Locks and Combinations

Imagine that a master locksmith has designed a combination lock and published

the entire inner workings—the nuts and bolts of every mechanism in the lock.

Alice buys a lock and changes the combination. The design is so secure that no

one, not even the locksmith, can figure out the new combination. Of course, this

means that if Alice forgets the combination, no one can open the lock without

trying every combination or breaking the lock.

Further imagine that this one lock design is used to make many locks. Sup-
One lock design

pose Bob also buys a lock and changes the combination. Just like the locksmith
used to make many

who designed the lock, Alice has no clue how to figure out the combination on
locks

Bob’s or anyone else’s lock. So Alice can’t open Bob’s lock, and Bob can’t open
Alice’s lock (see Figure 1-1).

12 Right, 18 Left… 34 Right, 28 Left…
Figure 1-1

Alice’s and Bob’s individual locks are only two of many instances of the
identical lock design.