--- title: "One key to lock and unlock" subtitle: "Secret messages · Secret codes · Lesson 5" --- # One key to lock and unlock **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Most of the secret messages on the internet are locked with a key that both ends already share. The locking step is much like this lesson, only with far bigger numbers. :::teacher-note **In one sentence:** Students lock and unlock numbers with XOR and a shared key, and meet the weakness of sending the same locked message every time. **Students should be able to say:** I can lock a number with XOR and a shared key and unlock it with the same key. I can explain why a wrong key gives a wrong answer without an error. I can say why sending the same locked message each time is a weakness. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict ![The program as blocks](https://studio.learningwaypoints.com/tutorials/_pictures/makecode/code/bbda7337c79a.png?v=0f879c9f00a53964) :::keep-together **A is pressed. The radio carries a number. What does the receiving micro:bit show?** ☐ 2 ☐ 5 ☐ 7 ☐ 12 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 7. The radio carried 7 ^ 5 = 2. The receiver computes 2 ^ 5 = 7, the original number. ::: ## Run Run the program in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Investigate ![The program as blocks](https://studio.learningwaypoints.com/tutorials/_pictures/makecode/code/bbda7337c79a.png?v=0f879c9f00a53964) :::keep-together ### Locking a number **What number does the radio carry when the sender encrypts 6 with key 3? (6 is 110 in bits and 3 is 011.)** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5 110 XOR 011 = 101, which is 5. ::: :::keep-together ### A wrong key **The sender encrypted 6 with key 3, so the radio carries 5. A receiver wrongly uses key 4. What does it show?** ☐ An error message ☐ 6 ☐ 1 ☐ Nothing ::: :::teacher-note **Answer:** 1 5 ^ 4 = 101 ^ 100 = 001 = 1. The receiver gets a wrong number and no warning. Nothing in XOR tells you the key was wrong. ::: :::keep-together ### Why it works both ways **Why does the receiver use the very same operation the sender used?** ☐ Because XOR undoes itself when you repeat it with the same key ☐ Because the micro:bit remembers the number ☐ Because 5 is a special key ☐ Because the radio flips the bits back ::: :::teacher-note **Answer:** Because XOR undoes itself when you repeat it with the same key (message ^ key) ^ key = message. The key cancels itself. ::: :::typical ## Modify Let **B** change the key and show it. Set the key the same on both micro:bits, then press **A**. Then make the keys different. What happens? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} :::teacher-note **One possible solution.** Other correct programs are fine; check that the program runs and does what the task asks. ![The program as blocks](https://studio.learningwaypoints.com/tutorials/_pictures/makecode/code/93005f34cb5c.png?v=cfdb23e1fe3601dd) ::: ::: ## Make **The PIN.** **The same number again.** Send a four-digit PIN, locked with a shared key, to a second micro:bit that unlocks and shows it. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} :::teacher-note **One possible solution.** Other correct programs are fine; check that the program runs and does what the task asks. **The PIN:** ![The program as blocks](https://studio.learningwaypoints.com/tutorials/_pictures/makecode/code/4a113ba628d5.png?v=2d69874acb3f976a) ::: ## Exit ticket :::keep-together **Why does the receiver use the same key and the same operation as the sender?** {{lines-3}} ::: :::teacher-note **Answer:** XOR with the same key undoes itself: (message ^ key) ^ key = message. :::