CODES & CIPHERS

ADFGX & ADFGVX Cipher

ADFGVX a fractionating transposition cipher which combined a modified Polybius square with a single columnar transposition. It is derived from the original ADFGX Cipher.

The cipher is named after the six possible letters used in the ciphertext: A, D, F, G, V and X. The letters were chosen deliberately because they are very different from one another in the Morse code. That reduced the possibility of operator error.

ADFGX

Operation

For the plaintext message, "Attack at once", a secret mixed alphabet is first filled into a 5 × 5 Polybius square:

A D F G X

A b t a l p

D d h o z k

F q f v s n

G g i/j c u x

X m r e w y

i and j have been combined to make the alphabet fit into a 5 × 5 grid.

By using the square, the message is converted to fractionated form:

a t t a c k a t o n c e

AF AD AD AF GF DX AF AD DF FX GF XF

Next, the fractionated message is subject to a columnar transposition. The message is written in rows under a transposition key (here "CARGO"):

C A R G O
_________
A F A D A
D A F G F
D X A F A
D D F F X
G F X F

Next, the letters are sorted alphabetically in the transposition key (changing CARGO to ACGOR) by rearranging the columns beneath the letters along with the letters themselves:

A C G O R
_________
F A D A A
A D G F F
X D F A A
D D F X F
F G F X

Then, it is read off in columns, in keyword order, which yields the ciphertext:

FAXDF ADDDG DGFFF AFAX AFAFX

In practice, the transposition keys were about two dozen characters long. Long messages sent in the ADFGX cipher were broken into sets of messages of different and irregular lengths to make it invulnerable to multiple anagramming. [3] Both the transposition keys and the fractionation keys were changed daily.

ADFGVX

In June 1918, an additional letter, V, was added to the cipher. That expanded the grid to 6 × 6, allowing 36 characters to be used. That allowed the full alphabet (instead of combining I and J) and the digits from 0 to 9. That mainly had the effect of considerably shortening messages containing many numbers.

The cipher is based on the 6 letters ADFGVX. In the following example the alphabet is coded with the Dutch codeword 'nachtbommenwerper'. This results in the alphabet: NACHTBOMEWRPDFGIJKLQSUVXYZ. This creates the table below with the letters ADFGVX as column headings and row identifiers:

A D F G V X

A N A 1 C 3 H

D 8 T B 2 O M

F E 5 W R P D

G 4 F 6 G 7 I

V 9 J 0 K L Q

X S U V X Y Z

The text 'attack at 1200am' translates to this:

A T T A C K A T 1 2 0 0 A M

AD DD DD AD AG VG AD DD AF DG VF VF AD DX

Then, a new table is created with a key as a heading. Let's use 'PRIVACY' as a key. Usually much longer keys or even phrases were used.

P R I V A C Y
A DD DD D A
DA GV GA D
DDA F D GV
F V F A D D X

The columns are sorted alphabetically, based on the keyword, and the table changes to this:

A C I P RV Y
D D D A DDA
GA GDA V D
D GA DDF V
D D F F V A X

Then, appending the columns to each other results in this ciphertext: DGDD DAGD DGAF ADDF DADV DVFA ADVX

With the keyword, the columns can be reconstructed and placed in the correct order. When using the original table containing the secret alphabet, the text can be deciphered.