Scrambling is not a secret

Classroom resources

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Students will be able to

• I can write a function that scrambles text and one that unscrambles it.
• I can explain why a secret method is not enough.
• I can name the parts of a code: method, key, plain text and cipher text.

Timing

Predict and Run 7 min · Investigate 10 min · Modify 6 min · Make 15 min

Before class

The idea: a cipher is a method for scrambling a message. If the method is the only secret, everything is lost the moment someone learns it. Real ciphers have a public method and a secret key; Caesar's cipher, next, is the smallest example.

Vocabulary: plain text (before), cipher text (after), method (steps), key (the secret value). Use them every time from now on.

Code: this lesson teaches the code every later cipher is built from. Foundations functions were named jobs with nothing in or out; reverse(text) takes a parameter and returns a text. The for index loop visits each place 0 to length − 1, and text.charAt(i) is the letter at place i (counted from 0, like a list). The Investigate trace task (result after i = 0 and 1) checks students can follow it; spend time here, because Caesar, Checksum and the CTF reuse the same shape.

Running the lesson

1. Predict: students expect HELLO. Ask: where in the program is the reversing undone?
2. Make: let pairs swap and guess. The point is that a guess at the method is cheap.

The hard part (on purpose)

A method everyone knows hides nothing. Ask what a listener who knows the method would need to read the message.

When students get stuck

Answers to the checks

1. Predict: A is pressed. What does the other micro:bit show?
   OLLEH. The receiver shows exactly what the radio carried, and the radio carried the reversed text. The receiver never undoes it.
2. Inside reverse: In reverse("HELLO"), what is result after the loop has run for i = 0 and then i = 1?
   EH
   At i = 0 the letter at place 0, H, is joined in front of the empty result: H. At i = 1, E is joined in front: EH. Each new letter goes on the front, so the order flips.
3. Undoing it: Sam knows the sender reverses every message. A message arrives: OLLEH. What does Sam do to read it?
   Reverse it again
   Reversing twice gets back the original. Once the method is known, the scrambling is no protection.
4. The parts of a code: Match each part of a code with its job.
   The method → C. the steps for scrambling and unscrambling; can be public; The key → B. a secret value the method needs; only the two people know it; The plain text → A. the message before it is scrambled; The cipher text → D. the scrambled message that travels
5. What to protect: Which is the better rule for a code?
   Assume the method is known, and keep only the key secret
   Methods leak: they get copied, written down and guessed. A key can be changed in a moment, so the key is what to protect.

Solutions

One possible solution for each task. Other correct programs are fine.

Modify

function reverse(text: string): string {
    let result = ""
    for (let i = 0; i < text.length; i++) {
        result = text.charAt(i) + result
    }
    return result
}
radio.setGroup(5)
input.onButtonPressed(Button.A, function () {
    radio.sendString(reverse("HELLO"))
})
radio.onReceivedString(function (receivedString) {
    basic.showString(reverse(receivedString))
})

Make

function scramble(text: string): string {
    let result = ""
    for (let i = 0; i < text.length; i++) {
        result = result + text.charAt(i) + "X"
    }
    return result
}
function unscramble(text: string): string {
    let result = ""
    for (let i = 0; i < text.length / 2; i++) {
        result = result + text.charAt(i * 2)
    }
    return result
}
radio.setGroup(5)
input.onButtonPressed(Button.A, function () {
    radio.sendString(scramble("MEET AT 3"))
})
radio.onReceivedString(function (receivedString) {
    basic.showString(unscramble(receivedString))
})

Stretch and support

Stretch: Make the scrambler swap each pair of letters (HELLO → EHLLO).

Support: Give scramble complete and ask only for unscramble.

Exit ticket

Why is a message that is scrambled with a method everyone knows not private?

Anyone who knows the method can undo it. A code needs a secret key that is separate from the method.

What each step is for

• Investigate: Scrambling with a method everyone knows hides nothing from someone who knows the method. A code needs a secret, and the secret must be separate from the method.
• Modify: The receiver must undo the sender's scrambling, using the same function.

Where it leads

Next: a code with a key, the Caesar cipher.