Rejewski's Test Message as a Crib

Abstract

After Marian Rejewski had determined the Enigma wiring, he used a test message to help resolve the turnover and correct twist of the rotors [7, p. 258]. However, it is of historical interest to note that this message could have been used as a crib in its own right. It is shown that using only hand methods and Rejewski's guess that the entry permutation was alphabetic, the message could have revealed the wiring of rotors I and III despite its short length of 90 letters.

Keywords:

• adding up
• boxing
• Enigma
• rod coupling
• rotor wiring

Acknowledgments

The author thanks the reviewers for some very constructive comments and their generosity in providing additional background information which has helped to improve this article.

Notes

¹The term twist was used for this effect at Bletchley Park and by the American cryptanalytic agencies, and this is now the generally adopted term for this situation. Further details on the problems of recovering rotor wirings by cryptanalysis are provided by Philip Marks [8].

²It should be recognized that the various techniques (e.g., rodding, adding up, and boxing) described by Turing were actually developed by Dilly Knox, probably in the period 1936–1937 [2, 3]. Explanatory articles on rodding and adding up have been written by Frank Carter and can be found as appendices to Mavis Batey's book on Dilly Knox [3, Appendix 2 and 3].

³I am indebted to a reviewer who has reminded me that occasionally Turing's measures could be too pessimistic. Hugh Alexander recounted that Leslie Yoxall broke an Offizier message of 80 letters about a day after Turing had stated his opinion that 200 letters constituted a theoretical minimum [1, p. 33].

⁴Labelling the columns from the ring setting results in the recovered upright being the first upright of the rod square (or a rotation of it). This is the upright that would be found by measuring an original German rotor with the ring set at “A” [8].

⁵The notation AD* means that A and D are the window positions of the left-hand and middle rotors. The position of the right-hand rotor is marked with a*. Its actual position is irrelevant, because all connections have now been coupled through the right-hand rotor and appear at the entry face to the middle rotor. Remember that the message started at window position ABM (after the key press) so that AB* is the first position at which the middle rotor alphabets are available.

Additional information

Notes on contributors

John Wright

John Wright is a physicist, who is now retired after a career spent in telecommunications research and development. He currently pursues various software and mathematical interests.