As you know the passwords on many systems are stored like hash, if the password has almost the same size of the hash you will have more success to recover, but if you think that the password has a bigger size, you will get so much collisions, that is very simple to understand, the hash has one fixed size and no matter whats the size of what you use like an input, the function always will generate the output in the same size.So you think, your password is something like 400 bytes, the hash have always 64 bits of size, there you go:
(your pwd) => 2^(8*400) = the number of combinations that you have with 400 bytes
(hash) => 2^64 = the number of combinations that the hash can hold
I don't need to tell you that for represent something more than 2^64 will generate same "identifications", think about 2^65 ((2^64)*2), the half of values will be collisions, in other words each "identification" can represent 2 different values.
However for each algorithm somethings like the forecast of the collisions would appear distinct from each other.
Well, if you want to know more about hash, here is a link:
http://en.wikipedia.org/wiki/Cryptographic_hash_function
Lets back to the LM hash:
http://en.wikipedia.org/wiki/LM_hash
size: 16 bytes(string)
Windows Passwords:
size: 15 characters long(OEM)
Here we have a good success rate.
The tool:
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Image .iso
http://lasecwww.epfl.ch/~oechslin/projects/ophcrack/
Author: Dr Philippe Oechslin
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Testing
If you want test with a VM like i did.
In Virtual PC:
Menu Bar >> Capture ISO Image... >> ophcrack-livecd-1.2.2.iso
Choose VESA Mode, and just look :)
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