Each of the following is a different kind of password. An attacker can always tr

Question

Each of the following is a different kind of password. An attacker can always try to bypass password security by guessing every possible password that might exist. In the worst case (for the attacker), the correct password is the last one that they guess. So increasing the number of potential passwords makes password protection more effective. For each password type, compute the number of passwords of that type that exist. Justify your answers (show your work).
(a) Eight lower-case English letters.
(b) Four base-10 digits.

ALGORITHM ENGINEERING

Explanation / Answer

a. So we have to choose 8 lower-case letters. Total no. of lower case letters= 26(a-z).

So basically we have to select 8 out of 26 letters in a random order. Assuming that letters can be repeated. Let's approach it this way. For the first letter, we have 26 options and we can choose any 1 of them. similarly, for 2nd, we have 26 options, for 3rd also we have 26 options and so on.

So the total no. of 8 digit passwords that can be formed will be 26 * 26 * 26 ... 8 times = 268 = 208827064576 options. How is that? for the 1st letter, we have 26 options. for each option of the 1st letter, we have 26 options for 2nd letter. so for 2 letters, we have 26 * 26 options. similarly, for the 3rd letter, we will have 26 options for each of the 26 *26 letter combinations that we have found for the 1st 2 options. so going on up to 8 digits we arrive at the said answer.

b. By the same analogy, there are 10 options in base 10 digits(0-9) and we have 4 digits. so no. of combinations will be 104 =10000.

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