How Hard Is It To Crack A Password?


With modern computer hardware, you can guess 100,000,000 passwords/sec, using readily available graphics processing units (that number is probably conservative).  These computers have specialized co-processors that are designed to do math-intensive calculations for rendering computer graphics.  They’re equally good at doing math-intensive calculations for cracking passwords. If you don’t own such a system, you can rent one on-line for a little over $2 per hour from Amazon.

 Let’s take the worst case:

 A password made up of upper and lower case letters, numerals and punctuation, gives 96 possible characters.  A 14 character length password (NIST recommended) gives you 4.8 x 10^27 combinations.  Even at 100,000,000 per second, that would take you more than a million years to guess if you had to try every possible combination.  Since, on average, you’ll guess the password after trying only half of the possible combinations, we’re down to 500,000 years.

 If you can’t wait that long, here are some strategies to make things go faster:

 Those numbers presume a real random password.  Unfortunately, we humans (as Randy Munroe points out) don’t do well with random characters.  We can’t reliably remember them.  So we tend to come up with non-random passwords that we can remember. 

 It’s well known that most people pick easy to guess passwords, even if they’re trying not to.  And it’s also true that the more often you have to change your password the worse your choice will become.  If you have to change your password every few weeks or months, you’re more likely to choose an easily guessable one. 

 Depending on whom you ask, there are about 250,000 words in the English language.  Most people base their passwords on one of them. If you’re forced to add a number or punctuation character, you most likely add it to the end of the word.  You might use “leet speak” (‘4’ for ‘A’; ‘1’for ‘L’; ‘3’ for ‘E’; etc.) character substitutions too.

Two digits in front or after the word increases the search space by 10000 times.    Adding leet substitutions increases it 16 times.

 With those additions to standard words we get 2.5 x 10^5 x 16 x 10^4 = 40 x 10^9 possible passwords.

So, using my rented graphics-rendering computer, searching every English word, with one or two digits in front or after it, using any combination of “leet” substitutions would take less than 10 minutes to crack (40 x 10^9 / 10^8 = 400 seconds).  And I still haven’t used up my $2.

 Let’s make it just a little more complicated:  I’ve seen many passwords that vary the letter case, usually adding one or two capital letters.  Assuming an average word length of 6 letters, that increases the time by a factor of 36.  That ups the cracking time to around four hours.

So for a little less than $10, I can find every password that’s based on an English word, that adds one or two digits, one punctuation character and up to two mixed case letters.  In my experience visiting lots of client systems, I’ve covered 90% of the passwords in use.  And it’s only lunchtime.

 There are many additional strategies to search for more complicated passwords.  A simple one is based on the idea that we tend to make up passwords that can be pronounced – that is, ones that use standard English consonant blends and diphthongs.  For example, if I want to invent a word, I’m much more likely to come up with “grooz” than “zmloqk.” The first uses standard blends (“gr”) and standard diphthongs (“oo”).  “Zmloqk” uses nonstandard combinations.  We’re much less likely to choose those, and a password cracker can take advantage of that fact.

 Another oft-touted strategy is to use a phrase or combination of words.  This is a good idea if you do it right.  With my same rented computer, I can guess 3 word combinations (“blue pickled trucks”) of the 50,000 most common words in about a day and a half.  Four words, however, increases the cracking time to almost 200 years.

 In the end, we’re stuck with this dilemma of human nature:  we can create complex passwords that are impossible to guess, but we can’t remember them.  On the other hand, most passwords we do come up with can be cracked with a few hours’ time and beer money.  Keep that in mind the next time you choose a password.

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