The Caesar cipher

Classroom resources

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Students will be able to

• I can explain what the key of a Caesar cipher is.
• I can encrypt and decrypt a message with the same key.
• I can explain why a receiver with the wrong key shows nonsense.

Timing

Predict and Run 8 min · Investigate 10 min · Modify 10 min · Make 18 min

Before class

The idea: every letter moves along the alphabet by the key. The method (shift) is public; the key (the number) is the secret. Both people need the same key.

New code: ALPHABET.indexOf(letter) is the letter's place in the alphabet (A is 0, and −1 if it is not found, which is why spaces pass through). % 26 wraps: 28 % 26 = 2. Treat these as recipes; the Investigate step makes the wrap visible.

A pattern worth naming: decrypting is encrypting with the rest of the circle, 26 − key. Students often expect a separate "undo" method.

Honesty about strength: this code is easy to break, as the next lesson shows. Say so now; the lesson after turns it into the point.

Running the lesson

1. Investigate: the Z → C question is the whole idea. Give time to do it by hand.
2. Make: when keys differ, the receiver shows plausible-looking nonsense. Ask: does the receiver know it is wrong?

The hard part (on purpose)

Wrapping round the alphabet with % 26, and undoing a shift. Ask them to shift one letter by hand, including one near Z, before testing.

When students get stuck

Answers to the checks

1. Predict: A is pressed. What does the micro:bit show?
   KHOOR. H→K, E→H, L→O, L→O, O→R: each letter moves three places along.
2. Z wraps round: With key 3, which place does Z (place 25) move to? (A is 0.)
   2
   25 + 3 = 28, and 28 % 26 = 2: place 2 is C. Without % 26 it would run off the end of the alphabet.
3. Key zero: What does encrypt do with the key 0?
   Nothing is changed
   A shift of 0 leaves each letter where it is. Key 26 does the same, because 26 % 26 is 0. A key of 0 or 26 would be no secret at all.
4. Going back: Ana encrypted a message with key 5. To decrypt it, which key should she use with the same encrypt function?
   −5, or 21 (26 − 5)
   Shifting by 5 and then by 21 is 26 places in all: the full circle back to the start. So decrypt(message, key) is encrypt(message, 26 − key).

Solutions

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

Modify

let ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
function shift(letter: string, key: number): string {
    let place = ALPHABET.indexOf(letter)
    if (place < 0) {
        return letter
    }
    return ALPHABET.charAt((place + key) % 26)
}
function encrypt(message: string, key: number): string {
    let result = ""
    for (let i = 0; i < message.length; i++) {
        result = result + shift(message.charAt(i), key)
    }
    return result
}
function decrypt(message: string, key: number): string {
    return encrypt(message, 26 - key)
}
input.onButtonPressed(Button.A, function () {
    basic.showString(decrypt(encrypt("HELLO", 3), 3))
})

Make

let ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
let key = 3
function shift(letter: string, key: number): string {
    let place = ALPHABET.indexOf(letter)
    if (place < 0) {
        return letter
    }
    return ALPHABET.charAt((place + key) % 26)
}
function encrypt(message: string, key: number): string {
    let result = ""
    for (let i = 0; i < message.length; i++) {
        result = result + shift(message.charAt(i), key)
    }
    return result
}
function decrypt(message: string, key: number): string {
    return encrypt(message, 26 - key)
}
radio.setGroup(5)
input.onButtonPressed(Button.A, function () {
    radio.sendString(encrypt("MEET AT 3", key))
})
input.onButtonPressed(Button.B, function () {
    key += 1
    basic.showNumber(key)
})
radio.onReceivedString(function (receivedString) {
    basic.showString(decrypt(receivedString, key))
})

Stretch and support

Stretch: Add a numeric key menu: B counts up and A sends, and the key resets to 1 after 25.

Support: Give encrypt and decrypt complete; students wire up the buttons and radio.

Exit ticket

What is the key in a Caesar cipher?

The number of places each letter shifts. Sender and receiver must use the same number.

What each step is for

• Investigate: The key is the number of places to shift; % 26 wraps the end of the alphabet; to undo a shift you shift the rest of the way round.
• Modify: Decrypting is encrypting with the rest of the circle.

Where it leads

Next: how long does it take to break this?