The Key Rules


Break an Enigma Key with Bombe

A complete example

Introduction

As early as the spring of 1940, cryptologists at Hut 6 assumed, without any certainty, the existence of key rules. They began to search the broken keys for any building rules followed by the enemy. However, to be certain, they had to accumulate many keys.

The rules were used as soon as they were discovered. They made it possible to significantly reduce the tests carried out in conjunction with manual methods and when using the Bombe.

The most important key rules

Non-clashing rule

On any two consecutive days in the same month, the same wheel could not be used in the same place. By this rule alone, if any one day was out, the wheel order for the next day was automatically reduced to 32 instead of 60.

Non-repeating rule

Within a month, the same wheel order was not used twice. This rule was never quite so absolute.

Clarkian rule

This rule held on Red and Light Blue from August to November 1941 and was named after its discover, L.E. Clarke. The rule states that, in the same column, no wheel is followed by a consecutive wheel: 5 and 1 are not, however, regarded as consecutive.

An example of using key Rules

Suppose we want to test menus for the red network on February 14 and have broken all the previous days. It is possible to drastically reduce the number of Wheel Orders to be tested.

Walzenlage (WO) for the beginning of February 1941
1	251			
2	534
3	152
4	531
5	354
6	532
7	154
8	231
9	524
10	451
11	124
12	512
13	234
Deductions:
  • As on February 13, the Walzenlage had a value of 234 (II, III, IV), on February 14, according to the non-clashing rule, the first rotor cannot be rotor II, the second rotor could not rotor III and the third rotor (the one on the right) could not be rotor IV.
  • Due to the non-repeating rule, the following WOs are not possible:
    251, 534, 152, 531, 354, 532, 154, ...
  • The clarkian rule narrows the possibilities even further. Thus the following WOs are not possible: 315, 541, ...
Conclusion: If all these rules apply, there are only the following WOs left to test: 132, 134, 254, 413, 521.