Tri-Square
History
The Tri-Square cipher was developed by the American Cryptogram Association (ACA) member THALES and first appeared in the Sep-Oct 1959 edition of the ACA's magazine The Cryptogram.
Description
It is similar to the Two Square and Four Square ciphers but is produced from three keyed 5 x 5 square matrices, each filled with different keyed alphabets using all the letters of the alphabet, with J being replaced by I. These are positioned in the bottom left, top right and bottom right, or middle, positions. If 6 x 6 square matrices are selected the 26 letters of the alphabet and numbers 0-9 are used with A followed by 1, B by 2, C by 3 and so on up to J followed by 0. Each keyed alphabet is created from a keyword, with repeated letters being omitted, followed by the unused letters of the alphabet in alphabetical order. The keyed alphabet is written into the matrix in a selected route, e.g. horizontal, diagonal or clockwise. For example the key word OSCAR is appended with unused alphabet letters and produces the following keyed alphabet:
OSCARBDEFGHIKLMNPQTUVWXYZ
Encryption is performed by separating the plaintext into pairs of letters or digraphs. If the plaintext contains an odd number of letters a null letter is added at the end of the text to complete the last letter pair. Each plaintext letter pair is enciphered into three ciphertext characters. The first letter of each plaintext pair is located in the left matrix and any letter in the same column is used as the first ciphertext letter. The second letter is located in the top matrix and any letter in the same row is used as the third ciphertext letter. The letter in the middle matrix at the intersection of the two plaintext letters forms the second ciphertext letter of the three letter group.
O S C A R
B D E F G
H I K L M
N P Q T U
V W X Y Z
W A H P U
I B K Q V
L C M R X
D F N S Y
E G O T Z
Q U O T E
M N P R A
L Y Z S B
K X W V C
I H G F D
Example
Left keyword: OSCAR (Rows from top left)
Top keyword: WILDE (Columns from top left)
Middle keyword: QUOTE (Clockwise from top left)
Plaintext: The only way to get rid of a temptation is to yield to it.
Plaintext: th eo nl yw ay to ge tr id of at em pt at io ni st oy ie ld to it
Ciphertext: LWU QPZ HKR TIW AES AWT RME YVL ILD NUS FTO QPL PVZ ATO PZE VKI WTZ OEN ILG TLY LWG PSE
Solving
Solving methods: Dictionary keyword search.
Tri-Square cipher types require a tip for the solving routine. On selecting the Solve cipher icon the dialog box below will appear to enable the tip and tip location to be set. On selecting OK the program will search for a solution.
Tip – Enter the tip in the Tip field. Spaces and punctuation will be ignored.
Click on the Locate tip button to populate the Tip location list with possible locations for the tip.
Tip location – Select the location of the tip from the list then press OK. When a tip location is selected the ciphertext and plaintext positions are shown below the Tip location.
The tip location within the cipher will also be displayed in the Addition tip location textbox along with any other letters resulting from the tip. In this textbox additional plaintext can be entered to help improve the solution.
If the Tri-Square cipher is rerun the previous setting for the tip will be displayed. The Locate tip button will need to be clicked to re-populate the tip location list.
Show table and possible keys – Selecting this option will open a new window, when the solving routine is finished, to display the partially completed Tri-Square table based on the entered tip and location selection and a list of possible keywords and key squares found. If a solution isn’t found the table can be useful for seeing the possible keys and solving the cipher by hand.
If at least one of the keywords is known this can be entered into the Enter Key field on the main window separating them by commas and leaving unknown keywords blank. E.g. “SPECULATION,,CREDULITY” or “SPECULATION,,”. The order of keywords is left square key, top square key and base square key.
