Fractionated Ciphers

A fractionated cipher is one where a plaintext letter is enciphered over two or more ciphertext letters. The process will become clearer as we discuss the encipherment process.

As we have stated many times in the past, the best learning technique and starting point in developing a comfort level with the solving of any cipher type is to become aware of its encipherment process. We will begin our study of the fractionated cipher with a look at one of our favorite ciphers, the Fractionated Morse Cipher.

The Fractionated Morse Cipher contains most all of the fascinating elements of the solving process, including crib placement and keyword recovery, while providing us with the opportunity to become familiar with the use of the Morse Code system and its interaction with enciphered message plaintext.

Morse Code

The Morse Code was developed in the early 1840’s by Samuel F. B. Morse for use with his electromagnetic telegraph system. Although it was not designed as a secret messaging system, cryptographers quickly developed means to incorporate its design and contents into a system of secret messaging. The Fractionated Morse cipher is one example of such efforts.

The Morse Code letters, numbers and punctuation can all be found in the Appendix of The ACA and You Handbook. Although this ACA periodical makes the claim of “not intending to be a solve book” its pages reflect volumes upon the enciphering process. Understanding this process remains a fundamentally sound approach into the unraveling of ciphertext construction into that of clear or plaintext.

Fractionated Morse Encipherment

Each plaintext letter is converted to Morse Code using “×” between letters and “××” between words. “×××” does not exist. Punctuation is optional but is not normally used for Cm construction purposes. “Solving is fun” becomes:  •••×–––ו–••×•••–ו•×–•× ––.×ו•×•••×ו•–•×••–×–•××.  Before proceeding with the encipherment we need to create a key alphabet which will give us the ciphertext substitutions for the Morse Code plaintext.

The Fractionated Morse key alphabet is set up in three tiers with a series of dots, dashes and ×’s. The first row is composed of nine dots, nine dashes and eight ×’s to fill the 26 letter alphabet. The second row is composed of three dots, thee dashes and three ×’s until the final two ×’s. The third row is a series of dot, dash and ×’s until the final dot and dash.

A picture is worth a thousand words. We will use “CIPHER” to set up our key alphabet which now appears over a fixed series of dots, dashes, and ×’s.

C I P H E R A B D F G J K L M N O Q S T U V W X Y Z
• • • • • • • • • – – – – – – – – – × × × × × × × ×
• • • – – – × × × • • • – – – × × × • • • – – – × ×
• – × • – × • – × • – × • – × • – × • – × • – × • –

The keyword or key phrase can start at any point in the series of Morse Code symbols. The series of dots, dashes and ×’s beneath the keyed alphabet remain constant from encipherment to encipherment. The plaintext (Solving is fun) coded series of dots, dashes and ×’s, now in vertical groups of three, transformed into ciphertext based on the above key looks like this:

pt • × – – × • • – – × • • × – • × ×
   • – × • • – • • – × × • • • • – ×
   • – • • • × × × • • • × • × – •
CT C W N F S R P J K Y A P S J I V

CIPHERTEXT CONSTRUCTION: CWNFS RPJKY APSJI V

The fractionation process is now evident. Twelve plaintext letters (Solving is fun) have been enciphered into sixteen ciphertext letters. Becoming familiar with this encipherment process is the first step in its solving process. Our next column will address the decipherment of the Fractionated Morse Code Cipher.

We have defined the Fractionated Morse Cipher as the process of spreading a plaintext letter across two or more ciphertext letters through the use of a series of Morse Code dots and dashes complemented with ×’s used as letter and word separators. (A single × is used as a letter separator while two ×’s, ‘××’ indicate a word separation.) The above encipherment process defines the three-tier cipher construction process. Let’s begin the solving process of a typical Cm Fractionated Morse Cipher type.

MJ2000. E-13. Terse codes.     (frequency)       PHOENIX

LMUTR  DNRXG  LIUQL  RARVR  GPEDH  RHLTD  RQRDF  THARW  WLHMU
                                          80             92
XJZRD  RRIVY  MQQBG  AKFUQ  RBOQD  VBLMU  QHSUI  LCAAS  UKWLS
YFUNU  SQBRH  XMDZT  DNEYL  RIZHO  QVDTL  RMQWA  DAAHX  MDYRM
AKSXD  PRMQW  ADLFQ  BNKXM  DZNKM  XVHJW  WWNBB  DXLTD  R.

Crib Placement:

We assign the appropriate Morse Code symbols to the crib word “frequency” with a single × to indicate a separation between letters and a double ×× to indicate word dividers. Thus, a double ×× must appear before the f and after the y of the crib “frequency.” Since the fractionated process can spread a plaintext letter across more than one ciphertext letter, we must examine three possible locations of the ×× word separator before the crib word “frequency.” Apply the Morse Code symbols to the plaintext letters, being sure to place a single × letter separator between the interior letters of the crib.

 
f   r e q   u e n c   y
× • × • × • • × – – • • ×
× – • × – – • • • • × – ×
• • – • – × – × × – – –
1 2 3 4 5 6 7 8 9 10 11 12
 
No pattern  
f   r e q u   e n c y
× – • × – – • • • • × – ×
• • – • – × – × × – – –
• × • × • • × – – • • ×
1 2 3 4 5 6 7 8 8 3 9 10
Q H S U I L C A A S U K
f   r e q u e n c   y
• • – • – × – × × – – –
• × • × • • × – – • • ×
– • × – – • • • • × – ×
1 2 3 4 5 6 7 8 8 3 5 9
Pattern match Positions 80 thru 92  No Construction Pattern Match

The pattern line beneath the three coded crib placement analyses represent the pattern of the Morse Code symbols applied to the crib word “frequency.” Examine the ciphertext to look for repeated ciphertext letters matching the Morse Code symbol patterns. You will find an identical pattern match between the second crib placement analysis and positions 80 thru 91 of the ciphertext. Verify the validity of this crib placement by placing the crib cipher text letters to the Morse Code keyword alphabet process referenced above.

* * * S * C * A * * * H I * K L * * Q * U V * * * *
• • • • • • • • • – – – – – – – – – × × × × × × × ×
• • • – – – × × × • • • – – – × × × • • • – – – × ×
• – × • – ×  .– × • – × • – × • – × • – × • – × • –

Keyword Alphabet (Educated Judgments):

This alphabet sequence allows us to SWEG (Scientifically Wild Educated Guess) additional letters in the ciphertext alphabet. HI*KL clearly is not part of the keyword; so this part of the alphabet will be in order and J can be inserted. Low frequency letters (F, G, P, W,

X, Y and Z) can also be placed in the above alphabet. Beware of improper SWEG leading to plaintext garbage.

* * * S * C * A * F G H I J K L * P Q * U V W X Y Z
• • • • • • • • • – – – – – – – – – × × × × × × × ×
• • • – – – × × × • • • – – – × × × • • • – – – × ×
• – × • – × • – × • – × • – × • – × • – × • – × • –

The keyword appears at the beginning of this alphabet sequence. The cipher title gives a good clue to the key. Plaintext Recovery: Apply the symbols to the ciphertext letters. The additional “educated judgment” letters will allow much plaintext recovery and keyword completion.

FM-1. Fractionated Morse. Morton Salt?   (rains)      LIONEL

ESPBD PQHTS VSDPN KWNRH SDRJG AAVXT JHWNI UHFD.

Morbit Cipher

We have defined the Fractionated Morse Cipher as the process of spreading a plaintext letter across two or more ciphertext letters with the use of a series of Morse Code symbols. We will continue the discussion of a fractionated cipher with a look at the Morbit Cipher. The Morbit Cipher also complements the Morse Code dot and dash symbols with the use of X as a letter separator and ×× as a word separation. It differs from a Fractionated Morse Cipher, with a two-tier encipherment rather than three. We will begin with the encipherment process to understand the cipher’s foundation.

 A nine-letter keyword is selected to assist in randomly assigning numerals 1 to 9 to the Morse symbols array. Numerals are assigned based on the alphabetic order of the letters in the key word. Since more than one nine letter word fitting the numerical pattern may be found, this keyword cannot be recovered with confidence. Again, a picture is worth a thousand words.

Morbit Keyword:    A M U S I N G L Y
                   1 5 8 7 3 6 2 4 9
1 5 8 7 3 6 2 4 9
• • • – – – × × ×
• – × • – × • – ×

The plaintext, “good day” is enciphered:

g   o   o   d   d   a   y
– – – – – – × × – – –
– × – × – × × – • • × –
3 8 3 6 3 6 7 8 4 1 2 6 7 3

The Morse Code symbols are entered for the plaintext letters and a ciphertext number is assigned to the Morse Code symbols in units of two based on the numbers under the keyword (AMUSINGLY). If the plaintext “good day” appears in the middle of a sentence, we would add ×× before “g” and after “y.” Let’s try solving one.

M-1. Morbit. Munsters Ball.  (threat)   LIONEL

                                    31       40
91543 15693 82679 15513 71912 47638 79442 62299 34515 42432
65565 24321 34564 26553 15121 24234 78382 63254 54429 45242
82299 34549 15829 24245 12495.

Solution Process

  1. Assign Morse Code symbols to the crib.
  2. Determine Morse Code symbols pattern.
  3. Seek Morse Code pattern in ciphertext.
  4. Post recovered plaintext for all ciphertext.

Crib Pattern Determination

(Two possibilities)                             

Pattern 1 Pattern 2
  T H   R   E A   T
× – • • × – × × – – ×
× × • • • • • • × ×
1 2 3 3 4 5 4 4 2 2
7 9 4 4 2 6 2 2 9 9
  T   H   R   E A T
× × • • • • • • × ×
× – • • × – × × – – ×
1 2 3 4 5 4 4 5 1 6

Ciphertext Positions 31 thru 40  

The three pairs in the first pattern provide a good start for examining the ciphertext for a similar letter pattern. You will find the same letter pattern beginning in position 31 of the ciphertext highlighted below. This is an excellent indication that you have found the correct crib placement and are ready to begin the plaintext recovery process.

91543 15693 82679 15513 71912 47638 79442 62299 34515 42432 65565 24321 34564 26553 15121 24234 78382 63254 54429 45242 82299 34549 15829 24245 12495.

Plaintext Recovery

Insert the recovered plaintext Morse Code symbols above the crib pattern for the ciphertext numbers they represent.

7 9 4 4 2 6 2 2 9 9  

× – • • × – × × – –

× × • • • • • • × ×
  t h   r   e a   t

Apply the known ciphertext Morse code symbols (79426) to the ciphertext, and find the plaintext equivalents. Partial word recovery will lead to symbol recovery for remaining ciphertext. No more than four Morse Code symbols may appear in a row without a separator immediately following. (See the ACA and You Handbook, Appendix 1 for numeral and punctuation exceptions.)

Here is a reference to a Holiday personage to challenge your learning retention. Recall that we stated a nine-letter keyword is used to assign numbers 1 through 9 to our Morse Code symbols array. The keyword(s) for this Morbit Cipher is either CHRISTMAS or BOXINGDAY. Find the correct key, and readable plaintext will follow.

M-2. Morbit.     Kris Kringle.       LIONEL

92258  75948  39221  78766  92652  62528  32594  64752  83576 34546  35352  58753

52183  13691  67995  46797  94954  62135  82631  69384  45463 53528  42535  41938

26225  92358.

Keyword Analysis   (Pick a winner)

C H R I S T M A S
B O X I N G D A Y
. • • – – – × × ×
. – × • – × • – ×

Our next Morbit Cipher does not provide the keyword. Refer to the crib pattern determination process above and the proper placement of the crib in the ciphertext. This will lead you to the recovery of the plaintext.

TG-2. Morbit. A Lot to be Thankful For. (your)                         LIONEL

62751  78386  81757  15413  19742  84394  31327  24946  25762  45651  65512  65715

48642  72451  26571  94313  27972  42941  31938  42938  64943  13272 49442  42162

58387  565.

Pollux Fractionated Cipher Definition

The Pollux Cipher is a construction where a plaintext letter is spread across two or more ciphertext digits through the use of a Morse Code series of dots and dashes, with “×’s” used as letter (×) and word separators (××). The cipher assigns numbers to the Morse Code dots, dashes and spaces. Since there are ten digits, three each are assigned to dots, dashes or spaces and the tenth digit can be assigned to any of these.

The following Lesson Plan will familiarize you with the Pollux Cipher construction and provide you with the analytical techniques to make an entry level attack to its solution process.

This MA 2009 Cm Pollux Cipher provides an opportunity to present an excellent approach to the solving process of this cipher type.

E-7. Pollux. So be of good cheer.    (always)                       OZ

72731 68416 42945 54295 09471 92674 73317 22385 53052 91049 16547

10735 00347 53104 10734 20096 51415 92995 23747 20630 40124 40204

23748 19302 73515 34223 70879 92114 03357 54230 37860 99108 73270

09037 30529 00873 72842 62799 06540 33013 71732 94759 25203 25132

63805 59272 99625 89511 47053 50488 79325 91248 27997 59133 05773

26470 29839 82292 29239 72350 33876 84115 42784 13227 03403 72089

79509 45472 00961 14725 36509 07709 35058 40908 97609 70099 17123

81632 06310 31942 75470 74311 69252 79100 3.

Crib Dragging

Morse Code characters are assigned to the crib letters (always) with one “×” used as a letter separator and two “×’s” used between word breaks:

  × × • – × • – • • × • – – × • – × – • – – × • • • × ×
    a     l         w       a     y         s

The Morse Code characters crib is now dragged through the entire ciphertext digits until a location is identified which will allow no conflicting character assignment to the same ciphertext digit. Note the crib posting location below.

Crib Morse code Character Posting to Ciphertext Digits (Near end of fourth row)

     94759 25203 25132 63805 59272 99
    ×ו–× •–••× •—–ו –×–•– –ו•• ××
        a   l     w   a    y    s

Ciphertext Digits Morse Code Character Assignments

      0 •
     1 –
     2 •
     3 ×
     4 ×
     5 –
     6 –
     7 •
     8 –
      9 ×

The crib placement has identified all ten ciphertext digits’ Morse Code character values.

No one digit in the crib ciphertext location represents more than one Morse Code character.

All that is left to do is to assign these character values to the remaining ciphertext digits, identify the letters and recover the plaintext.