Matt Blaze developed a very cool attack against master-key lock systems: http://www.crypto.com/papers/mk.pdf

It requires access to one (non-master) key as well as a lock which is open-able by that key. It also requires being able to generate a modest number of new keys with a key cutter (however significantly fewer than brute forcing the entire space).

IIRC, the attack boils down to: - Start with the known non-master key - Hold all but one of the teeth constant, and try different values of that one tooth until you get a different working key. This other value must be the master key's value. - Repeat until you have the master value for each tooth.

If TSA locks work the same way as the locks described in this paper, a single lock/key seems sufficient to generate the master key.