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Password strength

A password is strong when there are a huge number of possible combinations. The number grows with the character set and quickly with the length. Entropy in bits is the base-2 logarithm of the number of combinations, and each extra bit doubles the time needed to try them all.

K = N^L

number of possible passwords

E = L\cdot\log_2 N

entropy in bits

Symbols

$N$	number of possible characters
$L$	length
$E$	entropy	bit

Example

12 lowercase letters ( $N = 26$ ):

$E = 12\cdot\log_2 26 \approx 56$ bits.

Length beats complexity. Four random words are stronger than a short password with symbols.

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