Locks, boggles, and scream cheese

I wound up needing to get into a locked cabinet today. On a hunch, I tried one of the keys on my half-pound key ring. When the very tip was inserted, the lock turned and I was able to get in to the cabinet.

The lock is kind of old, and it may be wearing out, but the fact that only the front one or two pins needed to be moved makes me suspect that the lock is keyed to multiple keys.

Normally, Yale pin-and-tumbler locks are pretty secure. You have a number of pins, which can be broken at different points along their length. Normally, each pin is broken in only one spot, and if all the spots don't line up, the lock won't turn.

If you have seven pins in a lock, and each can be broken at ten different points, you have ten million different possible combinations for keys.

To key a lock to more than one key, you break each pin at more than one spot. With a sensibly designed master/slave key arrangement, this is still fairly secure. You shouldn't need to have multiple breaks on more than one or two pins. If you have two breaks in one pin, the number of combinations that won't work in the lock drops to five million. If you have two breaks in two pins, the number of combinations drops by a factor of four, to 1.25 million.

My dad lived in a place where the pool gate was (for a while) keyed to open to the front door key of all 36 units. The result was that you could stick anything in the lock and it would open. Not secure.

Let's imagine that the keys for 36 units were made at random. In principle, there's no reason to expect any kind of relationship between any pair of keys – if you compare any two keys, we can expect all of them to raise the same pin in the lock to different heights.

If you try to key a lock to 36 different keys, the chances that any one of ten break positions will not be used is a little under three percent. If you stick in a random key, with seven pins, there's about an eighteen percent chance that it will open that lock. That's nearly one out of five keys, chosen at random. When you consider that a key need not be inserted all the way, each random key is actually a bunch of random keys.

Keying a lock to 36 different keys increases the odds that a random key will open the lock, not to one in 278,000, but to one in five.

People who don't know enough about the workings of the system may come to seriously wrong answers about it.

This, by the way, is very similar to the arguments from complexity put forth against evolution.

We've seen how badly we can go awry when we don't understand the math behind a simple door lock. Before I buy into an argument against evolution based on complexity, I want some assurance that the person making the argument has studied the topic very thoroughly.

In other words, show your work, and justify your assumptions.