Message exchange with textbook RSA 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?
Basically $M = 9$ is a challenge. Alice will have to sign it (compute $M^d \pmod {21})$, because only she knows $d$.
As $(M^e)^d = (M^d)^e = M \pmod{21}$, it should be clear what Bob should do to verify that the reply indeed equals $M^d$, which only Alice could have produced...