You can't get there from here

Secrets

Now V flips a coin and tells P what it is
If heads, P reveals all the encryption keys

Aix ai500 Brussels br558

Cannes ca426 Dayton da573

Erie er054 Panang pa910

Peoria pe379 Perth pe442

Philadelphia ph160 Portland po839

ai500 br558 ai500 po839 ai500 er054

br558 ca426 br558 da573 br558 ph160

ca426 da573 ca426 pa910 da573 er054

da573 pe379 er054 pe442 pa910 po839

pe379 po839 pe379 ph160 pe442 ph160

V can confirm that P did in fact encrypt the HC problem under discussion
But she has no idea which routes were part of the itinerary

If tails, P reveals only the keys for the routes in the itinerary

V can readily verify that they do form an itinerary of the right length
But since she doesn't know what city ai500 represents, she doesn't know the real itinerary