Sequence Transposition Tutorial

Background

This cipher is an extension of the Null Sequence cipher introduced by SCORPIUS (JA2012) to a transposition type of cipher. It was inspired by conversations between LIONEL and MSCREP concerning the sequence technique. The Sequence Transposition Cipher (STC) was introduced in the ND2015 issue of the Cryptogram (Cm). Continue reading Sequence Transposition Tutorial

Myszkowski Tutorial

Introduction

The Myszkowski (Msyz) cipher is a transposition cipher similar to the Incomplete Columnar (IC) cipher. Like the IC, the Mysz uses a keyword to order the plain text columns for removal as cipher text. Unlike the IC, the Msyz gathers up the columns with identical keyletters at the same time, further mixing up the plaintext. Continue reading Myszkowski Tutorial

Polybius Square

As we begin to set our sights upon Cm Cipher Exchange (CE) constructions, it will aid us to become familiar with the makeup and working of a keying device known as the Polybius Square that is used to key many of the CE ciphers. Ciphers using the Polybius Square are substitution type ciphers in which each letter of the plaintext is represented by a pair of digits.

Polybius was a Greek historian (203-120 B.C.) who first proposed a method of using a unique two digit number for each letter of the alphabet. A five by five square with numbered columns and rows is used to “store” the alphabet.

   1  2  3  4  5
1  A  B  C  D  E
2  F  G  H I/J K
3  L  M  N  O  P
4  Q  R  S  T  U
5  V  W  X  Y  Z

Note that the letters “I” and “J” are written in the same cell to divide the letters evenly. To encode, we simply substitute the numbers in the rows and columns for the letter we wish to use. Always put the row number before the column number. For example, the number for the letter “S” will be 43. The numbers for the word “encode” will be:

15  33  13  34  14  15

Are you thinking that this is far too simple and easily decipherable? It is until we complicate the scenario with the introduction of a keyword. Look what happens to our ciphertext numbers for “encode” when the keyword “SQUARE” is introduced to our Polybius Square.

   1  2  3  4  5
1  S  Q  U  A  R
2  E  B  C  D  F
3  G  H I/J K  L
4  M  N  O  P  T
5  V  W  X  Y  Z

Ciphertext for “encode” becomes:

21  42  23  43  24  21

The diabolical constructor can magnify the complexity of the keyword square by changing the order of the letter pattern. The letters can be written in vertically, in reverse order, in a spiral or  diagonal formation. They need not even begin in the upper left hand corner of the square. What is a poor innocent solver to do? As with Aristocrats, Patristocrats and Xenocrypt ciphers, cribs, frequency counts and knowledge of the general properties of letters, ACA and You Handbook, page 14, become very valuable in observing just which direction the keyword square letters are aligned. We will start the solving process with a straight forward example, accompanied by a crib.

PS-1 Polybius Hybrid. Gram cracker.(solver)  LIONEL

15    12 14 51 42 31    11 12 13 14    45 14 35 52 24 13   

53 32 14   23 24 22 13 12 43 11 45   11 12 13 14            

31 13 15 41 45   33 45    15    31 13 15 41  

22 13 15 22 34 24 13.

Placement of the crib in the only place it will fit (the sixth word is hyphenated) leads to this plaintext and Polybius Square start.

15    12 14 51 42 31    11 12 13 14
         O                    r  o

45 14 35 52 24 13    53 32 14
s  o  l  v  e  r           o

23 24 22 13 12 43 11 45
   e     r           s

11 12 13 14    31 13 15 41 45
      r  o        r        s

33 45    15    31 13 15 41
   s              r

22 13 15 22 34 24 13.
   r           e  r.

PS-1 Use the title, short words and high frequency letters (senorita) to help you complete the plaintext and Polybius Square with its key word.

   1  2  3  4  5
1  .  .  R  O  .
2  .  .  .  E  .
3  .  .  .  .  L
4  .  .  .  .  S
5  .  V  .  .  .

We began our discussion of a Polybius Square with a construction we called a Polybius hybrid. We referred to it as a hybrid because we put the construction together in a manner to demonstrate its principles. As you use the Polybius Square for future Cipher Exchange constructions, each cipher type will have its own way of using the square as a key to its encryption. We will discuss the subtle variations in the uses of the Polybius Square as we study each cipher type. At present, we will continue to refer to the usage of horizontal and vertical numerals to identify each block of the square.

We presented a simplistic horizontal arrangement of letters in our square to allow us to more easily digest the instruction principles. We will increase the degree of difficulty just a bit in to illustrate how the diabolical constructor may alter a key square to increase the security of the message. Always keep in mind that the purpose of the Polybius Square is for it to be the keying device between the writer and the reader. Let’s look for the clues that indicate to us that a key square is something different than a simple horizontal letter flow.

Location of Low Frequency Letters

When crib placement letters result in the locating of low frequency letters in a place other than the last row of the 5 x 5 square, we have a clue that something may be amiss. Perhaps, VWXYZ is part of the keyword and appears in the first or second row of the square, but low letter frequency locations as below tell us even more about the order of the square.

  1 2 3 4 5        1 2 3 4 5
1 . . . . V      1 V . . . .
2 . . . . W      2 W . . . .
3 . . . . X      3 X . . . .
4 . . . . Y      4 Y . . . .
5 . . . . Z      5 Z . . . .
VERTICAL ORDER   REVERSE VERTICAL

1 2 3 4 5        1 2 3 4 5
1 . . . . .      1 Z X W . .
2 . . . . .      2 Y V . . .
3 . . . . W      3 . . . . .
4 . . . V Y      4 . . . . .
5 . . . X Z      5 . . . . .
DIAGONAL ORDER   REVERSE DIAGONAL

1 2 3 4 5
1 Z Y X W V
2 . . . . .
3 . . . . .
4 . . . . .
5 . . . . .    REVERSE HORIZONTAL

Keep in mind that the letters “I” and “J” are always written in the same cell to allow the complete alphabet to fit in the 25 cell square.

Keyword Recovery

With so many possible alphabet order variations, you may wonder how a key word can ever be recovered, but proper crib placement leads to both plaintext and five by five key square recovery. See how the crib placement below leads to both plaintext and keyword square recovery.

PS-2 Polybius Square. Old timer’s lament. (youth)            LIONEL

51 35 32 51 41 41    51 14 51 31 13 45
                                     y

23 41    25 12 41 44 51 42    21 14
                   t

44 11 51    45 21 54 44 11.
 t h        y  o   u  t  h

PS-2 Determine the square key and alphabet order.

   1 2 3 4 5
1  H . . . .
2  O . . . .
3  . . . . .
4  . . . T Y
5  . . . U . 

PS-3. Poly High. South Sea Adventure. (going)     LIONEL         

24 42    34 12 24 43 34    14 12    52 22 11 15  

14 15 22 14    42 22 43    45 24 34 15 14    12 13 14

12 25   42 54   15 22 14 45   12 43 32   11 33 43 32

15 24 42    12 43    15 24 11    52 22 54.

PS-4.  Holly Poly Xmas.  (Christmas)      LIONEL

53 42 25 23    42    53 21 31 31 41    12 21 31 31 41 52 53 34 12 32 15 24 42 32    12 15 32   

15 53 23  51 23 32 15    15 12 24 23    21 33    15 53 23   41 23 42 54   12   13 21 34 15 

14 34 21 35   12 33   15 53 23 54 23 31 31   51 23   32 34 21 35  51 22 15   53 42 25 23   42 

52 22 11   21 33  52 53 23 23 54   51 22 54 31   12 25 23 32

Checkerboard Cipher

We have had some fun in our chapter reviewing the Polybius Square. We will now devote attention to ciphers, appearing regularly in the Cm Cipher Exchange column, which make use of the Polybius Square as its keying device. Let’s start, here, with a discussion of the Checkerboard Cipher. It is a fun type cipher that uses pairs of letters as ciphertext. The pairs of letters represent the horizontal rows and the vertical columns of the five by five square.

Checkerboard Square Keywords

The ciphertext letters are generated by two five-letter keywords, one to represent the rows of the square and one to represent the columns. A third keyword inside the square allows us to set up the square key and alphabet order. Let’s work our way through an example of how the square is set up, along with the use of three keywords.

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

Checkerboard Construction

 A plaintext letter is represented by two ciphertext letters. The coordinate to the left of the square (RIGHT) is always the first of the two ciphertext letters and the coordinate at the top of the square (WRONG) the last. MISTAKE has been chosen as the keyword within the square. See if you can follow the encipherment of the plaintext (pt) below:

pt   c  r  y  p  t  o  g  r  a  m
CT  IN HN TN HR RN HW GR HN RG RW

This construction lesson points out a very important principle which aids in the recovery of our row and column keyword coordinates. The first letter of the ciphertext pair generates the left hand row coordinate and the last letter of the ciphertext pair, the column coordinate above the square. We need to anagram each of the first and last letters of the ciphertext pairs to arrive at these coordinates .Only five different letters will appear in each of the first and last letters of the ciphertext pairs. 

Checkerboard Decipherment

Keeping these principles in mind, we will place the crib and generate the resulting plaintext and square key in the following Checkerboard Cipher. You need only to complete it.

CB -1. Checkerboard. Colorful scene. (yellow)

KT BT BH BH AE KH   AW CT   AE AT BT              W H I T E
 y  e  l  l  o  w            o     e            B . L . E .
                                                L . . . . .
AE LI   CE LE BT   BW CI AW LT LE CE            A . . . . O
 o             e                                C . . . . .
                                                K . W . Y .
LW AE BH AE CI CT.  AW CE   AW CT
  o    l     o
                                        First letters of ciphertext pairs yielded
AE LI CE BT AT BI CT BT LH CE AE         KBACL, second letters of pairs THEWI,
o        e           e        o         anagramming nicely into keywords,
                                        BLACK and WHITE.
LW AE AI AI BI AT AW LW BE CE BT
   O                          e

LW BE BI CE AW AE AT    BE AT LH
               o
BE KH BE CI BT AT BT

Let’s take a look at the Checkerboard construction found in the JA2003 Cm:

JA 2003 Cm, E-4. An Irish blessing. (before)       DYETI

UR EA AU AU EE AE PA EZ ER PR TU EZ EA
                   b  f  o  r  e

PZ EZ PR TU EA AR TA EA PR TU EE AE UE


PA EZ TA EE UE EZ TE TU EZ AA EZ PZ ER
 b  f  o  r  e 

AR TR PR EE UZ EU AU EE AE UE EZ AA EZ EA AA.
       b  f  o  r  e

There are three possible crib location placements based upon the ciphertext letter intervals shown in bold print. We must evaluate the crib placement effect on the Polybius Square makeup.

Anagramming the five repeated first letters of the construction digraphs generates the word taupe for the row keyword of our square. Repeating this process with the second letter of the construction digraphs gives us azure as the column keyword of the square.

We now post our three possible crib placements in the Polybius Square:

      1                 2               3

A Z U R E         A Z U R E       A Z U R E
T . . R . .       T F . . . .     T . . . . .
A . . . . .       A . . . . .     A . . R . .
U . . . . .       U . . . . R     U . F . . .
P B . . O .       P B . . . .     P . . . B .
E . E . F .       E . E . . O     E . . O . E

Now we must enter the mindset of the diabolical constructor to attempt to get a read on his intended Polybius Square path. The first path that jumps out as a distinct possibility is a reverse vertical column path in the second square since the exact number of squares exist to fit the letters “A” thru “F” in reverse order in the first column. The letter “E” already located in the second column is quite likely to be part of the keyword.

   A Z U R E
T  F . . . .
A  D . . . .
U  C . . . R
P  B . . . .
E  A . E . O

Let’s see what effect these square placements have on the plaintext:

UR EA AU AU EE AE PA EZ ER PR TU EZ EA
  a        o     b  e           e  a

PZ EZ PR TU EA AR TA EA PR TU EE AE UE
  e        a        a        o     r

PA EZ TA EE UE EZ TE TU EZ AA EZ PZ ER
b  e  f  o  r  e        e     e

AR TR PR EE UZ EU AU EE AE UE EZ AA EZ EA AA.
         o           o     r  e  d  e  a  d.

It looks like we’re on the right track. Ciphertext AU and AE which surrounds plaintext “o” is ripe for plaintext “y” and “u.” This leads to an opening of UR equaling “m.” Ciphertext TE and TU look much like plaintext “he.” Let’s see what that does to the Polybius square.

CB-2 Complete the Polybius Square.

  A Z U R E
T F . H . T
A D . Y . U
U C . . M R
P B . . . .
E A E . . O

It looks like a breakthrough. Our “reverse columnar” key is taking the shape of a reverse spiral beginning in the upper right hand corner of the square and looking much like another color to complement taupe and azure. All that is left to do is to complete the reverse spiral key square and fill in the remaining plaintext.

CB-3. Checkerboard.  Detour. (between)        LIONEL

EK UN EA   TK UN UB OB EK EA TK EK

EB TN TK EK TB RN UA EA

RB EA EK US EA EA RN   EK US UB

OK UB TN RN EK TK   TN TK   RK RN EB EA OB

UA UB RN TK EK OB RK UA EK TN UB RN.

Railfence and Redefence Cipher

Cryptologists have long contended that encipherment construction is one of the best ways to learn many idiosyncrasies of the various cipher types that will aid in the solving process.

This is well illustrated with the Railfence Cipher, a transposition cipher that came into being during the American Civil War. This cipher looks like an aerial view of a railfence. A simple illustration of the technique should help.

T   A   E   I   R   P   T   C   E

 H R I F N E S T A S O I I N I H R

E   L   C   A   N   S   O   P

In this example the plaintext is written in a zigzag pattern between the three rails (lines). We refer to this pattern as a three rail fence with no offsets. An offset refers to the number of rails excluded from the beginning of the cipher’s plaintext. (See rail examples four through seven on the next page.) The text begins at the top left in a cipher with no offsets. The ciphertext is taken off in groups of five horizontally across the “fence” top to bottom and written in groups of five letters: TAEIR  PTCEH  RIFNE  STASO  IINIH  RELCA  NSOP.

ACA practice limits the number of rails used to three through seven rails.

It is the variation of rails and offsets that creates the complexity and challenge of this cipher type. A crib aids the process of evaluating the variations of rails and offsets but trial, error, and a good eraser are invaluable tools towards the solution.

However, this trial and error process makes us intimately familiar with the construction routine and is the very process that has aided computer-oriented members to work at the development of programs that produce solutions in the blink of an eye. It behooves us to work to learn the intricacies of the Railfence system to attain such a level of understanding.

The development of Railfence cons for the Cm is a good place to begin. As you increase the difficulty through rail and offset variations you will gain an expertise in the recognition of these variables when solving.

A good tool that helps with the trial and error determination of the correct number of rails and offsets is a Railfence template. (Appendix IV.)

Three through Seven Rail Types. Ciphertext read horizontally, plaintext is zigzag.

Three Rails, No Offsets

P     n         t         h        f        t
 l   i  t   x   w   t    n   o    f   e    s
   a      e        I          o        s 

Four

__           k           s              e           n           f           f
  A       n   f       t   p          r   p       e   t       o   f       o  o
    b   a       i   s       a    e         r   s       s   n       s   t       n
      l           r            c             e           a           e           e

Five

__                n               i               e
 __         a   k          s   s           s   t
    T        l       s       e       a       f       o       o
      w    b           p   c           n   f           f   w
        o                a               o               t

 

Six

__                   a                   q                   e
 __              l   n               e   u               s   t
   __          b      k           s       a           f       t
      T       e           s       e           l       f           h
        h   e              p   c         a   o               r   e
    r                   a                   n                   e

Seven (No offsets)

A                       I                       h                       a
C                   t   o                   t   r                   r   i
A             c       n               m       e               n       l
   C           u           s           o           e           e           s
     o       r               a       r               t       v
       n   t                   r   f                   o   e
           s                       e                       s 

RFC-1. Railfence. Paper & Pencil. (error)                                     LIONEL

(4 rails, you determine the offsets.)

RNLSL  CSROL  RSSEA  ECOUN  OIFEI  RRIET  FAARO  RUSPP  NPIST 

OFAEC  PEEUA  OTINE  ROCEA  DLIRN  HQLRD  FC.

Post the ciphertext along the horizontal template rows (See Appendix IV) until the crib “error” is observed in a zigzag diagonal position. Offsets are involved in this cipher so you will have to experiment with a varying number of offset blank spaces in the first diagonal line.

RFC-2. Railfence. Use a template. (cipher)               LIONEL

FIEAT  WESOA  LHRSG  NATOS  TTIUR  CPMSE  OISOF  SHRIE  CNF.

See Appendix IV For the Railfence Solving Template.

Redefence Cipher

 The same solving principles used to decipher the Railfence Cipher can be put to use for the solving of the Redefence Cipher with one slight twist. The Redefence Cipher construction mixes the fence rows to increase the complexity of the solving procedure. (There go those devious encipherers again attempting to stay one step ahead of the innocent cryptanalysts.)

We will follow the procedure to solve the Redefence Cipher in the MA 2012 Cryptogram issue with four rails, no offsets used in the construction, in a rail order of 3, 2, 4, 1.

MA2012  E-12  Redefence.  Tranquility.    MARSHEN

LIEOH  TMTOA  EFRSL  ANASH  UTIEI  DLSIA  

TUROM  SAPFL  EHYCT  LSELN FM.

There are fifty-two letters in the cipher construction. Count off fifty-two spaces in a zig zag path for a four rail cipher in the Railfence Template located in Appendix IV. Post the ciphertext letters horizontally in these four rails, beginning with the spaces in rail three and continuing with rails 2, 4 and 1, in this order. The cipher construction will reveal a plaintext solution in the following zig zag arrangement.

C        t           l           s           e           l           n           f           m
a     s   h       u   t       i   e       i   d       l   s       i   a      t   u       r   o
 l  i       e   o       h   t       m   t       o   a       e   f       r   s      l   a       n
  m           s           a           p           f           l           e          h          y

Just a bit more complex than the Railfence Cipher, the Redefence Cipher requires much trial and error to test the posting of the ciphertext letters in all possible rail sequence combinations. Become familiar with the process and those with computer programming aptitude can join the ranks of other ACA computer solvers in the development of a program which will generate a solution in the “blink of an eye.” (RISHU)

We will provide the number of rails and offsets in the following Redefence Ciphers to allow you to become familiar with the solving process as you “cut your teeth” on this cipher type.

SO 2012, E-11. Redefence. Oral Output. Four rails, one offset.   (more)          APEX DX

FEALS  ADNDN  MRISI  TADNA  RIIDE  EAHOT  LSAOO  SDNE.

MA 2011, E-8. Redefence. Divine right. Five rails, two offsets. (were)   RIG R MORTIS

UAYAC  TWRDS  NCVNO  GIHDO  SGWRH  POSTH  VRTES  EAOAD  ERTON  FROSE  SEGAA  AEFON  TSAEI  DSET.

Route Transposition Cipher

A cipher which retains all of the letters of the plaintext message but simply changes their order is referred to as transposition cipher, unlike a substitution cipher which substitutes one letter for another. There are many ways to rearrange the letters of a word or message. A simple reverse order of the word” transposition” in ciphertext becomes NOITISOPSNART. Cryptology’s battle of wits between the cryptographer and the cryptanalyst through the years discarded this encipherment as too easy to decipher, leading to encipherment processes of a more complex nature. The Route Transposition cipher type is one of those systems.

The Route Transposition Cipher (Construction)

One form of a transposition cipher is where plaintext is converted to ciphertext by constructing it in a specific arrangement of rows, columns, spirals or diagonal paths and extracting it by, yet, another predetermined path sequence. The letters must form a complete square or rectangle. A picture is worth a thousand words:

W A R L F
H S W S L
A F H A I
T O E N E
H U E D S

Extraction of the letters by rows in the above matrix produces a ciphertext of WARLF HSWSL AFHAI TOENE HUEDS, but a vertical read of its columns reveals a plaintext message of “What has four wheels and flies?” Let’s try another:

T R U C K
E O V E W
G C X R I
A O N H T
B R A G A

A vertical read of these columns produces a ciphertext of TEGAB ROCOR UVXNA CERHG KWITA but a counter-clockwise spiral read of the matrix beginning in the lower right hand corner will reveal a plaintext message of “A garbage truck with no cover.”

Complexity of the Route Transposition Cipher

The ease of construction of the Route Transposition Cipher, coupled with its infinite number of paths or routes of placing the plaintext in and extracting it out makes this a highly desirable form of encipherment.

Both messages above could have been enciphered in any number of paths, horizontal rows or vertical columns, consecutive or alternating paths, reverse order paths, diagonal routes, spiral routes, while making use of any number of starting points.

Solving the Route Transposition Cipher

Let’s begin with an easy ciphertext construction whose title line indicates the number of letters in the construction.

RT-1.   Abe Lincoln at Gettysburg (25)          LIONEL

FCNER  OODNS  URSYA  REEEG  SAVAO
  1. Determine the number of columns needed to form a complete square or rectangle.
  2. Post the ciphertext by column or row.
  3. Look for readable plaintext.

Route Transposition Possible Paths

Our completed square or rectangular matrices may use any of the following routes or combination of routes to insert plaintext and extract ciphertext:

  • Horizontal     – Alternating Horizontal
  • Vertical         – Alternating Vertical
  • Diagonal       – Alternating Diagonal
  • Clockwise Inward or Outward Spiral
  • Counterclockwise Inward or Outward Spiral
  • Starting Positions – Upper, lower left and right

These represent the common routes that you will find in our Cm cipher constructions, but do by no means represent all of the possible routes that may be available for encipherment in the real world of secret messaging. Routing can include geometric designs, pictorial artistry and ad infinitum schemes limited only to the boundaries of the creative mind. The seemingly limitless route choices and ease of cipher construction makes this a highly desirable cipher type for secret messaging.

Construction

We’ll use a twenty-five block matrix to review many of the available routes for the encipherment of the plaintext “A Route Transposition Cipher,”

A R O U T
E T R A N
S P O S I
T I O N C
I P H E R

The plaintext is entered in horizontal rows, but it need not be. Check out the variations in the ciphertext when the letters are extracted from various routes:

Rows    
  Alternating
AROUT NARTE SPOSI CNOIT IPHER
  Reversed
TUORA NARTE ISOPS CNOIT REHPI
Columns  
AESTI RTPIPOROOH UASNE TNICR
  Alternating
AESTI PIPTR OROOH ENSAU TNICR
  Reversed
ITSEA PIPTR HOORO ENSAU RCINT
Spiral    
  Clockwise
AROUT NICRE HPITS ETRAS NOIPO
  Counter Clockwise
OPION SARTE STIPH ERCIN TUORA
Diagonal  
AERST OTPRU IIOAT POSNH NIECR
  Alternating
AREST OURPT IIOAT NSOPH NICER
  Reversed
AREOT SURPT TAOII NSOPI NHCER

When we note that all of these extracted ciphertext variations begin at the upper right or left corners of the grid, you can appreciate the complexity of the Route Transposition with encipherment beginning options still available at other locations of the grid. Increasing the complexity of this cipher type, is the option of installing the plaintext in these same route variations, which prompts the question,” What is an innocent solver to do?” Getting started:

RT-2.  Heredity.    (56)    (from)            LIONEL

Look for the rest of the crib adjacent to the only “F” in the matrix.

L I H C T S O M
C S E D N E R D
O R F D E D N E
I L G N O L A M
M R I E H T E N
I L S R E H T O
O T D E N E T S

RT-3. Optical Illusion  (70)    (two)        LIONEL

X E E S R A Y
F L D E E I L
L C A S T C N
E A M S H I O
S T E A G T S
R C H L U P A
E E S G A O W
H P D O D E E
F S N W S H H
O A A T N T S

Now it’s on to the need for some cryptanalyst procedures for the remaining ciphers.

Route Transposition Solution Procedures

  1. Determine the grid size by the number of letters.
  2. Assume as near a square as possible (ACA Guidelines call for 8 x 8 square maximum and 8 x 10 rectangle maximum.
  3. Look for word portions in normal alphabetical order. (See row and spiral example above.)
  4. Where cribs are provided, look for grid adjacent letter sequences which support the crib.
  5. Reconstruction relies heavily on trial and error.
  6. The letter “X” is often used as a null letter to satisfy the number of positions needed in a Route Transposition and can be a signal to its ending.

RT-4. Just Desserts.   (45)  (job)                LIONEL

TFLDI  HOLHT   ERDAS  RAOVO  EJNEW  WOEOE  ABIOL  RWSNL  DETEX..

RT-5.  Geometric Detour     (56)    (between)      LIONEL

TOTAE  NOIES  THRDN  TTISR  RTIET  ICWWN  UCROS  ESEEO  TNOUN  HSTBE
PSDNC  X.

RT-6.  Vision.   (84)   (usual)       LIONEL

TRSWH  UEIDF  NSHVO  IASTS  UOCTE  OCLVU  IMERI  ACYIL  EANOT  ERNLA  ENILG  NOSCC  ANTOT  MTTUE  UEITY  TSEHH NEMS.

POLYOMINOES – CONGRUENT SQUARES

                                                                                                                         APEX DX

There exists an enormous amount of material on what has become known as recreational mathematics, popularized greatly by a most exceptional journalist, Martin Gardner, in his monthly contributions to Scientific American and much paperback and hardback publication extensions of such writings. Through Gardner you may have been introduced to Polyominoes, combinatory objects of connected congruent squares. Polyominoes, with letters in the squares have given rise to a number of Cryptogram Ornamental cover challenges which may not represent everyone’s starting point on a learning curve, so we offer below, a set of six, six square Polyominoes (Hexominoes) which when correctly assembled, form one six by six square. Read off its message, this one by row pattern and you may have your first “cover graphics” solving experience. From this starting point, the sky may become your limit. Good solving.

H   O G                
S S I     T         T  
          U       L A  
          M U   N I T  
      A   B N          
    O R             U T
T W I           E I S  
                  R    
H E F                  
R                      
I R                    

 

Appendix IV – RAILFENCE TEMPLATE

It would be foolhardy to label either pencil and paper or computer solving techniques as the “proper approach” for solving any cipher. They are inter-related and have a bond between them. Pencil and paper solving is the learning foundation for cryptography, and cryptographic computer programming and computer programs have much to offer pencil and paper enthusiasts in alternative routes of solving routines and the elimination of much of the grunt work and drudgery of trial and error erasures.

The Rail Fence Cipher was a popular American Civil War cipher. For some people, the construction process is the very best route of learning the idiosyncrasies of cipher types as an aid to the decipherment process. This template was developed to allow one to reverse the process of zig zag plaintext generating ciphertext rows. The template will be an aid to all wishing to encipher plaintext messages and also deciphering Rail Fence ciphers. It should be noted that this same template can be used to encipher and solve those dreaded Redefence ciphers as well.

The template can be enlarged on a copy machine to any workable size for the user. There are patterns for Rail Fences ranging from 3 to 7 rows (rails) and space for over 60 letters. If more letters are required, tape two templates together at an appropriate place. Be sure to make copies of your enlarged copy which can be used for future Rail Fence ciphers.

Simply post the ciphertext letters to the horizontal spaces for desired number of rails and look for readable plaintext in the zig zag pattern spaces. Use only the number of spaces, counting from left to right in a zig zag path, which equals the number of letters in the cipher construction. Offsets are observed by leaving blank the number of spaces on the left hand side of the template to equal the number of offsets required. As spaces are skipped on the left hand side of the template they should be added to the right until the spaces used equal the number of ciphertext letters in the construction.

Rails Ciphertext Letters

3 —       —       —       —       —       —       —       —       —       —
    —   —   —   —   —   —   —   —   —   —   —   —   —   —   —   —   —   —   — 
      —       —       —       —       —       —       —       —       —       —

4 —           —           —           —           —           —           —
    —       —   —       —   —       —   —       —   —       —   —       —   —
      —   —       —   —       —   —       —   —       —   —       —   —       —
        —           —           —           —           —           —           —

5 —               —               —               —               —               —
    —           —   —           —   —           —   —           —   —           —
      —       —       —       —       —       —       —       —       —       —
        —   —           —   —           —   —           —   —           —   —
          —               —               —               —               — 

6 —                   —                   —                   —                   —
    —               —   —               —   —               —   —               —
      —           —       —           —       —           —       —           —
        —       —           —       —           —       —           —       —
          —   —               —   —               —   —               —   —
            —                   —                   —                   —

7 —                       —                       —                       —
    —                   —   —                   —   —                   —   —
      —               —       —               —       —               —       —
        —           —           —           —           —           —           —
          —       —               —       —               —       —               —
            —   —                   —   —                   —   —                   —
              —                       —                       —

Special Note: Construction of the Railfence cipher will demonstrate that offset blank spaces at the start of the cipher are added to its end.

Use only the number of spaces that equal the ciphertext letters in the construction. Count off 52 spaces for a 52 letter construction, zig zag path, from left to right on the template.