Back to Number Theory and Cryptography

## Substitution Ciphers (March 11, 2004)

The name substitution cipher comes from the fact that each letter that you want to encipher is substituted by another letter or symbol, but the order in which these appear is kept the same. Another way to say this is that the message you want to keep secret (called the plaintext) is transformed into the enciphered message (called the ciphertext) by using a different alphabet. It is useful to keep track of the different alphabets by always writing your plaintext in lowercase and your ciphertext in uppercase. You have probably seen this type of cipher before; often in the newspapers there is a "cryptoquip" which challenges you to solve just such a cipher.

## Examples

Try to decipher the encrypted text below. Each cipher below uses some systematic way of replacing the plaintext letters with the ciphertext letters. In addition to figuring out what each says, try to figure out how the message was enciphered. Use the word breaks to give you clues as to what is being said, and look for patterns you recognize. All of these messages are in English! You can also look at some hints.

1. Caesar shift:

WKLV PHVVDJH ZDV HQFUBSWHG XVLQJ D FDHVDU VKLIW FLSKHU.

2. Atbash:

GL WVXLWV GSRH, BLF HLOEVW ZM ZGYZHS XRKSVI. VCXVOOVMG!

3. Keyword:

TCDR ROJTOJIO WAR OJIDMCOQOS WDTC TCO FOYWKQS AGDRKJ.

## Challenge Problems

After you have tried the examples above, try the ciphers on the challenge sheet.

## Questions for Thought

1. What allowed you to break these?

2. What if you didn't have any word breaks?
3. What else would make this harder?

4. Often the ciphertext alphabet is called the key to this sort of cipher (since knowing the alphabet allows you to instantly decrypt the ciphertext). How many possible keys are there?