Permutations and Combinations: How Safe is Your Password?

Using Combinatorics to Create Strong Passwords

This lesson is a brief introduction to combinatorics and its relationship to network security via strong passwords. Students will study combinations and permutations and their relationship to strong passwords. The lesson includes how to calculate combinations and permutations with the formula and using a TI-84 calculator. The lesson also includes information on common hacker techniques used to guess passwords.

The students will also test their own passwords at security.org and use the time it takes to crack a password as a measurement of the password’s strength. They can test out for themselves that longer, more complex password requirements have more possible combinations and are, therefore, harder to crack.

This lesson can be taught over one or two days. It can also be adapted for a 90 minute block period. (The password activity with security.org can be done as a stand alone activity as well, as a way to explore functions in a real world setting.

It has a modular design, so parts can be taught in parts or as stand alone lessons.
Steps 2-9 can be taught as a stand alone lesson (use the first section ONLY of Permutations vs Combinations.pdf as the assessment).
Steps 10-12 can also be taught as a stand alone lesson (use all of the Permutations vs Combinations.pdf as the assessment).
Steps 1 and 13 can be combined into a stand alone activity on password safety.