When creating a new password, people often recommend you use both uppercase and lowercase characters, numbers, and symbols. How does adding any of these increase the strength of a password?
26 lowercase alphabet characters. Lets assume that there are
100 characters in the entire group of capitalized alphabet characters, symbols, and numbers. Now let's look at any password of length
6. There are
(26 + 100) ^ 6 possible passwords of length 6. A hacker would have a
[1 / (26 + 100)] ^ 6 chance of guessing such a password. The hacker has no way to tell if you used only lowercase alphabet characters or you mixed lowercase alphabet characters with special characters, so he must guess with the entire sample space on each character. If, however, he knew you were only using lowercase alphabet, then, yes, the probablity of guessing your password would increase to
(1 / 26) ^ 6. But in the real world, a hacker wouldn't be able to figure which set of characters you used.