Vernam cipher
The Vernam cipher uses a one time pad to encrypt messages. We XOR each character in the plaintext message with the corresponding character in the one-time pad to produce the ciphertext character.
For example, if the plaintext message is “HELLO” and the one-time pad is “XMCKL”, we can encrypt the message as follows:
| Plaintext | H | E | L | L | O |
|---|---|---|---|---|---|
| Pad | X | M | C | K | L |
| Ciphertext | ? | ? | ? | ? | ? |
To encrypt each character, we can convert the letters to their ascii values and then XOR them:
- H (72) XOR X (88) = 16
- E (69) XOR M (77) = 8
- L (76) XOR C (67) = 15
- L (76) XOR K (75) = 7
- O (79) XOR L (76) = 3
So the ciphertext would be the characters corresponding to the ascii values 16, 8, 15, 7, and 3.
Decryption
Decrypting a message encrypted with the Vernam cipher is exactly the same process as encrypting it! We XOR the ciphertext character with the corresponding character in the one-time pad, which gives us the ascii value of the original plaintext character.
For example, if we have the ciphertext characters corresponding to the ascii values 16, 8, 15, 7, and 3, and we know the one-time pad is “XMCKL”, we can decrypt it as follows:
- 16 XOR X (88) = H (72)
- 8 XOR M (77) = E (69)
- 15 XOR C (67) = L (76)
- 7 XOR K (75) = L (76)
- 3 XOR L (76) = O (79)
So we would recover the original plaintext message “HELLO”.
Security
IF we use it with a truly random one-time pad, and we never reuse the same pad for multiple messages, then the Vernam cipher is considered to be unbreakable (assuming nobody else gets access to the one-time pad). This is because each character in the plaintext message is encrypted with a different key, so there is no way to analyse patterns in the ciphertext to try to crack the key.
Issues
The main issues really come from the fact that it uses a one-time pad, which can be difficult to distribute securely. How do you share the OTP with only the intended recipient without it being intercepted by an attacker?
flashcards
| Question | Answer |
|---|---|
| What cipher uses a one time pad to encrypt messages? | The Vernam cipher. |
| In the Vernam cipher, how do you combine each plaintext character with the corresponding one-time pad character? | We XOR each character in the plaintext message with the corresponding character in the one-time pad. |
| What is the ASCII value of ‘H’? | 72 |
| What is the ASCII value of ‘X’? | 88 |
| What is the result of 72 XOR 88? | 16 |
| What is the result of 69 XOR 77? | 8 |
| What is the result of 76 XOR 67? | 15 |
| What is the result of 76 XOR 75? | 7 |
| What is the result of 79 XOR 76? | 3 |
| How do you decrypt a message encrypted with the Vernam cipher? | We XOR the ciphertext character with the corresponding character in the one-time pad, which gives us the ASCII value of the original plaintext character. |
| What is the result of 16 XOR 88? | 72 (the ASCII value of ‘H’) |
| What is the result of 8 XOR 77? | 69 (the ASCII value of ‘E’) |
| What is the result of 15 XOR 67? | 76 (the ASCII value of ‘L’) |
| What is the result of 7 XOR 75? | 76 (the ASCII value of ‘L’) |
| What is the result of 3 XOR 76? | 79 (the ASCII value of ‘O’) |
| Under what conditions is the Vernam cipher considered unbreakable? | If we use it with a truly random one-time pad, and we never reuse the same pad for multiple messages. |
| Why does the Vernam cipher prevent pattern analysis in ciphertext? | Because each character in the plaintext message is encrypted with a different key. |
| What is the main practical issue with the Vernam cipher? | Using a one-time pad can be difficult to distribute securely. |
| What is the key security question about sharing the one-time pad? | How do you share the OTP with only the intended recipient without it being intercepted by an attacker? |