Consider the following challenge-response authentication protocols:

Protocol 2

1. c v: Hi

2. v c: Enc(n)

3. c v: Enc(n + 1)

Protocol 3

1. c v: Hi ||Enc(dc)

2. v c: Enc(dc)||EncDH(n)

3. c v: Enc(n + 1)

c and v denote the claimant and verifier, respectively; Enc denotes encryption with a long-term shared secret key known to c and v; dc and dv denote public Diffie-Hellman values computed by c and v respectively; || denotes concatenation; and EncDH denotes encryption with a shared secret derived using the Diffie-Hellman protocol.

Explain which of Protocols 2 and 3 are vulnerable to an off-line key recovery attack, justifying your answers carefully?