Common password crackers will take a dictionary and then extend that basic dictionary by using common transformations.
Moving a letter around on a keyboard or replacing vowels with numbers, all of these increase the dictionary size, but since they are reducible to simple rules, the crackers can keep up. These methods aren't adding significant complexity.
When you add additional words, then you get some exponential complexity. Say we have five words in our dictionary:
apple
beggar
catapult
dice
entropy
If we include reversals, we double the size of the dictionary. This is true for any sized dictionary.
If we include versions which substitute all vowels with numbers, we double the size of the dictionary. This is true for any sized dictionary.
If we include shifting the characters up, down, left, or right, we multiply the size of the dictionary by 5. Better, but true for any sized dictionary.
If we instead use passwords that combine two words, the dictionary grows by 24 times. This increase becomes more dramatic as the dictionary grows, and it outpaces all other simple substitutions. If our dictionary contains 100 words, the number of passwords to check is well over 100 digits long. None of the other simple transformations is as powerful as the addition of another word.
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[ 5.0 ms ] story [ 8.8 ms ] threadMoving a letter around on a keyboard or replacing vowels with numbers, all of these increase the dictionary size, but since they are reducible to simple rules, the crackers can keep up. These methods aren't adding significant complexity.
When you add additional words, then you get some exponential complexity. Say we have five words in our dictionary: apple beggar catapult dice entropy
If we include reversals, we double the size of the dictionary. This is true for any sized dictionary. If we include versions which substitute all vowels with numbers, we double the size of the dictionary. This is true for any sized dictionary. If we include shifting the characters up, down, left, or right, we multiply the size of the dictionary by 5. Better, but true for any sized dictionary.
If we instead use passwords that combine two words, the dictionary grows by 24 times. This increase becomes more dramatic as the dictionary grows, and it outpaces all other simple substitutions. If our dictionary contains 100 words, the number of passwords to check is well over 100 digits long. None of the other simple transformations is as powerful as the addition of another word.