Cracking a Caesar cipher with letter frequencies

What you are doing

Encryption scrambles data so that only someone with the key can read it. People rely on it every time they send a password, a bank card number or a medical form. But encryption is only useful if it is hard to break. You will use a Caesar cipher, break it two different ways, and then decide which kinds of data really need strong encryption before they are stored or shared.

Step 1: encrypt

Encrypt LEAVE AT DAWN with key 5. Use the alphabet strip in section 3 of the stimulus. The first letter is done for you.

(b) Show the MOD working for the letter W: (position of W + 5) MOD 26 = ?

Step 2: decrypt

Rhodri sent Nia this message with key 4. Decrypt it by moving each letter back 4 places.

XLI OIC MW YRHIV XLI QEX

(b) Rhodri wrote “key = 4” at the bottom of the same note. Why does that make the encryption useless?

Step 3: brute force

Nia sent this, but nobody knows the key: PHHW DW QRRQ

Try keys on the first word only, moving each letter back. Stop when you get a real word.

(b) Use the key you found to decrypt the whole message.

(c) What is the greatest number of keys you would ever need to try for a Caesar cipher? Explain why.

Step 4: frequency analysis

The long message in section 4 of the stimulus has a key nobody knows. Instead of trying every key, you will use data.

(a) Count. With your partner, one of you tallies lines 1 and 2, the other lines 3 and 4. Count every letter. Then add your two counts.

(b) Check. Add up all your counts. The total should be 94 + 90 = 184. My total: ______. If it is not 184, recount the line that is out.

(c) Percentages. For your 5 most common letters, work out the percentage of all 184 letters. Round to 1 decimal place.

(d) Draw. Draw a bar chart of your 5 letters, most common first. Label both axes and use a scale of 1 square = 2%.

(e) Compare. Put your chart next to the English chart in section 5 of the stimulus. Which ciphertext letter most likely stands for E? Use the alphabet strip to work out how many places E has moved. That is your key.

(f) Test. Check your key on your 2nd and 3rd most common letters. Do they decrypt to letters that are also common in English (look at the chart)? Then check the word that appears most often in the message.

(g) Decrypt line 1 of the message.

(h) Your E percentage is not exactly 12.7%. Give two reasons why a single message does not match the English chart exactly, and explain why frequency analysis would not work on Nia’s 3-word message in Step 3.

Step 5: how long would brute force take?

A computer can try about 1,000,000,000 (10⁹) keys every second. There are about 31,500,000 seconds in a year.

Give each time in a sensible unit (seconds, minutes or years).

Step 6: when should data be encrypted?

(a) For each situation, say whether the data should be encrypted when it is stored or sent, and give a reason.

(b) Write a short explanation (3 to 5 sentences) for a Year 7 pupil: what the padlock and https in a web address mean, why modern encryption is safe when a Caesar cipher is not, and one thing the padlock does not tell you. Use your answers to Steps 4 and 5 as evidence.

Step by step

1. 5 min Read sections 1 to 3 of the stimulus.
2. 6 min Step 1: encrypt with key 5.
3. 4 min Step 2: decrypt with key 4.
4. 6 min Step 3: brute force Nia’s message.
5. 20 min Step 4: count, work out percentages, draw, compare and decrypt.
6. 7 min Step 5: how long brute force would take.
7. 10 min Step 6, then tick the success criteria you have met.

If you finish early

• Encrypt a 2-sentence message of your own with a key from 1 to 25. Swap with your partner, without telling them the key, and crack each other’s message.
• A different cipher uses key 3 for the 1st letter, key 1 for the 2nd letter, key 4 for the 3rd letter, then repeats. Why would frequency analysis on the whole message no longer find E easily?