Doing Cryptography without Paper Tools
The cipher wheel and St. Cyr slide are nice tools to do encryption and decryption with the Caesar cipher. But we can implement the Caesar cipher with just pencil and paper.
Write out the letters of the alphabet from A to Z with the numbers from 0 to 25 under each letter. 0 goes underneath the A, 1 goes under the B, and so on until 25 is under Z. (There are 26 letters in the alphabet, but our numbers only go up to 25 because we started at 0, not 1.) It will end up looking something like this:
A B C D E F G H I J K L M
0 1 2 3 4 5 6 7 8 9 10 11 12
N O P Q R S T U V W X Y Z
13 14 15 16 17 18 19 20 21 22 23 24 25
With the above letters-to-numbers code, we can use numbers to represent letters. This is a very powerful concept, because math uses numbers. Now we have a way to do math on letters.
Now to encrypt we find the number under the letter we wish to encrypt and add the key number to it. This sum will be the number under the encrypted letter. For example, we encrypt, “Hello. How are you?” with the key 13. First we find the number under the H, which is 7. Then we add the key to this number. 7 + 13 = 20. The number 20 is under the letter U, which means the letter H encrypts to the letter U. To encrypt the letter E, we add the 4 under E to 13 to get 17. The number above 17 is R, so E gets encrypted to R. And so on.
This works fine until we get to the letter O. The number under O is 14. But when we add 14 + 13 we get 27. But our list of numbers only goes up to 25. If the sum of the letter’s number and the key is 26 or more, we should subtract 26 from it. So 27 – 26 is 1. The letter above the number 1 is B. So the letter O encrypts to the letter B when we are using the key 13. One by one, we can then encrypt the letters in, “Hello. How are you?” to “Uryyb. Ubj ner lbh?”
So the steps to encrypt a letter are:
1. Decide on a key from 1 to 25. Keep this key secret!
2. Find the plaintext letter’s number.
3. Add the key to the plaintext letter’s number.
4. If this number is larger than 26, subtract 26.
5. Find the letter for the number you’ve calculated. This is the ciphertext letter.
6. Repeat steps 2 to 5 for every letter in the plaintext message.
Look at the following table to see how this is done with each letter in “Hello. How are you?” with key 13. Each column shows the steps for turning the plaintext letter on the left to the ciphertext letter on the right.
Write out the letters of the alphabet from A to Z with the numbers from 0 to 25 under each letter. 0 goes underneath the A, 1 goes under the B, and so on until 25 is under Z. (There are 26 letters in the alphabet, but our numbers only go up to 25 because we started at 0, not 1.) It will end up looking something like this:
A B C D E F G H I J K L M
0 1 2 3 4 5 6 7 8 9 10 11 12
N O P Q R S T U V W X Y Z
13 14 15 16 17 18 19 20 21 22 23 24 25
With the above letters-to-numbers code, we can use numbers to represent letters. This is a very powerful concept, because math uses numbers. Now we have a way to do math on letters.
Now to encrypt we find the number under the letter we wish to encrypt and add the key number to it. This sum will be the number under the encrypted letter. For example, we encrypt, “Hello. How are you?” with the key 13. First we find the number under the H, which is 7. Then we add the key to this number. 7 + 13 = 20. The number 20 is under the letter U, which means the letter H encrypts to the letter U. To encrypt the letter E, we add the 4 under E to 13 to get 17. The number above 17 is R, so E gets encrypted to R. And so on.
This works fine until we get to the letter O. The number under O is 14. But when we add 14 + 13 we get 27. But our list of numbers only goes up to 25. If the sum of the letter’s number and the key is 26 or more, we should subtract 26 from it. So 27 – 26 is 1. The letter above the number 1 is B. So the letter O encrypts to the letter B when we are using the key 13. One by one, we can then encrypt the letters in, “Hello. How are you?” to “Uryyb. Ubj ner lbh?”
So the steps to encrypt a letter are:
1. Decide on a key from 1 to 25. Keep this key secret!
2. Find the plaintext letter’s number.
3. Add the key to the plaintext letter’s number.
4. If this number is larger than 26, subtract 26.
5. Find the letter for the number you’ve calculated. This is the ciphertext letter.
6. Repeat steps 2 to 5 for every letter in the plaintext message.
Look at the following table to see how this is done with each letter in “Hello. How are you?” with key 13. Each column shows the steps for turning the plaintext letter on the left to the ciphertext letter on the right.
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