The Zygalski's sheets: a complete example

Zygalski's sheets home page

Raw data

Blist

In early 1940, Hut 6 at Bletchley Park housed the British cryptanalysts tasked with deciphering Enigma messages. They received intercepted ciphertexts from Y-stations.

The Blists contained message headers and all the information needed to use Zygalski sheets.

Here is an excerpt from a Blist:

  Number Call-sign Time Part number Length Grund. The first Three groups                                         
  236    2EX RN2   1525             176    =DOT=  OUPWO  NEQAI  JKLFU
  237    TOH IDM   1755 2TL=1TL     145    =OUN=  ULZNU  WDKYD  JMZFM  
  238    TOH IDM            2TL      69    =BNC=  ARNDQ  CEPKN  DDGKR
  ...

The first group contains the Kengruppe, which identifies the network to which the message belongs. The recipient examines this group to determine whether the message is intended for them.

By examining a set of multi-part messages, one can deduce the daily Kengruppes for each network. For instance, the Kengruppes ZNU and NDQ belong to the same network.

Message Interception

Bletchley Park naturally receives the complete encrypted messages. They are indexed using the number listed in the Blist.

Here, for example, is message number 237:

237 TOH IDM   1755 2TL=1TL  145  =OUN=    ULZNU WDKYD JMZFM 
TZSOX ZBEBJ IYUQS PTSRL PIZWD EVAXB BROLN GORMS DHWVZ CPVIM 
TRJIV DEEKJ UIVKI GIOLT ZDBLC QOBKK PGEWN PSRNY CKGKA MJDBX 
RGFYC FTDIK XIPAE FODOA TJHRN ISEIO

Females derived from traffic

From the B-lists, we extract all messages containing indicators that include females for the same network. From these, we deduce the Grundstellungs for the first letter of the female.

	grund. indicators type of females grund. for menus

	HKH    CVZCQQ     1-4             HKH
	RTK    KISSHS     3-6             RTM
	QTS    TDCTCO     1-4             QTS
	IVU    ZJEZZG     1-4             IVU
	OUN    WDKYDY     2-5             OUO
	LLC    OYLOTW     1-4             LLC
	EZA    TFETRS     1-4             EZA
	NSK    CCMPCP     2-5             NSL
	DUE    PTUPBR     1-4             DUE
	BYL    MPCKPG     2-5             BYM
	IRE    AWXAKK     1-4             IRE
	QRJ    USLUMX     1-4             QRJ
	JUB    AOGCOR     2-5             JUC
	JUS    TFJTIR     1-4             JUS

Notes:

At this stage, we cannot rule out indicators involving turnovers. This will be addressed once a specific Walznlage is assumed.
A single Grundstellung can contain multiple females.

Writing the menus

We must now write the menus used by the personnel handling the sheets.

Note: To simplify the example, we assume that only the three rotors I, II, and III are being used.

For each Walzenlage, we list the Grundstellungs to be tested.

	Walzenlage	Grundstellungs
	I-II-III	HKH, RTM, OUO, LLC, EZA, NSL, DUE, BYM, IRE, QRJ, JUC
	I-III-II	HKH, RTM, QTS, EZA, OUO, NSL, BYM, QRJ, IVU, JUS
	II-I-III	HKH, RTM, OUO, LLC, EZA, NSL, DUE, BYM, IRE, QRJ, JUC
	II-III-I	HKH, QTS, LLC, EZA, NSL, BYM, DUE, IRE, QRJ, JUC, JUS
	III-I-II	HKH, RTM, QTS, EZA, OUO, NSL, BYM, QRJ, IVU, JUS
	III-II-I	HKH, QTS, LLC, EZA, NSL, BYM, DUE, IRE, QRJ, JUC, JUS

Note: For rotor arrangements ending with rotor III, ground settings ending in STUV, which entail a turnover are omitted (specifically QTS, IVU, JUS). For those ending with rotor II, ground settings ending in BCDE are omitted (specifically LLC, EZA, DUE, IRE, JUC). For those ending with rotor I, ground settings ending in NOPQ are omitted (specifically OUO).

Find the Walzenlage and the Ringstellung

First attempt: I-II-III

We test Ringstellungs A, B, C, ...

$ python3 zygal_sheets.py 123 A HKH,RTM,OUO,LLC,EZA,NSL,DUE,BYM,IRE,QRJ,JUC 
$ python3 zygal_sheets.py 123 B HKH,RTM,OUO,LLC,EZA,NSL,DUE,BYM,IRE,QRJ,JUC 
$ python3 zygal_sheets.py 123 C HKH,RTM,OUO,LLC,EZA,NSL,DUE,BYM,IRE,QRJ,JUC

It can be seen that, in every case, there are no holes at the end of the stacking process.

However, when testing Ringstellung V, a result is obtained: Ringstellung VON.

Notes:

Only certain stackings are shown: a single Grundstellung, two, four, nine.
For each Grundstellung, the sheet used is indicated (HKH:L, therefore sheet L).

$ python3 zygal_sheets.py 123 V HKH,RTM,OUO,LLC,EZA,NSL,DUE,BYM,IRE,QRJ,JUC 
123 V ['HKH', 'RTM', 'OUO', 'LLC', 'EZA', 'NSL', 'DUE', 'BYM', 'IRE', 'QRJ', 'JU
C']
Grunds:  ['HKH:L']
 A stacked sheets for left Ring V and Walzenlage 123
    H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
    Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
K Z         *   * *       *   *     *             *
L Y * * *   *             *         *       *   *
M X         *     * *       *     *           *     *
N W *           * *   * *       *   * * * * *   * *   *
O V   * *       * *                 *     *
P U * * * *     * *         * *             * *   * *
Q T   *     *   *     *     * *     * * *     * *   *
R S       *   * *     *   *                 *
S R   *   *                               * *   *
T Q   * *       * *                               * *
U P * * * * *     *   *   *     *       * *   *   *   *
V O *         * * *   *     *     * * * *   *   * * *
W N * *     *     *               *   * *     *       *
X M   *           *   * * *   *   * *       *       * *
Y L *       * *   *   *   *   * *       *   *
Z K         *         * *     *   *     * * *         *
A J         *           *                     * *
B I * *     * *       * *         *           *   *
C H *       * *     * *         *       * *       *
D G                   * *     *   *               * *
E F * *   *             *     *     *       *
F E *   * *     *       *         * *           *     *
G D     *   * *           *   *     *   *     * *
H C * * *             *     * *   * *       *
I B * *   * *   *     * *     *   *       *           *
J A   *   *   *     * *         * * *   * *       *
Grunds:  ['HKH:L', 'RTM:V']
 A stacked sheets for left Ring V and Walzenlage 123
    M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
    Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
T Z             * *       *
U Y     *   *                               *   *
V X               * *             *                 *
W W             * *             *   *     *     *
X V   * *                           *
Y U *   *                   *                 *
Z T   *     *   *           * *       *             *
A S
B R   *                                     *
C Q               *                                 *
D P
E O *           *     *     *         *             *
F N   *     *     *               *     *     *       *
G M                       *   *   *                 *
H L *                     *     *
I K
J J
K I   *                 *                     *   *
L H *       * *                 *         *       *
M G                           *                     *
N F                                 *
O E             *       *         *             *
P D     *                 *         *
Q C   *                     * *
R B *       *         * *     *   *
S A   *             *                   *         *
...
Grunds:  ['HKH:L', 'RTM:V', 'OUO:S', 'LLC:P']
 A stacked sheets for left Ring V and Walzenlage 123
    C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
    Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
L Z                       *
M Y                                             *
N X
O W                             *
P V                                 *
Q U                                           *
R T
S S
T R
U Q
V P
W O                   *     *
X N   *                                 *     *
Y M                               *
Z L
A K
B J
C I
D H *
E G                           *                     *
F F
G E
H D                       *
I C
J B
K A
...
Grunds:  ['HKH:L', 'RTM:V', 'OUO:S', 'LLC:P', 'EZA:I', 'NSL:R', 'DUE:H', 'BYM:F'
]
 A stacked sheets for left Ring V and Walzenlage 123
    M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
    Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
Y Z
Z Y                                             *
A X
B W
C V
D U
E T
F S
G R
H Q
I P
J O                         *
K N
L M
M L
N K
O J
P I
Q H
R G
S F
T E
U D
V C
W B
X A
Grunds:  ['HKH:L', 'RTM:V', 'OUO:S', 'LLC:P', 'EZA:I', 'NSL:R', 'DUE:H', 'BYM:F'
, 'IRE:M']
 A stacked sheets for left Ring V and Walzenlage 123
    E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
    Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
R Z
S Y
T X
U W
V V
W U
X T
Y S
Z R
A Q
B P
C O                         *
D N
E M
F L
G K
H J
I I
J H
K G
L F
M E
N D
O C
P B
Q A
...

Note: We were lucky; we found the correct solution with the very first Walzenlage tested. In fact, there are other possible Ringstellungs, but they turn out to be incorrect when tested.

	321: Nothing
	312: GXE, NST, RAN
	213: HYR
	231: Nothing
	132: HKJ, KYB, PMT, SAI, SBB

Find the Steckers

The general principle is to attempt to decipher the indicators and identify the plugboard settings (steckers) that reveal the key, which must correspond to a repeated trigram.

However, we first look for grundstellungs with only two "females" assuming no steckers are active, as these must correspond to plain letter and the corresponding ciphered letter. You can easily see the stecker being used in the grundstellung found in the traffic (or potentially the absence of a stecker).

Here are the indicators and their associated Grundstellung, valid for Walzenlage I-II-III:

	grund. indicators type of females 

	HKH    CVZCQQ     1-4             
	RTK    KISSHS     3-6             
	OUN    WDKYDY     2-5             
	LLC    OYLOTW     1-4             
	EZA    TFETRS     1-4             
	NSK    CCMPCP     2-5             
	DUE    PTUPBR     1-4             
	BYL    MPCKPG     2-5             
	IRE    AWXAKK     1-4             
	QRJ    USLUMX     1-4             
	JUB    AOGCOR     2-5

Searching for Cycles

Once the Ringstellung has been determined, the absolute position of the Grundstellung derived from the traffic can be deduced. Then, using the Cyclometer, the cycles associated with each ground setting can be calculated.

To save time, I explore the catalog generated by the Cyclometer:

$ grep 'LVT$' sheets/123.txt
1-1-2-2-5-5-5-5 IXOCE:PMRAK:VUQLG:YZNHD:WS:JF:T:B I,II,III ZZZ LVT

Thus, for the Grundstellung HKH, we obtain the two females T:B. We then extract all the females by proceeding in the same way.

	POS = GRUND – RING – [1,1,1],	Cycles of length 1 (females)
	
	HKH – VON – [1,1,1] = LVT	T:B
	RTM – VON – [1,1,1] = VEY	Q:N
	OUO – VON – [1,1,1] = SFA	T:X:D:L
	LLC – VON – [1,1,1] = PWO	Z:R
	EZA – VON – [1,1,1] = IKM	Y:T:O:J
	NSL – VON – [1,1,1] = RDX	F:B
	DUE – VON – [1,1,1] = HFQ	I:F:N:L
	BYM – VON – [1,1,1] = FJY	N:G:U:T		
	IRE – VON – [1,1,1] = MCQ	O:E
	QRJ – VON – [1,1,1] = UCV	W:T
	JUC – VON – [1,1,1] = NFO	R:S:B:O

With T:B cycles, the plaintext letter T yields the ciphertext letter B (or vice versa). With T:X:D:L cycles, the plaintext letter T yields the ciphertext letter X, D, or L.

As can be seen, it is easier to use only the Grundstellungs associated with just two females.

Initial deductions

Let us consider the first indicator (CVZCQQ, or rather CxxCxx). For the associated Grundstellung HKH, the two cycles T:B indicates that, in the absence of Steckers, encrypting the letter T yields the letter B (or encrypting B yields the letter T). Consequently, there are two mutually exclusive possibilities for the steckers: BC or CT.

We can thus construct the following table, based solely on the pairs of females. This yields the following possible plug connections (steckers):

	(1) HKH	  CxxCxx  B:T   BC or CT
	(2) RTK	  xxSxxS  Q:N	SN or SQ
	(3) LLC   OxxOxx  Z:R   OZ or OR
	(4) NSL   xCxxCx  F:B	CF or CB
	(5) IRE   AxxAxx  O:E	AO or AE
	(6) QRJ   UxxUxx  W:T	UW or UT

Hypotheses 1 and 4 dictate that only the BC stecker is possible.

Hypotheses 3 and 5 dictate that the AO and OZ/OR steckers are incompatible; therefore, only the AE stecker is possible.

In conclusion, we have identified two steckers: BC and AE. We also have three pairs of hypotheses: (SN or SQ), (OZ or OR), and (UW or UT).

Subsequent deductions

We take the first indicator, CVZCQQ, and test the two steckers, SN and SQ.

$ echo CVZCQQ |python M3.py B I II III "BC:AE:SN" VON HKH
TCPTAB
$ echo CVZCQQ |python M3.py B I II III "BC:AE:SQ" VON HKH
TCPTCE

TCxTCx decryption involves the SQ and VV steckers.

Next, take the third indicator WDKYDY, and test the two UW or UT steckers:

$ echo WDKYDY |python M3.py B I II III "BC:AE:SQ:UW" VON OUN
MTQMTM
$ echo WDKYDY |python M3.py B I II III "BC:AE:SQ:UT" VON OUN
EUQMUM

Full RCDRCD decryption involves OR and GG steckers.

Now we have five steckers. Then you just have to try all the possible letters for each stecker of which you have a single letter. The goal is to decipher the indicators and to have key twice each time, as before RCDRCD.

We take the sixth indicator CCMPCP, and we try all the letters associated with the letter P?: PD, PF, PG, PH, PI, PJ, PK, PL, PM, PN. In the latter case we obtain the MFxMFx decryption.

$ echo CCMPCP |python M3.py B I II III "BC:AE:SQ:UW:OR:PN" VON NSK
MFYMFV

Then for the same indicator we try all the letters associated with the letter M?: MD, MF, MG, MH, MI, MJ, MK. In the latter case, we obtain the KFVKFV decryption.

$ echo CCMPCP |python M3.py B I II III "BC:AE:SQ:UW:OR:PN:MK" VON NSK
KFVKFV

Next, we take the indicator associated with the Grund DUE and test all the Steckers involving T?: TD, TF, TG, TH, TI, TJ. In the last case, we obtain the decryption LJWLJW.

$ echo PTUPBR |python M3.py B I II III "BC:AE:SQ:UW:OR:PN:MK:ZX:TJ" VON DUE
LJWLJW

Finally, we take the indicator associated with the Grund EZA and test all the Steckers involving F?: FD, FG, FH, FI. In the last case, we obtain the decryption YMRYMR.

$ echo TFETRS |python M3.py B I II III "BC:AE:SQ:UW:OR:PN:MK:ZX:TJ:FI" VON EZA
YMRYMR

There you go, we’ve found all 10 Steckers: "BC:AE:SQ:UW:OR:PN:MK:ZX:TJ:FI".

Deciphering traffic

Key of the Day

Here is a summary of the key of the day:

	Walzenlage :   I-II-III
	Ringstellung :  VON (22-15-14)
	Steckers : AE, BC, FI, JT, KM, NP, OR, QS, UW, XZ

Deciphering message 237

The Grundstellung OUN and the indicator WDKYDJ are extracted from the Blist. The indicator is deciphered:

$ echo WDKYDJ |python M3.py B I II III "AE:BC:FI:JT:KM:NP:OR:QS:UW:XZ" VON OUN
KJEKJE

Thus, the key to the message is KJE. We can then decipher the message:

$ cat msg_237.cry
             MZFM TZSOX ZBEBJ IYUQS PTSRL PIZWD EVAXB BROLN
GORMS DHWVZ CPVIM TRJIV DEEKJ UIVKI GIOLT ZDBLC QOBKK PGEWN
PSRNY CKGKA MJDBX RGFYC FTDIK XIPAE FODOA TJHRN ISEIO

$ python M3.py B I II III "AE:BC:FI:JT:KM:NP:OR:QS:UW:XZ" VON KJE < msg_237.cry
ANXGENERALXDIETLXVOMGENERALSTABXSIESINDMITDEMGEBIRGSJAEGERREGIMENTEINSDREINEUNX
INNARVIKGELANDETXIHRETRUPPENSTAERKESCHEINTAUSREICHENDUM

References

Netz simulator