Anoraks Corner by Tony Sale

Calculating the Zygalski Sheets

The original Zygalski sheets were two alphabets wide by two alphabets deep in order for overlap to occur when sheets were offset from one another. This is not practicable for a web based demonstration, so just the one alphabet overlap portion has to be calculated and reproduced.

The first sheet is calculated for a given wheel order (132) and given left hand wheel ring setting (QZZ) and then for all wheel start positions within the left hand wheel start position of the given Indicator, (first one PTJ).

The calculation procedure runs through all middle wheel and right hand wheel positions (676) testing to see if there is a keyed in letter which gives the same encipherment three places on (a female). If there is such a keyed letter, a "1" is put into the 676 element matrix.

When the whole matrix has been investigated it is written to the screen, together with the alphabets with a dot (full stop) where there was a zero and a "0" to represent a hole, where there was a female.

The next Indicator to be laid down (CEH) has to generate a sheet as if its origin were offset on the viewing table from the first sheet. This is achieved by using not QZZ for its rings but Q,(Z + E - T), (Z + H - J).

The result of running through all middle and right hand wheel positions and testing for females is added into the 676 matrix. A negative result removes a "1" a positive result leaves a "1", giving the effect of the two sheets being overlaid and light shining through overlapping holes.

As more and more Indicators are entered, giving more and more sheets being overlaid, two outcomes are possible. Either all holes are eliminated, in which case the original assumptions of wheel order and ring letter were wrong, or one hole is left which is not eliminated by more Indicators causing sheets to be added. This hole represents the resultant middle and right hand ring settings used on the original Enigma encipherment of the intercepts. But it has to be transformed from the sheet alphabets co-ordinates, in this case JD to allow for the first sheet offset, TJ.

Resultant rings = Q, (T - J), (J - D) giving QJF, which was the original setting to generate the list of intercepts.

Note that Indicators ending in letters in the range (turnover - six) up to turnover must not be used. The sheets know nothing about real Enigma wheel turnovers and are generated assuming no turnover. In the demonstration, Indicator last letters A through F must not be used. As I discovered in 1994 when I first reproduced the Zygalski sheets, this can be avoided by forcing a hole into the 676 matrix for all right hand letter settings in this range since the wheel order is known and therefore the right hand wheel turnover is known for this sheet. The resultant sheets do not cause a correct stacking to fail.

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