Foursquare Cipher

In our last chapter we examined the usage of the Checkerboard Cipher to replace plaintext pair of letters (digraphs) with an equivalent cipher-text pair keyed by a single Polybius Square. The Foursquare Cipher, as its name implies, uses four such squares, numbered in clockwise order, to replace plaintext with ciphertext.

Squares one and four contain unkeyed plaintext letters always in horizontal alphabetical order. Squares two and three contain keyed ciphertext letters in any patterned order (vertical (horizontal, straight, reversed, spiral, diagonal, etc.). Ciphertext location is aided with a provided crib. Square numbering order is 1, 2, 4, 3. A picture and an example are worth a thousand words.

1-pt

2-CT

Normal PT

Alphabet

Order

Mixed CT

Alphabet

Sequence

Mixed CT

Alphabet Sequence

Normal PT

Alphabet

Order

4-CT

3-pt

FS-1. Foursquare. Commonality. (th ey bo th pr od uc eg-) (fa=NN) (bc=LA)     LIONEL

XO TP TL FB TO QB FI KB QE TZ MT GD RY
                        th ey

RQ QD SV TF HB GL KH GX CX QE TP BT SS
                          th

RX QE TZ TH QE GU KI QS AF OA HA OA ID AU QX.
   th ey bo th pr od uc eg

The bold ciphertext letters indicate a good fit for our crib with repeat “th” digraphs and we fill in the identified ciphertext letters. Let’s examine the effect of this crib placement on the ciphertext squares.

    1              2
a b c d e      . A L T .
f g h i k      N . . . .
l m n o p      . G . K .
q r s t u      . . Q . .
v w x y z      . . . . .

N A . I S      a b c d e
. . . E F      f g h i k
. H . . .      l m n o p
. . . . U      q r s t u
. . . . Z      v w x y z
    4              3

The first letter of each plaintext pair in the crib is found in square one, the second in square three. Those two cells are considered the opposite corners of a rectangle. Cipher letters are found at the other corners of that rectangle, the first in square two and the second in square four. Post the ciphertext letters of our crib plaintext results in the sequence below for squares two and four. Complete the two squares for the keywords. 

FS-2 Keyword Squares.

    2             4
. A L T .     N A . I S
N . . . .     . . . E F
G K M . .     G H K L M
O P Q . .     P Q R T U
. . . . .     V W X Y Z

We have filled in the bold type letters where alphabetical sequencing permits us to do so.

(You can probably make a good guess at square two, row five.)

The decipherment process of converting ciphertext to plaintext is the reverse of the procedure that we used to post our crib letters to squares two and four. The first ciphertext letter is located in square two and the second in square four. Those two cells form the corners of a rectangle. Plaintext letters are found at opposite corners of that rectangle, the first in square one and the second in square three.

Our ciphertext Square blocks two and four now allow us to find the plaintext letters in the partly solved cipher below. The ciphertext digraphs XO, HB and ID are easily identifiable and the solution is close at hand.

FS-1. Foursquare. Commonality.                           LIONEL

XO TP TL FB TO QB FI KB QE TZ MT GD RY
   at do                th ey ou

RQ QD SV TF HB GL KH GX CX QE TP BT SS
         ei    om mo nw    th at

RX QE TZ TH QE GU KI QS AF OA HA OA ID AU QX
   th ey bo th pr od uc eg ra mc ra    er sx.

We will continue our discussion of the Foursquare Cipher by working our way through one with a bit more challenge to it than our introductory example. This was published in the Cipher Exchange as E-22 in the JA2001 Cm, so you can be assured that there is some trickery involved.

Remember the enciphering and deciphering principles for solving a Foursquare Cipher.

Encipherment: The first letter of each plaintext pair is found in square one, the second in square three. Those two cells are considered the opposite corners of a rectangle. Ciphertext letters are found at the other corners of that rectangle, the first in square two and the second in square four.

Decipherment: The process of changing ciphertext to plaintext is the reverse of that of encipherment. The first ciphertext letter is located in square two and the second in square four. Those two cells form the corners of a rectangle. Plaintext letters are found at the opposite corners of that rectangle, the first in square one and the second in square three.

JA2001. E-22. Unwarranted Admiration. (su/pe/rs/ti/ti/ou/s ;il=OR)      BITWISE

QT LC PK XH XG AE PD CV PW EE HL CL CY

IP HL QL SH XC WQ MQ CY HY RX KM DP OR
                 th

QT VP SE YP RM PO KD IT QO IS SQ EE CO
                             ti

PO KM LP YM XV MA SQ SQ XT LN BL LV SQ
        su pe rs ti ti ou s        ti

KR WQ UY SH XV VC EM TQ CL HY.
           pe

The repetitive ciphertext digraph “SQ” allows for easy placement of the crib. We complete all of the plaintext that our crib placement permits and post our identified ciphertext digraphs to our foursquare matrix using our principles of encipherment from above.

    1              2
a b c d e      . . . . .
f g h i k      O . . . .
l m n o p      . . . . X
q r s t u      . . M S Y
v w x y z      . . . . .

. . . . V      a b c d e
. . . Q .      f g h i k
. . . R .      l m n o p
. A M T .      q r s t u
. . . . .      v w x y z
    4              3

Ciphertext letters, X and Y in square 2 and Q, R and T in square 4 suggest vertical columnar alphabetical sequencing. We are able to add ciphertext letters to squares two and four.

(Bold type.)

FS-3 – Find the Keywords.

    1              2
a b c d e      . . . P U
f g h i k      O . . Q V
l m n o p      . . . R X
q r s t u      . . M S Y
v w x y z      . . N T Z

. . . P V      a b c d e
. . . Q W      f g h i k
. . . R X      l m n o p
. A M T Y      q r s t u
. . N U Z      v w x y z
    4              3

Our Foursquare deciphering rules now allow us to recover additional plaintext on route to a solving completion.

FS-4. Complete the Plaintext.

QT LC PK XH XG AE PD CV PW EE HL CL CY
it                      ei

IP HL QL SH XC WQ MQ CY HY RX KM DP OR
                 th       po       il

QT VP SE YP RM PO KD IT QO IS SQ EE CO
it ie    te nt                ti

PO KM LP YM XV MA SQ SQ XT LN BL LV SQ
        su pe rs ti ti ou s        ti

KR WQ UY SH XV VC EM TQ CL HY.
     eu    pe       yj

Hint: Look for Europe and responsibilities.

FS-5. Tooting one’s horn.       (al  lr  ai  lr  oa  dm  en  fr  om  th)            LIONEL

SA DI RO DI EO BQ HX CI DQ LP HV KQ VS OL DS RL QS WG HX PC XG BY YH

QK UE TG RS WG RL SV QE TG FO QA NE LP BZ PH RL XT SG QL VB LY OV RQ

YS LD LP BZ WG SX LM.