When our burglar alarm goes off, it generates a 4 digit code on the panel, which in order to reset it, one reads out to the monitoring centre - they respond with another 4 digit code which one types into the panel, and it allows you to reset it.
These codes are obviously algorithmically related. How? I've never had enough samples to work it out (and usually can't be bothered to write them down when a spider in a PIR has awoken us at 2AM).
And are the codes common to all panels, or manufacturer specific?
If it was me designing it, I'd be using a simple hash function.
These take one number - the embedded in the unit serial number, for example, and another number (the number it thought of first, and which hasn't been used in the last 5000 alarms), and from these produce a third number (which it presents as the number on the front).
The ideal hash function cannot simply be reversed, certainly not without _vastly_ more information than you have, as well as computer time in the centuries.
I'd use this not because it's needed, but because I've already written such a function for use in other stuff, and it's not especially hard to code. (though having theives get to know how to compute the code would be bad.
It's possible the alarm instead simply adds this number to a secret number, and rounds off any extra digits, this is quite easy to work out.
Or any other possible scheme, some of which are vulnerable to paper and pencil, some of which will need a computer, and some which are practically impossible to solve.
Its panel specific, in the Galaxy range I'm sure its five digits. There is a seed number put into the panel (usually 1-255), and the algorithm is run from that. I haven't seen any programs around that emulate it though.
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