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.