Proteus <proteus@uselessemail.net> writes:

>How much more secure, mathematically, is a 6 digit password than a 4

Security is not a mathematical question. the mathematical question is " How
may passwords are there with 6 digits rather than 4). However it is very
easy to make a 6 digit password far less secure than a 4 digit one.

If by digit, youmean the numbers 0-9, then 10^n is the number of numbers
with n digits. If by digit you mean character, then it is something like
96^n, if you allow any (printable) character.

>digit, an 8 digit than a 4 digit, etc.? I mean, if a site says I can make
>up a password of 4-10 characters, I am wondering if going beyond the 4
>chars to 5,6,7,8,9,10 makes the password more secure in a linear or
>exponential manner. I am finally learning to take passwords seriously,

The number of possible passwords increases exponentially. However, unless
you choose your password at random from all possibilities (almost noone
ever does) that is largely irrelevant. What is relevant is the space from
which you pick your actual password. If it is words in a dictionary, then
there are about an equal number ( not very large number) or 4 and 6
character words.


>making stronger, more randon, non-dictionary passwords. Just curious about
>the mathematical relationship between password length and strength.

Only a weak relationship between length and strength.
Far stronger relationship between how the password is chosen and strength.