ADFGVX


ADFGVX
Using ADFGVX
Breaking of ADFGVX


ADFGVX

ADFGVX, is one of the best known field ciphers in the history of cryptology. Originally a 5 x 5 matrix of just 5 letters, ADFGX, the system was expanded on June 1, 1918 to a 6th letter V. The letters were chosen for their clarity in Morse.

W. F. Friedman describes one of the first traffic analysis charts regarding battle activity from May to August, 1918 at Marne, and Rheims, France. It was based solely on the ebb and flow of traffic in the ADFGVX cipher. This cipher was restricted to German High Command communications between and among the headquarters of divisions and army corps.

The ADFGVX cipher was considered secure because it combined both a good substitution (bipartite fractionation) and an excellent transposition in one system. During the eight month history of this cipher, only 10 keys were recovered by the Allies (in 10 days of heavy traffic) and fifty percent of the messages on these days were read. 


Using ADFGVX


26 letters and 10 digits of the ADFGVX were placed into a 6 x 6 Bipartite Square:

¡@
A
D
F
G
V
X
A
8
p
3
d
1
n
D
l
t
4
o
a
h
F
7
k
b
c
5
z
G
j
u
6
w
g
m
V
x
s
v
i
r
2
X
9
e
y
0
f
q

Using ADFGVX to encrypt message, for example, plaintext "7" is in the "F" row and in the "A" column, then "7" is encrypted to "FA".

Below is the example of encrypting "attack at 10pm" with ADGVX.

Plaintext: a t t a c k a t 1 0 p m
Ciphertext: DV DD DD DV FG FD DV DD AV XG AD GX

The bilateral cipher which results is transposed with a key, written in by row and removed by column. (The example below is using the key "MARK".)

M
A
R
K
D
V
D
D
D
D
D
V
F
G
F
D
D
V
D
D
A
V
X
G
A
D
G
X

Rearrange the columns according to the alphabetical order of the key.

A
K
M
R
V
D
D
D
D
V
D
D
G
D
F
F
V
D
D
D
V
G
A
X
D
X
A
G

Write the letter by the column vertically. (In this example, write the "A" column first, then "K" column, etc.)

and the final ciphertext  is: VDGVV DDVDD GXDDF DAADD FDXG

¡@


Breaking of ADFGVX
In France, a remarkable cryptanalysis was achieved by Painvin. He broke the German system ADFGVX in April 1918. Before they launched their last offensive, the Germans modified the system, and in a few days Painvin broke it once more. The French then discovered where Ludendorff wanted to attack, and could stop the offensive.

Solution by the famed French Captain Georges Painvin was based on just two specialized cases. No general solution for the cipher was found by the Allies. In 1933, William Friedman and the SIS found a general solution. French General Givierge, of the Deuxieme Bureau also published a solution to the general case.