Dilly

by Batey, Mavis;

  Rod square for rotor II

  If the middle rotor is assumed to be rotor II, initially set to its 1st position, then from the 1st and 2nd columns of this rod square, the three post-TO rod couplings (o w), (k i) and (l t) are found to have the corresponding pre-TO couplings (j u), (w k), and (r p). Comparing these with the list of couplings given above, it can be seen that all three are inconsistent, (for example the couplings (u q) and (j u) are contradictory); this implies that at least one of the initial assumptions must be wrong.

  If the setting of the assumed middle rotor (still rotor II) is changed to position 3, then the 3rd and 4th columns of the rod square table give the corresponding pre-TO couplings (r k), (b x) and (t s). As each of these appears on the original list of couplings, there are no inconsistencies, and consequently the two assumptions (i.e. that the middle rotor is rotor II and that it was set to the 3rd position) are probably correct. The rod pairs for these couplings also confirm some of the bigrams found previously, thus providing further evidence that these assumptions are the correct ones. By using the 3rd and 4th columns in the rod square in the reverse order, the remaining original rod couplings can be used to find their corresponding post-TO couplings, and two of them providing additional information are (u q) → (b v) and (l z) → (h g).

  The new rod coupling (b v) gives at the 31st place the bigram (K T), and the new coupling (h g) gives at the 30th place the bigram (R A).

  The two additional bigrams give the plain text letters R and K, so that the plain text becomes ‘C O D E X B R E A K I N G X A T X B L E T C H L E Y ? ? ? R K’, credibly leading to the message:

  C O D E X B R E A K I N G X A T X B L E T C H L E Y X P A R K

  Concluding remarks

  In addition to the meticulous care that would have been necessary during the elimination procedures described above, the wartime successes required considerable linguistic ability and creative imagination. It was often necessary to make correct inferences about the context of messages expressed in German or Italian, based only on the fragmentary evidence of some of the letters contained in them.

  If the reader does not consider the deductions made in this example to be plausible, it is suggested that a visit to the exhibition at BP might be of interest, as some of the deductions actually made during the breaking of a genuine cipher message on display are quite surprising and show that much higher levels of skill and imagination were required for success than are suggested by the somewhat contrived example given above.

  A brief historical post-script

  The following short summary on how the first break was made in 1940 may give the reader some insight into the difficulties encountered at the time.

  When the Italians entered the war in June 1940, it was thought likely that their navy might still be operating the same type of Enigma machine as they had used at the time of the Spanish Civil War, and the attempts to break their ciphers were based on this assumption. For the technique of ‘rodding’ to succeed it was essential to have accurate cribs, and initially a serious difficulty was the lack of knowledge about the stereotyped forms of text that were likely to occur in the Italian messages.

  In the absence of anything more specific, Dilly Knox instructed his assistants (a group of young women known as ‘Dilly’s girls’) to use ‘PERX’ as a crib for the first four characters of each intercepted signal (= ‘FOR’ followed by a ‘space’) and, for those cases when this did not lead to any inconsistencies between the crib and the first four letters of a cipher message, to record any other letters that could be found by the rods in the hope that these might provide some clues about the plain text.

  These assistants worked continuously for three months at this task without having any success until September 1940, when one of them, Mavis Lever, a nineteen-year-old student whose university course had been interrupted by the war, achieved a remarkable break. With the message on which she was then working, for a particular starting position for the ‘green’ rotor (i.e. rotor I), the rods had given the letter S in the 4th place, which clashed with the letter X in the crib (i.e. resulting in the letter sequence ‘PERS’ instead of ‘PERX’, as was anticipated).

  If Miss Lever had obeyed her instructions, she would have rejected this rotor starting position and gone on to try the next one. However in a moment of inspiration she decided to assume that the crib ‘PERX’ was in fact wrong and guessed that it was ‘PERSONALE’. After making this assumption and continuing with the ‘rodding’ process, she was gratified to find that the additional letters of plain text then given by the rods made good sense, so that the first part of the message turned out to be ‘P E R S O N A L E X P E R X S I G N O R X…’ (X = ‘space’). (More information on how this was done is to be found in the exhibition.)

  This was a most remarkable and valuable achievement, as it proved (after three months’ effort!) that the Italians were indeed still using the same early version of the Enigma machine. From this message and others, which were subsequently broken, a vocabulary of useful cribs was built up which greatly increased the effectiveness (and speed) of the ‘rodding’ technique.

  Frank Carter

  APPENDIX 3

  ‘Buttoning-up’

  (A method for recovering the wiring of the rotors used in an un-Steckered Enigma)

  The description in Appendix 2 of the codebreaking technique known as ‘rodding’ shows how the rod square tables for the Enigma rotors were used to make the required sets of rods. However, before a particular table could be constructed it was first necessary to determine the complete sequence of letters in the left-hand column of the table, known as the 1st upright. From this upright it was then possible to construct the entire table, and also find the internal wiring of the corresponding rotor.

  Clearly the establishment of a procedure for finding the 1st upright was of fundamental importance, and in the following notes an account is given of the one originally devised by the veteran codebreaker ‘Dilly’ Knox. These include an illustrative example to demonstrate the effectiveness of the procedure, which involved a process referred to by Knox as ‘buttoning-up’.

  In order to understand what is to follow, it is essential to have read the notes on ‘rodding’ in Appendix 2.

  During the Spanish Civil War the Italian navy made some use of the commercial Enigma machine but with differently wired rotors, and it was in 1937 that Knox recovered the internal wiring of these. The so-called ‘Railway’ Enigma has the same basic structure as the machine used by the Italians, and as a computer emulation of it happens to be available, it has been used instead of the Italian machine, to generate the cipher messages used in these notes.

  Rod square for Rotor I

  Both of these versions of the Enigma machine (which did not have plugboards) had an entry disc on which the electrical contacts were connected to the keyboard in the sequence QWERTZUIOASDFGHJKPYXCVBNML (in a clockwise sense when viewed from the right-hand side of the machine). As a logical consequence of this, the letters in all the diagonals (from top right to bottom left) of the rod squares form cyclic sequences of letters in the order shown above. As described elsewhere, a set of rods was based on the strips formed by dividing the corresponding rod square into its 26 individual horizontal rows.

  The basis of the method that Knox employed to find the 1st upright from a rod square depended upon the property of the diagonals in the rod squares described above, and on the way in which the rods were to be used to decipher messages. Initially of course the details of both the rod squares and the individual rods would not have been known.

  The ‘rod square’ table for Rotor I from the ‘Railway’ Enigma is shown opposite, and it will be observed that the letter sequences in the diagonals in the table (top right–bottom left) do conform to the cyclic QWERTZU… sequences previously described.

  Two of the rods formed by individual rows from this table are shown below side by side, and above them a short sequence of letters from a message in cipher (it is supposed that the rods are correc
tly aligned with the cipher and are paired through the machine as described in the notes on ‘rodding’ in Appendix 2).

  The four letters from the message that have been deciphered by the rods are W, O, B and A. Note that two adjacent letters in the cipher message (A and N) happen to be the same as a pair of adjacent letters on the upper rod, and this leads to the corresponding pair of adjacent letters O and B on the lower one. A pair of adjacent letters on the same rod was referred to by Knox as a ‘beetle’, so that the letter pair AN is one example of a beetle and the letter pair OB is another.

  If in a cipher message two successive letters form a beetle in the correct rod position, the corresponding deciphered letters will form a beetle on another rod.

  In their original fixed locations in the rod square it is unlikely that the two rods will be in adjacent rows, and usually they will be separated from each other by an unknown number of other rows, as is the case for the pair of rods in the example. These are shown in their true locations in the following diagram, which only illustrates the relevant part of the rod square.

  The two corresponding rows from the rod square (beetles outlined)

  The diagonals in this rod square will have the invariant property previously described, namely that the letters in each diagonal always conform to the cyclic sequence based on the letter order of the terminals on the entry disc. For the version of Enigma machine being used here, as already noted the letters in each diagonal reading from top right to bottom left are in the cyclic sequence QWERTZUIOASDFGHJKPYXCVBNML. Using this information it is possible to insert additional letters into the cells of the diagonals, to the left and below each of the beetles shown in the following diagram, which conform to this cyclic sequence. (Some additional empty rows have been introduced into the diagram in order to avoid overlaps between these additional letters.) This provides a useful starting point for an explanation of the procedure used to recover the letter sequence forming the 1st upright in a rod square.

  Consider the above diagram from a point of view in which there is no prior knowledge about the structure of the upright, but it is known that the two ‘Enigma alphabet’ letter pairs (AO) and (NB) occur at the 3rd and 4th positions in the message (i.e. A would encipher as O at the 3rd position, and N would encipher as B at the 4th position). The sequences of letters in the two ‘descending’ diagonals from the two letters A and N are respectively ASD and NMLQ, and likewise the two ‘descending’ diagonals from the pair of letters O and B are respectively OAS and BNML. It will be observed that as a consequence of these sequences, the 1st upright contains the two pairs of adjacent letters DQ and SL.

  Alternatively from another point of view if it is assumed that the 1st upright contains the letter pair DQ, then the existence of the two alphabet letter pairs AO and NB jointly leads to the conclusion that the 1st upright will also contain the letter pair SL.

  This conclusion can also be established by the use of the following procedure:

  The two letters A and O at the 3rd position are replaced by the corresponding two letters D and S at the 1st position in their ‘descending’ diagonals.

  Likewise the two letters N and B at the 4th position are replaced by the corresponding letters Q and L at the 1st position in their descending diagonals.

  In this way the two Enigma letter pairs AO and NB are replaced by two new letter pairs, DS and QL. (This is the process that was originally referred to by Dilly Knox as ‘buttoning-up’.) The new letter pairs DS and QL lead directly to the two deductions D→S and Q→L, which when considered jointly give the same result as before (i.e. that if the 1st upright contains the letter pair DQ, it must also contain the letter pair SL). This procedure is illustrated in the diagram and tables below.

  The final conclusion can be obtained directly from the table containing the pairs of ‘buttoned-up’ letters, without any reference to the diagram. In general, once such a table has been constructed from a number of Enigma letter pairs, it can be used to derive the deductions for adjacent letter pairs in the 1st upright without any further reference to the sequences of letters in the diagonals.

  The process of buttoning-up is carried out by using the diagonal sequence QWERTZUIOASDFGHJKPYXCVBNML. For example suppose that letter X from an Enigma pair occurs at the 6th position. Then, beginning at X in the above sequence, a displacement of five positions down the diagonal (from right to left) will lead to M, the corresponding ‘buttoned-up’ letter at the 1st position. If instead the given letter from an Enigma pair happened to be N then a displacement of five positions down the diagonal will lead to the ‘buttoned-up’ letter E (a consequence of the cyclic nature of the diagonal sequence).

  In order to apply this process usefully, it is first necessary to discover a number of Enigma alphabet letter pairs for about six consecutive positions of the Enigma rotors. (An analysis by Alan Turing showed that roughly around 100 Enigma alphabet letter pairs are required.) All of the letters in the alphabet pairs are then ‘buttoned up’ and by means of them, an initial assumption about the identity of one pair of adjacent letters on the 1st upright can be used to make logical conclusions about other adjacent letter pairs, which in turn can then be used as the basis for further similar conclusions. If the initial assumption happens to be false, then this will soon become evident, as logical contradictions will arise between some of the outcomes.

  These ideas lead to a procedure in which a sequence of possible initial assumptions are tested one by one, until a correct assumption is found that does not lead to any inconsistent conclusions and indeed is very likely to generate some confirmatory (repeated) ones.

  Success in the task of identifying Enigma alphabet letter pairs depends upon finding cribs for the intercepted cipher messages. The precise pre-war circumstances that enabled Knox and his colleagues to obtain a sufficient number of these letter pairs are not known, but it is believed that during the Spanish Civil War the Italian navy sometimes transmitted signals that had been enciphered with the same Enigma configuration. Provided that a sufficient number of these had been intercepted and identified, they would have provided a set of messages ‘in depth’, enabling the task in hand to be successfully completed.

  Given such a set of messages in depth, and starting with one or two cribs based on likely words, it is possible to find cribs for the others by using the reciprocal rule imposed on Enigma encipherments, and also applying some of the skills of a solver of crosswords. Once this task has been completed, then from the resulting Enigma alphabet letter pairs, the 1st upright in the rod square table can be found, this in turn leading to the wiring of the corresponding rotor.

  The following contrived list of clear texts and enciphered texts will be used as a basis for a practical illustrative example of the task of finding the 1st upright in a rod square. (A number of these were composed by someone with real wartime experience of this type of work, and are reminders of episodes from the past that were in some way related to cryptology.)

  In order to obtain a set of cipher messages in depth, all the clear text sequences shown in the above list were enciphered on the Railway Enigma emulation, using the same key: rotor order 3,2,1; ring settings ZZZZ; message settings FLCZ.

  From the above tabulation a number of Enigma alphabet letter pairs were obtained, and Table I (below) gives these letter pairs, all from the first six positions in the messages. (For example at the 2nd position, AU indicates that A is enciphered as U and U is enciphered as A). Table II shows the corresponding letter pairs at the 1st position obtained by means of the ‘buttoning-up’ process. (Note that the first column is the same in both tables.)

  Table II will be used extensively in the following work and it is important to understand how the entries in it were derived from those in Table I. As an example consider the letter pair DV in the 5th column of Table I. By means of the diagonal sequence QWERTZUIOASDFGHJKPYXCVBNML, the letter D is replaced by the letter J (four places forward in the sequence). Likewise the letter V is replaced by the letter L (again four plac
es forward). Note that the resulting letter pair (JL) appears in the 5th row of Table II.

  By means of the information in this table, the somewhat lengthy process of constructing the 1st upright in the rod square for the right-hand rotor can begin. Without any prior knowledge about this upright, the strategy used will be to carry out a search for a correct letter pair contained in it. The choice will be made systematically from the list of possibilities A/B, A/C, A/D etc., so that if the hypothesis ‘A/B’ (i.e. A is above and adjacent to B) is found to lead to inconsistencies then a fresh start will be made using the next hypothesis, ‘A/C’, and so on. The correct hypothesis related to letter A will be readily identified as it will be the only one not leading to any inconsistent conclusions.

  From the initial hypothesis A/B and the information contained in Table II, the following conclusions can be made:

  Letter pair AS in the 1st column indicates that A→S and the letter pair VB in the 2nd column indicates that B→V. Jointly these show that A/B→S/V. As the letter pair AS occurred in the 1st column of the table, this result can be expressed more precisely as AB–1–SV.

  Likewise in the 2nd column letter pair QA indicates that A→Q and in the 3rd column letter pair BY indicates that B→Y. Jointly these show that A/B→Q/Y. As the letter pair QA occurred in the 2nd column of the table this result is expressed more precisely as AB–2–QY.