice has sent Bob the binary sequence

$0$b$10100100(0$xA$4$ in hex$).$

You check Bob's public key: his $8-$bit modulus is $0$xFD $($hexadecimal$)$ and his exponent is $7.$

Can you break $8-$bit RSA?

$6.$ What is the secret number Alice sent to Bob? Enter the decimal value.

This example illustrates, that RSA has no secrecy: theoretically, the public key gives you all the

information you need to decrypt. While easy to do for an $8-$bit modulus, it is very hard to repeat

these steps for very large modulus $(2048-$bits or higher$).$ It is this difficulty of computation that

makes RSA secure$.$ At least for today.

Hint: For both parts, do a sanity check: Once you decrypt y and obtain x$,$ encrypt x to

make sure that it matches the original y$.$