Password complexity

In terms of information security, there are many recommendations to have a password with a minimally reasonable strength, the recommendation is usually to add special characters and also that the password is long.

But why the use of special characters combined with letters and numbers and also a long string make a string of characters a strong password?

The answer is math, an exponential function =)

A simple example, you need to create a numeric password with four digits and in each digit you can use the digits from 0 to 9. How many password possibilities are possible?
 

10 x 10 x 10 x 10


Or rather, 10 to the fourth power.

Imagine that you have two possibilities (V or F), how many combinations is it possible to form with these two options, let's see:

V or V
V or F
F or V
F or F


Or rather, 2 squared (2²).

Now go back to the example of the password with four numbers and calculate how many combinations are possible in the account (10 x 10 x 10 x 10), I already tell you that the answer is 10000. But what if we add more houses? (10 x 10 x 10 x 10 x 10 x 10 x 10 x 10), this is equal to 100000000, and we can verify that (10 x 10 x 10 x 10 x 10 x 10 x 10 x 10) is equal to 10 to the at the power of 8, the increase in password digits makes increasing complexity an exponential function.

Now add even more possibilities for characters like letters (a-z) and also in capital letters (A-Z) plus special characters which could generate, for example, a type calculation (36 x 36 x 36 ....)

See why passwords with more character possibilities and longer become stronger? An attacker will have to make a much longer attempt to guess a password with uppercase and lowercase letters, numbers, and special characters than one that has only numbers.

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