Anoraks Corner by Tony Sale

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The Zygalski Sheets

When they had been studying the double enciphered message settings in order to construct Rejewski's characteristics, cases had been noticed where the same enciphered letter occurred in either the 1st and 4th, or 2nd and 5th, or 3rd and 6th positions in the enciphered message settings. These positions, which were called females, corresponded to positions at which the same letter had been keyed by the German operator into the Enigma machine because of the repeat of the three letter message key.

Zygalski realised that whether this occurred or not depended on the wheel order and the start position, therefore inversely if it did occur it implied one of a set of possible Enigma configurations. If enough of these doubles occurred during a days traffic it might be possible to find a unique configuration for which all of these doubles could occur.

Zygalski realised that the analysis of the vast amount of information required could be achieved by a grill method using perforated sheets.

The sheet procedure involves working through each of the six possible wheel orderings for three wheels and for each wheel order working through the 26 possible left hand wheel ring letters, 156 tries in all, but on average only half before the answer is found.

There were sheets prepared for each left wheel letter for each wheel order. Each sheet contained four squares of 26 by 26 ie two alphabets along the top and down the side.

The first decision was which wheel order to try, (in our case 132) and which ring first letter, in this case Q. Next take the first letter of the first indicator that gives a 1,4 female in this case P and get the sheet 123 Q P. Place this on the table offset by the next two letters of the indicator, TJ. Now get sheets for succeeding indicators overlaying them on the table. If the wheel order and the first ring letter are what was used to encipher the message key then one square will line up and let light through from below the table. The original ring setting can now be deduced from the co-ordinates of this lit square.

Click here to try overlaying Zygalski sheets.

This emulation of the Zygalski sheets calculates the offset of a sheet and recreates the overlaid portion of each sheet at run time. This minimises the downloaded information but takes a little time to recalculate each sheet. Click here for a description of the calculations required to do this.

In order to deduce the steckers, the set of indicators and enciphered message keys which have repeated letters, need to be extracted and listed. Then by setting up an Enigma machine to the wheel order and ring setting just found, but no steckers, the wheels can be turned to one of the indicators from the list. Now successive keyboard letters can be input looking for a letter which repeats in the same positions as in the enciphered message keys. At least one letter will do this, sometimes two will. This letter or one of these letters is the stecker of the original repeated letter. By going through this for all the 1,4 2,5 3,6 sets the steckers can be deduced.

This page was originally created by the late Tony Sale
the original curator of the Bletchley Park Museum