Problem 4 (RSA Digital Signature): Bob has modulus n and exponent e as his RSA public key (e, n). he has told Eve that she can send him any message M n and he is willing to sign it using a simple RSA signature method to compute S = M d nod n, where d is his private RSA exponent, and he will return the signature S to Eve. Unfortunately for Bob, Eve has captured a ciphertext C that Alice encrypted for Bob from her plaintext p using his RSA public key. Bob actually never got C. Eve wants to trick Bob into decrypting C for her and she does not want Bob to see the original plaintext P that goes with C. So, Eve asks Bob to sign the message M = reC mod n using his private RSA exponent, and send her back the signature S for M, where r is a random number that Eve chose to be relatively prime to n. Explain how Eve can use Bobs signature S on M to discover the plaintext P for C.