Question

Suppose that you open an email account and you are told that you need six-character password & the characters must be alpha-numeric ( either alphabetical or numerical). Assume that a lower case letter is different from an upper case one.

a) How many passwords are possible? Give the exact answer and do not use scientific notation. Show some work.

b) Suppose a computer hacker tries to guess what your password is by testing all possible passwords and it takes his program one second to test 400 passwords. What is the maximum amount of time (in hours) that it will take the hacker to discover your password? Let's assume that the hacker has a simple program that will randomly check all password and that it is allowed to use as much time as it needs. Show some work.

c) What is the probability that the hacker's program will discover your password in at most an hour? Write your answer as a fraction and a decimal rounded with three nonzero digits.

Answer 1

a)

For each character there can be 26 lowercase alphabets, 26 uppercase alphabets or 10 numbers. So, each character can be any of 26+26+10 = 62 alphanumeric characters.

Number of unique six-character passwords = 62⁶ = 56800235584

b)

The program takes one second to test 400 passwords.

For 56800235584 different passwords, the maximum amount of time required = 56800235584 / 400

= 142000589 seconds

= 142000589 / 3600 hours

= 39444.608 hours

c)

Since the hacker randomly check all password, we can assume that the time to discover the password follows uniform distribution with minimum value as 0 and maximum value as 39444.61 hrs.

Probability that the hacker's program will discover your password in at most an hour = P(X < 1)

= 1/39444.608