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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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A computer system uses passwords constructed from the 26

Chapter 3, Problem 128E

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QUESTION:

A computer system uses passwords constructed from the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) passwords from the potential set.

(a) Suppose that 9900 users have unique six-character passwords and the hacker randomly selects six-character passwords. What are the mean and standard deviation of the number of attempts before the hacker selects a user password?

(b) Suppose that 100 users have unique three-character passwords and the hacker randomly selects three-character passwords. What are the mean and standard deviation of the number of attempts before the hacker selects a user password?

(c) Comment on the security differences between six- and three-character passwords.

Questions & Answers

QUESTION:

A computer system uses passwords constructed from the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) passwords from the potential set.

(a) Suppose that 9900 users have unique six-character passwords and the hacker randomly selects six-character passwords. What are the mean and standard deviation of the number of attempts before the hacker selects a user password?

(b) Suppose that 100 users have unique three-character passwords and the hacker randomly selects three-character passwords. What are the mean and standard deviation of the number of attempts before the hacker selects a user password?

(c) Comment on the security differences between six- and three-character passwords.

ANSWER:

Solution:

Step 1 of 4:

A computer system uses passwords that constructed from 26 letters (a-z) or 10 integers (0-9).

Let 10,000 users of the system have unique passwords.

A hacker randomly selects passwords from the potential set with replacement.

  1. We have to find the mean and standard deviation of the number of attempts before the hacker selects a user password, if 9900 users have unique six-passwords.

  1. We have to find the mean and standard deviation of the number of attempts before the hacker selects a user password, if 100 users have unique three-character passwords.

  1. We have to find the security differences between six and three-character passwords.

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