An intruder has a cluster of 64 machines, each of which can try 10^6 passwords per second. How long does it take him to try all legal passwords if the requirements for the password are as follows:
- passwords can be 6, 7, or 8 characters long
- each character is either a lower-case letter or a digit
- at least one character has to be a digit
My approach is that, for password of length k, there are 36^k possibilities - 26^k forbidden possibilities (because can't be all letters): ∑(k=6 to 8)(36^k−26^k) = 2,684,483,063,360 so 2,684,483,063,360 passwords × (1 second / 64*10^6 passwords) × (1 minute/ 60 seconds) × (1 hour / 60 minutes) = 11.651 hours
Am I approaching this the right way? Is my solution correct?