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A quick question re:the group 2 numbers..

PostPosted: Sun Mar 11, 2018 10:12 am
by castle 2
I have read time and time again that in order to qualify 'Group 2', a safe lock must
Have a relocker
Have one million different combinations,
Now, even by ignoring the Forbidden Zone numbers etc, the stats for a three-wheel lock are
1/99 of guessing ONE wheels number,
1/9702 of guessing TWO wheels numbers, and
1/941094 of guessing THREE wheels numbers, there being that amount of POSSIBLE permutations OF numbers...

Last time i was to check, that's not as much as wot it shud ov bin, so wotz wiv that?

Re: A quick question re:the group 2 numbers..

PostPosted: Sun Mar 11, 2018 12:12 pm
by MartinHewitt
A 6730 has one million different combinations. It is just that some of these can't be used to open the lock anymore. :) Perhaps these are just one million theoretically possible combinations.

Btw. one out of 100 is 1/100, not 1/99. And on the average you need only halve of that.

Re: A quick question re:the group 2 numbers..

PostPosted: Mon Mar 12, 2018 5:43 pm
by madsamurai
That word "theoretical" is the key... if you have a 100 number dial, minimum 5 digit difference between consecutive numbers in combo, and 10-digit forbidden zone on 3rd no., you're actually looking at around 720,000 legit combination possibilities (plus a few hundred or so if the 2nd digit is inside or within 4 digits of the fz... the math gets complicated there). If you take out the minimum 5 digit difference, you can squeak out 900,000 dialable combos, however some of those combinations will actually be somewhat different internally than what is actually being dialed... for example if you dialed 25-25-25, due to the overlap of the flys the second and third number would be pushing the previous number off by a digit or two, and you would actually be dialing something more like 24-27-25. So technically speaking, that 900,000 number is higher than the true number of combos that can be actually achieved internally (closer to 890,000ish I think).
I can only assume UL uses the theoretical number to qualify locks, since it's impossible to get a full million from a mechanical dial with 100 digits and any restrictions. Not positive, as it seems the only way to read the actual text of the UL 768 standard is to pay $500+ for it... am I wrong there?

Re: A quick question re:the group 2 numbers..

PostPosted: Mon Mar 12, 2018 6:52 pm
by MartinHewitt
The forbidden zone are normally advertised as 20 numbers. I tested it on my 6730 and it is really not much less. I think it had problems in the range of 3 to 19 starting with scratching and going up to really blocking the lock so that disassembly was necessary.

The 5 digit difference is technically not really necessary. I assume it is there that people make less error when dialing the combination. Because of the fly it is really possible to set a lock to L25-R25-L25. It is even possible to dial a tiny bit to far without disturbing the previous wheel. I would fix the minimum difference to the width of a gate in manipulation, which is nearly 5 digits.

W3 not at 1-20 and difference of two neighboring wheels at least 5 means there are 656629 possible combinations.

Re: A quick question re:the group 2 numbers..

PostPosted: Mon Mar 12, 2018 6:59 pm
by madsamurai
Oops, you are correct MartinHewitt... I was thinking the FZ was just 0-10, but they also include 90-99 in the instructions (splined at 41, or 0-20 if splined at 50). My bad, thanks for the clarification.

Re: A quick question re:the group 2 numbers..

PostPosted: Wed Mar 14, 2018 1:22 am
by Oldfast
Good discussion. I've never given it all too much thought,
but I remember Matt Blaze touching on it in great detail.

May not answer all questions we've brought up, but most.
Safecracking for the Computer Scientist
Page 5. Section 1.3.1 "The Combination Keyspace"