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Secret Writing

Three short lessons on codes and how they are broken: shifting the alphabet, counting letters to crack a shift, and why a longer key is harder to break.

Spark & Whetstone · sparkwhetstone.org/learn/secret-writing · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. Shift the alphabet

The Roman writer Suetonius tells us that Julius Caesar wrote some letters in a simple code: each letter replaced by the one three places later in the alphabet. A became D, B became E, and so on, wrapping round at the end.

This is now called a Caesar cipher, or a shift cipher. To read it, shift each letter back by the same amount.

Question. With a shift of 3, what does the coded word "FDW" say?

  1. CAT
  2. DOG
  3. BAT

Say it back. In your own words: how does a shift cipher work?

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Lesson 2. Count the letters

A shift cipher has only 25 possible shifts, so you could try them all. But there is a faster way, first written down by the Arab scholar al-Kindi in the 800s: frequency analysis.

In English text, E is the most common letter. Count the letters in a coded message; the most common one probably stands for E. Work out the shift from there.

Question. In a long coded message, the most common letter is H. What shift was probably used?

  1. A shift of 3
  2. A shift of 7
  3. A shift of 1

Say it back. Say it back: how does counting letters break a shift cipher?

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Lesson 3. Longer keys

A shift cipher fails because every letter is moved the same way. In the 1500s, codes used a keyword instead: each letter of the message is shifted by a different amount, given by the next letter of the keyword.

Now E is not always coded as the same letter, so simple counting stops working. Modern codes take this idea much further, which is why a longer key is generally harder to break.

Question. Why is a keyword cipher harder to crack than a shift cipher?

  1. Each letter is shifted by a different amount, so letter counts are scrambled.
  2. It uses a different alphabet.
  3. It has no rules.

Say it back. In your own words: why does a longer key make a code stronger?

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At the table: Make a cipher wheel

Players: a grown-up and a child, 7 or older. You'll need: two paper circles of different sizes, a pencil and a paper fastener (or pin).

  1. Write the alphabet round the edge of each circle and pin the small one on the large one.
  2. Turn the inner wheel three places. Write a short message in code.
  3. Swap messages and decode each other's.
  4. Try a mystery shift and crack it by counting letters.

Answers

  1. CAT — F → C, D → A, W → T: CAT.
  2. A shift of 3 — If H stands for E, the shift is E → F → G → H: three places.
  3. Each letter is shifted by a different amount, so letter counts are scrambled. — With different shifts for different letters, E no longer always becomes the same letter, so counting fails.