Needham-Schroeder Public Key (NSPK) protocol

The goal of NSPK is for mutual authentication, in effect:

• Alice chooses a nonce ($NA$) and sends it to Bob.
• Bob sends the nonce back (and since he could read it he must be Bob), but be also adds a challenge nonce ($NB$) and sends it back.
• Alice sends back the challenge nonce, since only Alice can read it and he sent it back, it must be Alice that he is talking to.

$$\begin{array}{rl}1.A\to B:& \{NA,A{\}}_{K_B}\\ 2.B\to A:& \{NA,NB{\}}_{K_A}\\ 3.A\to B:& \{NB{\}}_{K_B}\end{array}$$