Solving a Fractionated Morse Cipher

Someone has encoded a phrase using the Fractionated Morse cipher and told you that it ends with EARS. What does it say?

KMUPKSGHPDWWKDMUVDHVIZSRKPGBILTVORTNLJMXXEWOMIRDBQIVGCKQQIS

 

How to Solve:

The first step is to covert the EARS phrase to morse code and break it into groups of three.

●×● –×● –●× ●●●

 

Since the cipher text ends in KQQIS we immediately see that since all four groups of three are different, there is no way it will map which means that there must be one or two × at the end.  Generating the two versions adding the × at the beginning and the end gives us

?×● ×●– ×●– ●×● ●●×

×●× ●–× ●–● ×●● ●××

We can see that the one with a single × at the end has a repeated pattern of ×●– which gives us the mapping:

?×● ×●– ×●– ●×● ●●×

 K   Q   Q   I   S

allows us to fill in the table:

 

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

?×●??????????×●●●×????????????????????●??????

 

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

???????????????●×●???●●×????×●?????????●×●???

 

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

?????????????????????????????????????????????

 

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●??????????×●×●–×●–●×●●●×

                             E A   R   S

The first thing that we can do is determine where K is since we know two of the morse characters. As ?×● it can be one of ●×●, –×●, or ××●.  However since we already know that I maps to ●×●, we are left with two choices.  Given the position of Q near the end of the list and S already being used, we are left with 8 characters (RTUVWXYZ) to take up the 6 slots after it including ××● which means that where K must be –×● so we can fill it in and update the cipher:

 

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●?????????–×●●●×??????????????????–×●??????

T              S

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

???????????????●×●???●●×???–×●?????????●×●???

 

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

?????????????????????????????????????????????

 

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●?????????–×●×●–×●–●×●●●×

             R               E A  R   S

Next we have a couple of paths to take.  We could assume that Z doesn’t appear in the keyword and map it to ××–.  We can also notice that the cipher starts with the letter T and the next morse character is a ● which happens to be the first part of the letter H with THE being one of the most common words to start a phrase.  This gives us

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●×???–×●●●×??????????????????–×●???●●●

T H    E      S

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●×????????????●×●××–●●×???–×●?????????●×●???

 E               E/ D

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

????????????????????????●●●???????????????●●●

 

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●?????????–×●×●–×●–●×●●●×

             R               E A  R   S

And we can update the table as:

This turns out to be a really big break since we can see can assume that QU is not part of the keyword and the remaining 5 slots correspond to the last 5 letters in the alphabet after U. This gives us a table below that fills in a lot of the cipher:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●×???–×●●●×???????????×––×–––×●???●●●

T H    E      S               M  O

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●??????×–●●×●××–●●×???–×●?????????●×●???

 E/              E/ D

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

???×–●??????????????????●●●×–××–×???×––???●●●

                            T/ T

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●×–●??????–×●×●–×●–●×●●●×

             R   E           E A  R   S

This also leads to another lucky discovery since we believe that THE is the first word, we can guess that P must start with an ×, there is only one slot left and it happens to be right before the letter Q which strengthens our guess:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●××●●–×●●●×??????×●●???×––×–––×●???●●●

T H    E/ U   S                M  O

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●??????×–●●×●××–●●×???–×●×●●??????●×●???

 E/          D   E/ D        E

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

???×–●??????????????????●●●×–××–×???×––???●●●

                            T/ T

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●×–●??????–×●×●–×●–●×●●●×

             R   E           E A  R   S

Seeing the start of the phrase as THE US? certainly sounds like it starts out THE USE, so we can assume that G maps to ●××. Filling that in gives us:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●××●●–×●●●×●××???×●●???×––×–––×●???●●●

T H    E/ U   S   E/           M  O

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●??????×–●●×●××–●●×???–×●×●●●××???●×●???

 E/          D   E/ D        E S  /

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

???×–●??????????????????●●●×–××–×???×––???●●●

                            T/ T          H

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●×–●●××???–×●×●–×●–●×●●●×

             R   E D  /      E A  R   S

Looking at the end, we have a word that ends in EARS and has either four morse symbols ending in – or is two letters. A quick look at the four symbol morse characters ending with – gives us either V J or Y with YEARS being a very good choice. Filling the mapping for C gives us:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●××●●–×●●●×●××???×●●???×––×–––×●???●●●

T H    E/ U   S   E/           M  O

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●??????×–●●×●××–●●×???–×●×●●●××???●×●???

 E/          D   E/ D

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

???×–●??????????????????●●●×–××–×???×––???●●●

                            T/ T          H

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●?????????×●–●×●×–●●××–●––×●×●–×●–●×●●●×

             R   E D  / Y    E A  R   S

Also seeing the H???RED YEARS only leaves us with one word that fits there – HUNDRED YEARS – so we get the mapping of a few more letters:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●××●●–×●●●×●××???×●●???×––×–––×●–●×●●●

T H    E/ U   S   E/           M  O   R   S

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●–●×???×–●●×●××–●●×●–×–×●×●●●××–●●●×●???

 E/ C        D   E/ D   A  T E S  / B

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

???×–●?××●–×????????????●●●×–××–×???×––?××●●●

                            T/ T        / H

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●●–×–●×–●●×●–●×●×–●●××–●––×●×●–×●–●×●●●×

  U   N  D   R   E D  / Y    E A  R   S

This tells us that O must map to ?×× and since G already maps to ●×× it only leaves –×× for O which is conveniently right next to P. (Remember that ××× isn’t mapped to anything).  As we fill that in, we see T?O HUNDRED YEARS at the end which could only be TWO HUNDRED YEARS giving us the mapping for E. Likewise MORSE C?DE must be MORSE CODE:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●××●●–×●●●×●××–––×●●–●××––×–––×●–●×●●●

T H    E/ U   S   E/ O   F   / M  O   R   S

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●–●×–––×–●●×●××–●●×●–×–×●×●●●××–●●●×●???

 E/ C    O   D   E/ D   A  T E S  / B

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

???×–●–××●–×????????????●●●×–××–×●––×–––××●●●

    K  / A                  T/ T W   O  / H

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●●–×–●×–●●×●–●×●×–●●××–●––×●×●–×●–●×●●●×

  U   N  D   R   E D  / Y    E A  R   S

We can pretty much sight read the rest of the cipher and fill in the remaining letters:

 K  M  U  P  K  S  G  H  P  D  W  W  K  D  M

–×●●●●×●××●●–×●●●×●××–––×●●–●××––×–––×●–●×●●●

T H    E/ U   S   E/ O   F   / M  O   R   S

 U  V  D  H  V  I  Z  S  R  K  P  G  B  I  L

×●××–●–●×–––×–●●×●××–●●×●–×–×●×●●●××–●●●×●–×–

 E/ C    O   D   E/ D   A  T E S  / B    A  C

 T  V  O  R  T  N  L  J  M  X  X  E  W  O  M

●–●×–●–××●–×●–●●×––×–––×●●●×–××–×●––×–––××●●●

    K  / A  L    M  O   S   T/ T W   O  / H

 I  R  D  B  Q  I  V  G  C  K  Q  Q  I  S

●×●●–×–●×–●●×●–●×●×–●●××–●––×●×●–×●–●×●●●×

  U   N  D   R   E D  / Y    E A  R   S

This gives us the mapping of every letter except A and F and we can see that the keyword would have to be MASTERING.