I am working on this exercise but can't work out the answer to the question b. I have solved the question (a) by decrypting the ciphertext $C = 2$ using the formula: $$ M = C^d \bmod n = 2^{17} \bmod 21 = 11 $$
Alice and Bob agree to communicate using the RSA cryptosystem. Alice has a private key ($n = 21$, $d = 17$) and a public key ($n = 21$, $e = 5$).
(a) Alice receives the ciphertext $C = $2 from Bob. Decrypt this message, show your working.
(b) Bob wishes to ensure that he sent the ciphertext to Alice. Bob sends Alice the plaintext message $M = 9$, what message should Alice send back?
(c) Perform the calculation Bob would do to verify this returned message.
What do you guys think?