1. Suppose a system uses passwords that may contain only alphabetic (upper and l

Question

1. Suppose a system uses passwords that may contain only alphabetic (upper and lower case) and numerics (0..9). Assume every password is five characters long.

(a) how many possible passwords are there? (this would be the maximum number of passwords you would need to try to crack an account)

(b) if you now allow passwords to be six characters long, how many possible passwords are there?

(c) how many times more passwords would there be if the system has eight character passwords instead of just five character passwords?

(d) if the computer takes 5 ms to check a password for validity, how long would it take on average to guess a password? what would the worst case time be? Show results for five, six and 10 character password lenghts.

(e) same scenario as above, but now you have a cluster with 100 processors in it and so can check 100 passwords simultaneously in 5 ms; how long does it take to guess all the passwords?

Explanation / Answer

Solution:

Consider it like a boxer who can contain five items in five sub boxes.

Now we can put 26 uppercase letters, 26 lower case letters, and 10 digits.

a)

Total number of passwords that can be generated is

5^62

since 26+26+10= 62

b)

then it will be 6^62

c)

8^62/5^62

d)

for 5 it will take

1 password is taking 5ms

in 1 second 1/(5*10^-3) = 200 passwords will be checked

so

5^62/200 second

for 6 will take

6^62/200 second

for 10 digits it will take

10^62/200 second

e)

for 5 it will take

100 password is taking 5 ms

in 1 second 100/(5*10^-3) = 20000 passwords will be checked

so

5^62/20000 second

for 6 will take

6^62/20000 second

for 10 digits it will take

10^62/20000 second

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

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