Show that if p = 11, q = 5, x = 3, and k = 3, then (x k (mod q) and (x k (mod p) are different. alice and bob want to exchange encrypted signed messages. alice’s public key is (n, e) and private decryption exponent d, whereas bob’s public key is (n0 , e0 ) and private decryption exponent d 0 .

alice wants to send a message x to bob. she first signs a message encrypted by bob’s public key so sends y = (x e 0 (mod n0 ))d (mod n) to bob.

to read the message and verify the signature, bob computes z = y e (mod n) = x e 0 (mod n0 ) and then computes z d 0 (mod n0 ) = x e 0 d 0 (mod n0 ) = x.

will this work? explain why or why not.