Question

Suppose an automatic password cracking program takes an average of 10 minutes to crack one password that has 10,000 possible combinations. (This means it would take 20 minutes if there were 20,000 possible passwords and 30 minutes if there were 30,000 possible passwords).

a) 3 pts What is the maximum length of time the program would need to be able to crack a password of 8-character length made of only one number and seven lower-case letters?

b) 6 pts What is the maximum amount of time the program would need to be able to crack a password of 12-character length that includes at least one capital, at least one number, and at least one special symbol chosen from @,#, $ ?

Answer 1

a) The password has 8 characters. A character can have one number and 7 lower-case letters. The number of ways of choosing one number from a combination of 10 digits between 0-9 is 10. The number of ways of choosing a letter from 26 small letters is 26. Now, a password has one number and 7 lower-case letters. Hence, the total combinations become:

Now, the position of a number can be anywhere, and thus, the total combinations need to be multiplied by 8 for 8 positions. Hence, the total combinations of passwords are:

Now, to crack a password with 10,000 combinations, it takes 10 minutes. Hence, the time taken to crack a password from these combinations become:

Hence, to crack this code, it would take more than 1200 years.

b) The password is made of 12 characters. It has at least one capital letter, at least one number and at least one special character chosen from @, #, $.

The number of ways of choosing one capital letter is 26. The number of ways of choosing one number from 0-9 is 10. The number of ways of choosing one special character from @, #, $ is 3. The remaining characters are 12 - 3 = 9. These 9 characters can be either digits, small letters, capital letters or special characters @, #, $. Hence, each character can be any one of 10 + 26 + 26 + 3 = 65.

Also, the position of these characters can be irrespective of each other and there are a total of 12 positions. Thus, we get a total combination of:

Now, 10000 combinations can be cracked in 10 mins. Hence, the time required to crack these many combinations is: