http://arstechnica.com/security/2015/08/new-data-uncovers-the-surprising-predictability-of-android-lock-patterns/

The abundance of password leaks over the past decade has revealed some
of the most commonly used—and consequently most
vulnerable—passphrases, including "password", "p@$$w0rd", and
"1234567". The large body of data has proven invaluable to whitehats
and blackhats alike in identifying passwords that on their face may
appear strong but can be cracked in a matter of seconds.

Now, Android lock patterns—the password alternative Google introduced
in 2008 with the launch of its Android mobile OS—are getting the same
sort of treatment. The Tic-Tac-Toe-style patterns, it turns out,
frequently adhere to their own sets of predictable rules and often
possess only a fraction of the complexity they're capable of. The
research is in its infancy since Android lock Patterns (ALPs) are so
new and the number of collected real-world-patterns is comparatively
miniscule. Still, the predictability suggests the patterns could one
day be subject to the same sorts of intensive attacks that regularly
visit passwords.

Marte Løge, a 2015 graduate of the Norwegian University of Science and
Technology, recently collected and analyzed almost 4,000 ALPs as part
of her master's thesis. She found that a large percentage of them—44
percent—started in the top left-most node of the screen. A full 77
percent of them started in one of the four corners. The average number
of nodes was about five, meaning there were fewer than 9,000 possible
pattern combinations. A significant percentage of patterns had just
four nodes, shrinking the pool of available combinations to 1,624.
More often than not, patterns moved from left to right and top to
bottom, another factor that makes guessing easier.

"Humans are predictable," Løge told Ars last week at the PasswordsCon
conference in Las Vegas, where she presented a talk titled Tell Me Who
You Are, and I Will Tell You Your Lock Pattern. "We're seeing the same
aspects used when creating a pattern locks [as are used in] pin codes
and alphanumeric passwords."

ALPs can contain a minimum of four nodes and a maximum of nine, making
there 389,112 possible combinations. In a similar fashion as
passwords, the number of possible combinations grows exponentially
with the length, at least up to a point. Here's the breakdown:

Length - Number of combinations
4 - 1,624
5 - 7,152
6 - 26,016
7 - 72,912
8 - 140,704
9 - 140,704

As part of her thesis, Løge asked subjects to create three ALPs, one
for an imaginary shopping app, a second for an imaginary banking app,
and the last to unlock a smartphone. Sadly, the minimum four-node
pattern was the most widely created one by both male and female
subjects, followed by five-node ALPs. For reasons Løge still can't
explain, eight-node patterns were the least popular, attracting
significantly fewer subjects than nine-node choices, even though both
offered the same number of possible combinations. The slide below
contrasts choices of males on the top with those of females below,
showing that the former were much more likely to pick longer patterns
over shorter ones.
...

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