M-209 Workings - A paper analog


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Introduction

A cryptanalyst not necessarily has a M-209 available. If he wants to make decryption, using a method requiring only a pencil and paper (paper analog) is very useful.

Calculate in advance all possible keys values

We can calculate in advance the key for each Pins combination.
Lugs settings:
- Number of lugs front of a wheel:
  Wheel 26 =  2,    Wheel 23 =  1,    Wheel 19 = 10
  Wheel 25 = 12,    Wheel 21 =  5,    Wheel 17 =  3
- Number of Overlaps beetween two wheels:
  Wheels 23-17 = 1, Wheels 21-19 = 1,  Wheels 25-19 = 2
  Wheels 26-19 = 1, Wheels 26-17 = 1

     For example, for Pin combination [0,0,1,0,0,1]
K = 1 + 3  1 = 3
D = K + S = 3  1 = 2

------Pins--------   K   D      --------Pins------   K   D
[0, 0, 0, 0, 0, 0]   0  25	[1, 0, 0, 0, 0, 0]   2   1
[0, 0, 0, 0, 0, 1]   3   2	[1, 0, 0, 0, 0, 1]   4   3
[0, 0, 0, 0, 1, 0]  10   9	[1, 0, 0, 0, 1, 0]  11  10	
[0, 0, 0, 0, 1, 1]  13  12	[1, 0, 0, 0, 1, 1]  13  12
[0, 0, 0, 1, 0, 0]   5   4	[1, 0, 0, 1, 0, 0]   7   6	
[0, 0, 0, 1, 0, 1]   8   7	[1, 0, 0, 1, 0, 1]   9   8	
[0, 0, 0, 1, 1, 0]  14  13	[1, 0, 0, 1, 1, 0]  15  14	
[0, 0, 0, 1, 1, 1]  17  16	[1, 0, 0, 1, 1, 1]  17  16	
[0, 0, 1, 0, 0, 0]   1   0	[1, 0, 1, 0, 0, 0]   3   2
[0, 0, 1, 0, 0, 1]   3   2	[1, 0, 1, 0, 0, 1]   4   3
[0, 0, 1, 0, 1, 0]  11  10	[1, 0, 1, 0, 1, 0]  12  11	
[0, 0, 1, 0, 1, 1]  13  12	[1, 0, 1, 0, 1, 1]  13  12
[0, 0, 1, 1, 0, 0]   6   5	[1, 0, 1, 1, 0, 0]   8   7	
[0, 0, 1, 1, 0, 1]   8   7	[1, 0, 1, 1, 0, 1]   9   8
[0, 0, 1, 1, 1, 0]  15  14	[1, 0, 1, 1, 1, 0]  16  15
[0, 0, 1, 1, 1, 1]  17  16	[1, 0, 1, 1, 1, 1]  17  16
[0, 1, 0, 0, 0, 0]  12  11	[1, 1, 0, 0, 0, 0]  14  13
[0, 1, 0, 0, 0, 1]  15  14	[1, 1, 0, 0, 0, 1]  16  15	
[0, 1, 0, 0, 1, 0]  20  19	[1, 1, 0, 0, 1, 0]  21  20	
[0, 1, 0, 0, 1, 1]  23  22	[1, 1, 0, 0, 1, 1]  23  22
[0, 1, 0, 1, 0, 0]  17  16	[1, 1, 0, 1, 0, 0]  19  18
[0, 1, 0, 1, 0, 1]  20  19	[1, 1, 0, 1, 0, 1]  21  20
[0, 1, 0, 1, 1, 0]  24  23	[1, 1, 0, 1, 1, 0]  25  24	
[0, 1, 0, 1, 1, 1]  27   0	[1, 1, 0, 1, 1, 1]  27   0	
[0, 1, 1, 0, 0, 0]  13  12	[1, 1, 1, 0, 0, 0]  15  14	
[0, 1, 1, 0, 0, 1]  15  14	[1, 1, 1, 0, 0, 1]  16  15
[0, 1, 1, 0, 1, 0]  21  20	[1, 1, 1, 0, 1, 0]  22  21	
[0, 1, 1, 0, 1, 1]  23  22	[1, 1, 1, 0, 1, 1]  23  22
[0, 1, 1, 1, 0, 0]  18  17	[1, 1, 1, 1, 0, 0]  20  19	
[0, 1, 1, 1, 0, 1]  20  19	[1, 1, 1, 1, 0, 1]  21  20	
[0, 1, 1, 1, 1, 0]  25  24	[1, 1, 1, 1, 1, 0]  26  25
[0, 1, 1, 1, 1, 1]  27   0	[1, 1, 1, 1, 1, 1]  27   0

Decrypting example

Pins Values
ABCDEFGHIJKLMNOPQRSTUVWXYZ
11010001101011000011011000
1001101001110010011010100
11000011010111000111101
001011011000110100111
0101110110001101001
11010001001001101

External Key: PEOPLE, Active Pins: ESEGDO
(External key: AAAAAA, Active Pins: LLKJIH )

Active Pins  :  C     Pins          D  C =   P
==================================================
E S E G D O  :  W 22  0 1 0 0 1 1  22 -22 =   0  A
F T F H E P  :  U 20  0 0 0 1 1 0  13 -20 =  19  T
G U G I F Q  :  H  7  0 1 1 1 1 1   0  7 =  19  T
H V H J G A  :  D  3  1 0 1 0 0 1   3  3 =   0  A
I X I K H B  :  U 20  1 1 0 0 1 1  22 -20 =   2  C
J Y J L I C  :  A  0  0 0 1 0 1 0  10  0 =  10  K
K Z K M J D  :  J  9  1 0 0 1 0 1   8  9 =  25  Z
L A L N K E  :  R 17  0 1 1 1 0 0  17 -17 =   0  A
M B M O L F  :  J  9  1 0 1 0 0 0   2  9 =  19  T
N C N P M G  :  Q 16  1 0 1 1 1 0  15 -16 =  25  Z
O D O Q N H  :  T 19  0 1 0 0 1 1  22 -19 =   3  D
P E P R O I  :  L 11  0 1 0 0 0 0  11 -11 =   0  A
Q F Q S P J  :  R 17  0 0 0 1 1 0  13 -17 =  22  W
R G R T Q K  :  G  6  0 1 1 1 0 1  19  6 =  13  N

Replacing the calculations by a paper analog

It is not very easy to calculate Cipher letter or Plain letter:
D = K + S
D = Difference, K = Key, S = Slide ( = 25 or -1 )

C = D  P    
P = D  C

C = Cipher letter, P = Plain letter, D = Difference

But we can use a Alberti's disk  or a St Cyr rule:

0123456789012345678901234567890123456789012345678901
ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
                      AZYXWVUTSRQPONMLKJIHGFEDCB
Key = 22, Crypto = U, then Plain = C

0123456789012345678901234567890123456789012345678901
ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
             AZYXWVUTSRQPONMLKJIHGFEDCB
Key = 13, Crypto = U, then Plain = T


We can also use a De Sestri's (Beaufort) array too.

             1         2
   01234567890123456789012345
   ABCDEFGHIJKLMNOPQRSTUVWXYZ
 0 ZYXWVUTSRQPONMLKJIHGFEDCBA
 1 AZYXWVUTSRQPONMLKJIHGFEDCB
 2 BAZYXWVUTSRQPONMLKJIHGFEDC
 3 CBAZYXWVUTSRQPONMLKJIHGFED
 4 DCBAZYXWVUTSRQPONMLKJIHGFE
 5 EDCBAZYXWVUTSRQPONMLKJIHGF
 6 FEDCBAZYXWVUTSRQPONMLKJIHG
 7 GFEDCBAZYXWVUTSRQPONMLKJIH
 8 HGFEDCBAZYXWVUTSRQPONMLKJI
 9 IHGFEDCBAZYXWVUTSRQPONMLKJ
10 JIHGFEDCBAZYXWVUTSRQPONMLK
11 KJIHGFEDCBAZYXWVUTSRQPONML
12 LKJIHGFEDCBAZYXWVUTSRQPONM
   01234567890123456789012345
13 MLKJIHGFEDCBAZYXWVUTSRQPON
14 NMLKJIHGFEDCBAZYXWVUTSRQPO
15 ONMLKJIHGFEDCBAZYXWVUTSRQP
16 PONMLKJIHGFEDCBAZYXWVUTSRQ
17 QPONMLKJIHGFEDCBAZYXWVUTSR
18 RQPONMLKJIHGFEDCBAZYXWVUTS
19 SRQPONMLKJIHGFEDCBAZYXWVUT
20 TSRQPONMLKJIHGFEDCBAZYXWVU
21 UTSRQPONMLKJIHGFEDCBAZYXWV
22 VUTSRQPONMLKJIHGFEDCBAZYXW
23 WVUTSRQPONMLKJIHGFEDCBAZYX
24 XWVUTSRQPONMLKJIHGFEDCBAZY
25 YXWVUTSRQPONMLKJIHGFEDCBAZ
   01234567890123456789012345   

Replacing the Pins array by a paper analog

With a stuff build from strips which contained Pins setting, we can replace the Pins array.

It is necessary to build one strip for each Wheel.

We slide each strip according to the external key.

A picture of this stuff is present at the end of TICOM DF-120. Below, the author's reconstruction trial of all this means.

References

  • Cryptanalysis Of The Hagelin Cryptograph, by Wayne G. Barker, From Aegean Park Press
  • "Codes and Ciphers, Julius Caesar, the Enigma and the Internet", by Robert Churhouse, Cambridge University Press (2002).
  • "Report on the solution of messages in depth of the American cipher device M-209" TICOM DF-120.