Technology Corner: Calculating the Number of Android Lock Patterns: An Unfinished Study in Number Theory

Although one is unlikely to ever want to brute-force an Android lock pattern, many do wonder about the relative strength of the lock pattern versus a multi-digit personal identification number (PIN). It becomes obvious pretty quickly that there are many more lock patterns than the 10,000 possible four-digit PINs. Figure 1 Android lock pattern screen But, how many lock patterns are there? The often-cited number of Android lock patterns is 986,328, which I first found from A. Hoog (personal communication, October 2012) and S. Brothers (personal communication, October-November, 2012). Brothers went so far as to observe that this number could be found in the Android's gesture file and, more to the need for an actual formula, that the number can be derived from the formula for permutations.