You can't get there from here

Secrets

T can prepare data for which he knows an itinerary
Or he can prepare a legitimate encryption of the real map
But he can't do both at once
- Because he doesn't know an itinerary for the real map
But he doesn't know ahead of time what V will ask for
No matter what T does, V will catch him 50% of the time
If they play two rounds of this game, V will catch T 75% of the time
If they play 20 rounds, V will catch T 99.999905 % of the time
If P survives 20 rounds, V can be 99.999905 % sure that he really does know an itinerary