Assume passwords are selected from four character combinations of 26 lower case alphabetic characters. Assume an adversary is able to attempt passwords at a rate of 1 per second. Assuming feedback to the adversary flagging an error as each incorrect character is entered, what is the expected time to discover the correct password

Given:

Passwords are selected from 4 characters.

Character combinations are 26 lower case alphabetic characters.

Passwords attempts by adversary is at rate of 1 second.

To find:

Expected time to discover the correct password

Explanation:

Solution:

4 character combinations of 26 alphabetic characters at the rate of one attempt at every 1 second = 26 * 4 = 104

So 104 seconds is the time to discover the correct password. However this is the worst case scenario when adversary has to go through every possible combination. An average time or expected time to discover the correct password is:

13 * 4 = 52

You can also write it as 104 / 2 = 52 to discover the correct password. This is when at least half of the password attempts seem to be correct.