Question

**Scenario**: A computer system allows a user to
choose a password with a length of one to eight characters. A
system administrator needs to figure out how long a user’s password
should expire.

Assume that 1 million passwords can be tested per second by a hacker. The hacker can guess a user’s password 24 hours a day and 7 days a week. A password should be expired if it has an equal or greater than 10% probability of having been guessed. Given each of the following condition, determine the time (in measurement of days) users’ passwords should be expired.

Probability of having been guessed = total number of guess/total possible combinations.

You may Excel’s Power function to calculate m^{n}. Make
sure that you show your steps for partial credit.

- Password characters may be any ASCII characters from 1 to 127, inclusive.

- Password characters may be any alphanumeric characters (“A” through “Z,” “a” through “z,” and “0” through “9”).

- Password characters must be digits.

Answer #1

**Answer:**

Let it be for all instances

A = the number of alphabet characters.

R = the guessing rate, 104 scaled to the required unit of time.

N = Number of total passwords

T = the time to achieve the expected probability of having a broken password

then

(R x T) / N = 0.10 **The probability of the total number
of guesses over the total number of passwords is 1/10**

T = N/(10R)

This is the total number of passwords

N= S-1 = 80iiccc - 119

**Answer a.**

a = 127 and T= 6.82x1011 seconds = 21,629 years

**Answer b.**

A= 62 seconds so T= 2.2x109 seconds = 70 years

**Answer c.**

A= 10 then T= 1,111 seconds= 18 minutes

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