Question

2) Allowing (or requiring) users to use numerical digits (including 0) and one of 28 “special characters” dramatically increases the number of possible passwords. Furthermore, passwords often are case-sensitive, effectively doubling the size of the alphabet by defining 52 distinct letter characters.   

Assuming that passwords are case-sensitive and can include numerical digits and special characters, how many possible 6, 8 and 10 character passwords can be created? (8 points)

3) Allowing digits and special characters creates an enormous number of passwords. However, computers can check passwords very quickly. Let’s say that a computer can check 140 million passwords per second.

a) How long (in minutes) would it take a computer to check every possible 6 character password? (8 points)

b) How long (in years) would it take a computer to check every possible 10 character password? (8 points)

4) Question 2 asked you to compute the number of possible passwords with various numbers of characters. However, it seems more likely that most people will choose actual words for their password. According to the website wordfinder.yourdictionary.com, the English language has approximately 18,000 six-letter words.

a) Assume that a password must be at least 8 characters long and include at least 1 digit and at least 1 special character. If people form their password by taking an English word of exactly 6 letters (assume that this password is not case-sensitive) and then adding (in either order) a digit and a special character (e.g flames#1), how many passwords would be possible? (10 points)

(Hint: Find the number of passwords with 6 letters followed by a digit and a special character, then exchange the order of the last two characters.)

b) How does your answer change if we assume that we still have a 6 letter word, but now we assume that both the digit and the special character can be inserted into the word in any position (e.g. fla#me1s)? (4 points)

Answer 1

Solution:

2) The total possible combinations of passwords are 90! ( 52 alphabet+ 28 special characters+ 10 digits)

Possible 6 characters passwords = = 622614630

Possible 8 characters passwrods ==77515521435

Possible 10 characters passwords ==5.720645e+12

3) a)

Total time taken to check possible 6 character passwords = = 0.07412079 minutes

b) Total time taken to check possible 6 character passwords = =  681.0292 minutes

4)

a) Total 6 letter words in = 18000

Total 8 character passwords with one special character & one digit with the order reversed = =1224720000

b) Total 8 character passwords with special chacrcter & one digit in any position = = 4.092812e+21