How much additional complexity does adding a single character to the minimum length of passwords for an organization create?

When considering the complexity of passwords in terms of possible combinations, adding a single character to the minimum length of a password significantly increases the number of potential combinations. This complexity is determined by the set of characters allowed and the length of the password.

In a typical password scenario, there are various character classes, such as lowercase letters, uppercase letters, numbers, and special characters. If we take a common approach where we assume the password can include lowercase letters (26), uppercase letters (26), and digits (10), that gives us a total of 62 characters (26 + 26 + 10) that can be used in the password.

When you increase the length of the password by one character, the total number of combinations grows exponentially. Specifically, with each additional character, the number of possible combinations is multiplied by the number of characters available. So, if the password's original length is N, it has 62^N combinations. Adding one more character (making it N+1) results in 62^(N+1), which can be expressed as:

62^(N+1) = 62^N * 62

This means that for every additional character, the total number of combinations increases by a factor of 62.