# Fractionated Morse Cipher

## Introduction §

The Fractionated Morse cipher first converts the plaintext to morse code, then enciphers fixed size blocks of morse code back to letters. This procedure means plaintext letters are mixed into the ciphertext letters i.e. one plaintext letter does not map to one ciphertext letter. This makes it more secure than e.g. substitution ciphers, but it can still be broken with some effort.

One of the benefits of the Fractioned Morse cipher is that it can encipher spaces and punctuation just as easily as letters. The ciphertext message will generally be of a similar length to the plaintext message, but often will have a slightly different number of characters.

## Example §

To pass an encrypted message from one person to another, it is first necessary that both parties have the 'key' for the cipher, so that the sender may encrypt it and the receiver may decrypt it. For the Fractionated Morse cipher, the key is a mixed alphabet e.g. "ROUNDTABLECFGHIJKMPQSVWXYZ".

Here is a quick example of the encryption and decryption steps involved with the caesar cipher. The text we will encrypt is "defend the east", with a key of "ROUNDTABLECFGHIJKMPQSVWXYZ".

The first step is to encode our string as Morse code with 'x' between characters and 'xx' between words

```Morse Code:
A  .-    N  -.    .  .-.-.-  1  .----
B  -...  O  ---   ,  --..--  2  ..---
C  -.-.  P  .--.  :  ---...  3  ...--
D  -..   Q  --.-  "  .-..-.  4  ....-
E  .     R  .-.   '  .----.  5  .....
F  ..-.  S  ...   !  -.-.--  6  -....
G  --.   T  -     ?  ..--..  7  --...
H  ....  U  ..-   @  .--.-.  8  ---..
I  ..    V  ...-  -  -....-  9  ----.
J  .---  W  .--   ;  -.-.-.  0  -----
K  -.-   X  -..-  (  -.--.
L  .-..  Y  -.--  )  -.--.-
M  --    Z  --..  =  -...-
```

Here is an example of converting text to Morse code:

```plaintext:  defend the east
morse: -..x.x..-.x.x-.x-..xx-x....x.xx.x.-x...x-x
```

Now we take blocks of 3 morse code characters and encipher them using the key and the following table:

```R O U N D T A B L E C F G H I J K M P Q S V W X Y Z
. . . . . . . . . - - - - - - - - - x x x x x x x x
. . . - - - x x x . . . - - - x x x . . . - - - x x
. - x . - x . - x . - x . - x . - x . - x . - x . -
```

The first three morse characters in our message are '-..', this corresponds to the column with 'E' above it in the key table. The next three morse characters is 'x.x' which becomes 'S'. Our complete ciphertext becomes: ESOAVVLJRSSTRX. Note that the spaces in the plaintext are retained, when we decrypt we will recover any spaces or punctuation from the plaintext.

## Cryptanalysis §

Cryptanalysis of Fractionated Morse is not extremely difficult. Lets look at the following Fractionated Morse table:

```A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
. . . . . . . . . - - - - - - - - - x x x x x x x x
. . . - - - x x x . . . - - - x x x . . . - - - x x
. - x . - x . - x . - x . - x . - x . - x . - x . -
```

If you look at the table above, you can see that certain ciphertext letter combinations are not possible e.g. RS, RT, ... RZ cannot occur because we can't have xxx in the plaintext Morse. Also IS, IT, ... IZ can't happen for the same reason. Other impossible combinations: CY, CZ, FY, FZ, OY, OZ etc. We also can't have e.g. ABD because there are no Morse letters that go '.....-.-.'. You should be able to come up with many other impossible combinations. We can also use frequency information, since THE occurs very often in English, we expect 'xx-x....x.xx'='ZSCI' to be quite common in the ciphertext (with this particular key, if you look at the counts provided down below, we see ZSCI is actually the most common quadgram). This means certain keys will be very unlikely if they lead to impossible transitions, others more likely if they lead to likely transitions.

The trick to breaking Fractionated Morse is that finding the key can be done completely independently of the English->Morse translation. Knowing the statistics of a particular Fractionated Morse key means we can just find the key that translates to it, without ever checking to see if the putative plain text even decodes properly. The Idea is to start with a random key, then continuously swap characters in the key trying to make the ciphertext look like it has been enciphered with the key "ABCDEFGHIJKLMNOPQRSTUVWXYZ". Once this is done, we can just decrypt it. To do this we need quadgram statistics for a lot of English text that has been enciphered with the key "ABCDEFGHIJKLMNOPQRSTUVWXYZ".

This website has some code for breaking Fractionated Morse ciphers. References to other resources exist in the lanaki course references, but I havn't been able to access them. e.g. the article MOOJUB, "General Break For Fractionated Morse," AS51, The Cryptogram, The American Cryptogram Association, 1951 looks rather promising.