A to B: M1 = E(PU_b, [N_1 || ID_A])
B to A: M2 = E(PU_a, [N_1 || N_2])
A to B: M3 = E(PU_b, N_2)
A to B: M4 = E(PU_b, E(PR_a, K_s))
where PU_x is X's public key, PR_x is the corresponding
private key, E is encryption, N_i is a nonce, and
K_s is a session key.