RSA Digital Signatures Alice and Bob are discussing their favorite numbers in person. Alice tells Bob shell send him her favorite number, but include an RSA signature so that Bob will know for sure it came from Alice. Alices private key d = 7, public key e = 3, and N = 33.

(a) Alices favorite number is 5, so shell send the pair (5, S) where S is her RSA Signature of 5. What is S?

(b) Show Bobs work to verify that the pair (5, S) came from Alice.

(c) Why does this process guarantee that nobody but Alice could have sent the message?