We've been having this theoretical discussion and I'm supposed to find the answer to the question but I can't find what we've been discussing in a google search.
Someone suggested you people as the experts.
If we take all the dorm 7-pin room keys for an entire floor, and put them together, we should be able to derive the superset of the master key, for that one floor, right?
If we then do that for all 7 floors of that one dorm, we should get a superset master key for the entire dorm, right?
And if we do that for all the dorms, assuming there is a master key (and we know there is by methods elsewhere from people in the safety services squad), wouldn't we derive the master key for all the dorms that way?
That isn't the question as that makes too much sense to be a question.
The question is HOW MANY KEYS would we need as a minimum set to be accurate?
Do we really need ALL of the keys (hundreds if not thousands)? Or just a few?
Is there a mathematical algorithm for how many keys are needed to derive the master key?
Yes. Typically you'll find that all of the keys for that floor have the same cuts in several positions and vary only in others. The cuts that are the same on a floor/dorm are usually grouped together either at the tip or bow (handle) side of the key. These determine the floor. Those that vary on a single floor determine the individual door.
This exercise has been performed by inquisitive college students for decades, I speak from personal experience that far pre-dates Usenet. In
2003, a security researcher wrote a research paper on it. See here:
This should be very useful in your theoretical discussion.
If you're lucky, skillful with a file, and pay attention to the math, about a dozen blanks. In many cases you can derive the system master with ONE key to ONE lock.
Having a number of samples simplifies the process. In theory it can be done with one.
See the referenced article. Variations are the number of pins, the number of depths used per pin, how extensive the system is, the algorithm used by the locksmith who set it up, etc. Typical American cylinder locks used in schools, etc. have six pins, but the SFIC version (Best, etc.) uses seven. There are typically ten possible depths per pin. However due to mechanical tolerances most systems use either all even or all odd depths per pin position as a key that is only one depth off can operate locks that it isn't supposed to. If this is followed in your system, and it usually is, that means only five possible depths per pin will be used in that system.
You'll need several key blanks that fit the locks, a fine Swiss round or pippin (teardrop-shaped) file, a dial caliper or micrometer, and preferably a spreadsheet program to record things. Having the manufacturer's data sheet for the depth and spacing dimensions will help also, and are easily found online. A key machine and "depth and space keys" will make things a lot easier. A "Blue punch" and good understanding of the principle will make it a trivial joke.
What you're looking for is a key that operates the lock when one of the cuts is different from the single door key (called a "change key" in the industry). Then find a second position that also operates it, etc. You'll find as you progress that your key will operate some but not all of the locks in the system until you have determined the master position for all pin chambers. Start cutting high and work down. It's easier to remove metal than to add it.
If your system is SFIC (Best), there's another unique key that isn't related at all to the keys that open the lock that you should research in your theoretical discussion. It's way cool and can cause no end to mischief in the wrong hands. Careful destructive disassembly of a lock is one way to reveal the secret.
You are making several assumptions. First, that the locksmith or entity that set up the master key system did so logically and only changed one or 2 bittings on each floor. Second, that it is a Best IC Core system being referenced. Third, that there is only one master key, and not a grand master or great grand master key. Fourth, that there is a master key. Fifth, that there is only one control key in the system if it is in fact an IC Core lock system. Sixth, that at some point another locksmith or acting locksmith for the university did not randomly change any of the lock bittings at some point for some reason and thereby remove them from your logically created master key system.
I have worked at a college many times that uses a GGM, GM, and Master key system...everywhere EXCEPT the dorms. They do not want to be liable if there was a master key to a dorm room and it some how "got out". If a student gets locked out of their dorm, they call a locksmith to open the door.