Question

1. Compute the number of passwords of each type below along with how long it would taketo test all possible such passwords if it takes 1 nanosecond to test a password. Report the times in the most convenient human understandable form. In all of these, unless noted otherwise, order matters and repetition of characters is allowed.
   1. Passwords of length 8 with any combination of lowercase letters, uppercase letters,and numbers.
   2. Passwords that start with a capital letter, have 10 lowercase letters, and end with a number.
   3. Passwords that start with a capital letter, have between 10 and 20 lowercase letters,and end with a number.
   4. Passwords that have four words in them, where the words come from a list of 20,000 words.
   5. Passwords using the word ‘password’ with different uses of upper case and lowercase letters, and also allowing for a substitution of a number for the letters such as ‘96553014’; each letter is uniquely represented by a number, e.g., p can be replaced with 9 but with no other number. Basically, we have 3 choices per letter in ‘password’. No reordering allowed.
   6. Which of these schemes would you use for your bank account?

Answer 1

(there are more than 4 parts so as per policy i will answer forst 4 : a,b,c,d)

a.

total options for each unit of the password = 26 lowercase letters + 26 uppercase letters + 10 numbers

= 62

password length = 8

no. of possible passwords = (no. of options per unit)^(length)

= 62^8

= 2.1834011 * 10^14

time to test = (no. of possible passwords) * (time to test each)

= ( 2.1834011 * 10^14 ) * (1 nanosecond)

= 2.1834011 * 10^14 nanoseconds

b.

no. of passwords = (no. of uppercase letters)*[ (no. of lowercase letters)^10 ]*(no. of numbers)

= (26)*[ (26)^10 ]*10

= 3.6703445 * 10^16

no. of passwords = 3.6703445 * 10^16

time to test = (no. of possible passwords) * (time to test each)

= ( 3.6703445 * 10^16 ) * (1 nanosecond)

= 3.6703445 * 10^16 nanoseconds

c.

Passwords that start with a capital letter, have between 10 and 20 lowercase letters,and end with a number.

no. of passwords

= (no. of uppercase letters)*[ (no. of lowercase letters)^10 ]*(no. of numbers) + (no. of uppercase letters)*[ (no. of lowercase letters)^11 ]*(no. of numbers) + ...... + (no. of uppercase letters)*[ (no. of lowercase letters)^20 ]*(no. of numbers)

= (26)*[ (26)^10 ]*10 + (26)*[ (26)^11 ]*10 + (26)*[ (26)^12 ]*10 + (26)*[ (26)^13 ]*10 + (26)*[ (26)^14 ]*10 + (26)*[ (26)^15 ]*10 + (26)*[ (26)^16 ]*10 + (26)*[ (26)^17 ]*10 + (26)*[ (26)^18 ]*10 + (26)*[ (26)^19 ]*10 + (26)*[ (26)^20 ]*10

= 5.3885715 * 10^30

time to test = (no. of possible passwords) * (time to test each)5.3885715* 10^30 * 1 nanosecond

= 5.3885715 * 10^30 nanoseconds

d.

for each unit of the password there are 20,000 options

no. of possible passwords = (20,000)^4

= 1.6 * 10^17

time to test = (no. of possible passwords) * (time to test each)

= (1.6 * 10^17 ) * (1 nanosecond)

= 1.6 * 10^17 nanoseconds

(please UPVOTE)