Dilly

by Batey, Mavis;

  The result S/V obtained above also leads to further conclusions:

  Letter pair SI (2nd column) indicates that S→I and letter pair GV (3rd column) indicates that V→G. Jointly these show that S/V→I/G or SV–2–IG.

  Letter pair SR (4th column) indicates that S→R and letter pair DV (5th column) indicates that V→D. Jointly these show that S/V→R/D or SV–4–RD.

  Starting with the result Q/Y obtained above, letter pair OQ (1st column) indicates that Q→O, and letter pair YJ (2nd column) indicates that Y→J. Jointly these show that Q/Y→O/J or QY–1–OJ. Starting with the result R/D obtained above, letter pair GR (1st column) indicates that R→G. However, letter D does not appear in the letter pairs from the 2nd column of the table and consequently no conclusion for this letter can be made, and the process cannot be completed. However, the occurrence of the letter pair RP (2nd column) and the letter pair DJ (3rd column) jointly show that R/D→P/J or RD–2–PJ. In addition the letter pair XR (3rd column) and the letter pair DB (4th column) jointly show that R/D→X/B or RD–3–XB. These results are shown in the diagram below.

  The two conclusions O/J and P/J are inconsistent and the conclusion X/B is inconsistent with the initial assumption A/B, which consequently must be false. The procedure must now be repeated with the next initial assumption, ‘A/C’, and the details of this are shown (in a somewhat more abbreviated form) below:

  AS (1st column) and MC (2nd column): A/C→S/M or AC–1–SM.

  QA (2nd column) and FC (3rd column): A/C→Q/F or AC–2–QF.

  Starting again with S/M:

  SI (3rd column) and ZM (4 column): S/M→I/Z or SM–3–IZ.

  SR (4th column) and MF (5th column): S/M→R/F or SM–4–RF.

  GS (5th column) and CM (6th column): S/M→G/C or SM–5–GC.

  These results are shown in the diagram below.

  One of the conclusions reached is G/C, which conflicts with the initial assumption A/C, so that the assumption A/C is false.

  Starting with the initial assumption ‘A/D’:

  QA (2nd column) and DJ (3rd column): A/D→Q/J or AD–2–QJ.

  Starting again with Q/J:

  OQ (1st column) and YJ (2nd column): Q/J→O/Y or QJ–1–OY.

  EQ (4th column) and JL (5th column): Q/J→E/L or QJ–4–EL.

  Starting again with O/Y:

  OE (2nd column) and BY (3rd column): O/Y→E/B or OY–2–EB.

  These results are shown in the diagram below.

  The conclusions E/L and E/B are clearly inconsistent and hence the assumption A/D is false. This procedure must be repeated to systematically test in turn the initial assumptions A/E, A/F etc.

  When the assumption A/K is tested, the results are strikingly different. A large number of conclusions are obtained which do not logically conflict with one another, and some do indeed provide confirmation of others that have already been found. Some of these conclusions are shown below and are followed by a diagram showing the rather complex way in which they are related to each other. (In order to reduce as far as possible the length of the work, all of the confirmations have been omitted except for one that has been shown as an illustrative example.)

  Starting with the assumption A/K:

  AS (1st column) and EK (2nd column): A/K→S/L or AK–1–SL.

  Starting with S/L:

  SI (2nd column) and WL (3rd column): S/L→I/W or SL–2–IW.

  GS (5th column) and LY (6th column): S/L→G/Y or SL–5–GY.

  Starting with I/W:

  IY (1st column) and WT (2nd column): I/W→Y/T or IW–1–YT.

  UI (4th column) and WH (5th column): I/W→U/H or IW–4–UH.

  Starting with Y/T:

  YJ (2nd column) and TE (3rd column): Y/T→J/E or YT–2–JE.

  Starting with U/H:

  EU (1st column) and FH (2nd column): U/H→E/F or UH–1–EF.

  ZU (3rd column) and HG (4th column): U/H→Z/G or UH–3–ZG.

  Starting with J/E:

  BJ (1st column) and OE (2nd column): J/E→B/O or JE–1–BO.

  DJ (3rd column) and EQ (4th column): J/E→ D/Q or JE–3–DQ.

  JL (5th column) and XE (6th column): J/E→L/X or JE–5–LX.

  Starting with E/F:

  OE (2nd column) and FC (3rd column): E/F→O/C or EF–2–OC.

  EQ (4th column) and MF (5th column): E/F→Q/M or EF–4–QM.

  Starting with Z/G:

  ZM (4th column) and GS (5th column): Z/G→M/S or ZG–4–MS.

  Starting with B/O:

  UB (5th column) and HO (6th column): B/O→U/H or BO–5–UH.

  Starting with D/Q:

  DV (1st column) and QA (2nd column): D/Q→V/A or DQ–1–VA.

  Starting with M/S:

  CM (1st column) and SI (2nd column): M/S→C/I or MS–1–CI.

  MF (5th column) and US (6th column): M/S→F/U or MS–5–FU.

  Starting with C/I:

  FC (3rd column) and UI (4th column): C/I→F/U or CI–3–FU. (Note: this is a confirmatory conclusion.)

  CK (4th column) and RI (5th column): C/I→K/R or CI–4–KR.

  CN (5th column) and IB (6th column): C/I→N/B or CI–5–NB.

  Starting with F/U:

  FH (2nd column) and ZU (3rd column): F/U→H/Z or FU–2–HZ.

  Starting with H/Z:

  WH (5th column) and PZ (6th column): H/Z→W/P or HZ–5–WP.

  Starting with N/B:

  NX (1st column) and VB (2nd column): N/B→X/V or NB–1–XV.

  PN (3rd column) and DB (4th column): N/B→P/D or NB–3–PD.

  Starting with G/Y:

  GR (1st column) and YJ (2nd column): G/Y→ R/J or GY–1–RJ.

  Starting with W/P:

  WK (1st column) and RP (2nd column): W/P→K/R or WP–1–KR.

  WT (2nd column) and PN (3rd column): W/P→T/N or WP–2–TN.

  WL (3rd column) and PX (4th column): W/P→L/X or WP–3–LX.

  This rather protracted procedure has now been carried far enough for it now to be possible to deduce the complete letter sequence in the 1st upright. The following diagram will be very helpful in this final stage of the work.

  Combining the results

  The initial assumption that the letter pair AK forms a fragment of the upright leads to a long chain of conclusions for other letter pairs on the upright that is both consistent and confirmatory, and these are shown in the final diagram below. When they are combined the result is a complete list of 26 ordered letters that form the required 1st upright.

  Beginning with the letter pair AK, the above diagram can be used to list all the conclusions about the adjacent letter pairs existing in the 1st upright into an appropriate order: AK, KR, RJ, JE, EF, FU, UH, HZ, ZG, GY, YT, TN, NB, BO, OC, CI, IW, WP, PD, DQ, QM, MS, SL, LX, XV, VA. Combining these then leads to the upright sequence:

  A K R J E F U H Z G Y T N B O C I W P D Q M S L X V (A)

  This is a cyclic sequence that is closely related to the electrical connections between the contact ‘pins’ on the right-hand side of the rotor and the ‘plate’ contacts (denoted by the sequence of letters q, w, e, r, t, z, u etc.) on an imaginary fixed reference disc on the left hand side of the rotor. The fact that the letter A appears at the beginning of the sequence is of no significance and this has only happened because the initial assumption A/K was used to obtain all of the subsequent conclusions.

  If it is assumed that, for the 1st position in each message, pin ‘C’ on the rotor was connected to plate ‘q’ on the fixed reference disc (through the internal wiring of the right-hand rotor), then the connections between these two sets of contacts will be as shown in the following table:

  Reference to the rod square given earlier confirms that this corresponds to the 1st upright correct for Rotor I when set to ring setting ‘Z’ and rotor position ‘A’.

  A more practical version of this table can be constructed in the following way. Assign the numbers 1, 2, 3, 4 … 26 to the corresponding letters in the list q, w, e, r, t … l appearing in the
1st row and also to the corresponding capital letters in the 2nd row (e.g. both letters ‘q’ and ‘Q’ will be replaced by ‘1’; both letters ‘w’ and ‘W’ will be replaced by ‘2’). The table will then be transformed to:

  This table shows the internal core wiring connections from the 26 contacts on the left-hand face of the rotor to the corresponding contacts on the right-hand face.

  A final version gives the same connections but now considered in the opposite direction, from the right-hand face of the rotor to the left-hand one:

  Concluding remarks

  It is believed that ‘Dilly’ Knox developed the technique of ‘rodding’ in 1936. In the following year he was first able to apply this method to ‘live’ messages, after he had determined the rod squares for the Enigma rotors then in use by the Italian navy. This early work paid dividends later on, when in 1940/41 by means of ‘rodding’, some important Italian naval signals yielded the intelligence that resulted in the dramatic British success at Matapan. In 1941 Knox achieved perhaps his greatest success by breaking the Abwehr Enigma, in which the ‘buttoning-up’ procedure had again been usefully applied.

  Frank Carter

  APPENDIX 4

  Report on the ‘Lobster Enigma’

  I. Solution

  This was based on a theory, an observation and a procedure devised by the head of the section. These were:

  (a) The key-blocks were too scanty to be evaluated. Evaluation could only occur if we availed ourselves of two staggered settings of the key-blocks, e.g.

  ABCD or ABCD

  BCDE KLMN

  A sufficient hunt was made for these with the aid of Mr. Freeborn but no instances occurred. This was in itself suspicious.

  (b) It was no great surprise to the aforesaid Officer when he found what was wanted standing, like the abomination of desolation, precisely where it should not – on a single setting, e.g. (1) ABCD (2) BCDE (3) ???? (4) ???? (5) BCDH (6)CDEI (7) ???? (8) ????

  (c) It became clear with these data

  (1) that the diagonal was QWERTZU. No other fact emerged.

  (2) that we had to deal with frequent carries affecting all four wheels.

  (3) that we still had only partial evaluation of two of the four columns and could not guess the rest.

  (d) He then decided that, as everything that has a middle has also a beginning and an end that sometimes we should have, e.g. (1) ???? (2) ???? (3) ???? (4) ???? (5) ABCD (6) BCDE (7) ????(8) ????

  (e) The first phenomenon he named ‘a crab’ and condemned as useless; the second he named ‘a lobster’ and ordered an intensive hunt on ‘saga’ methods (the box).

  (f) The hunt was up and scent was good. One very fine ‘lobster’ (among others) was caught, and after two days Miss Lever, by very good and careful work, succeeded in an evaluation which contained sufficient non-carry units to ascertain the green wheel.

  (g) The blue wheel was sometimes harder and on semi-saga methods several evaluations were made, two of which coincided.

  (h) The red wheel proved very difficult. We diagnosed an apparent red wheel as a ‘double’ wheel (red and green) and Mr. Rees definitely proved this by obtaining the Umkehrwalze couplings.

  (i) The compound wheel was later dissected by him and the red wheel which usually carries obtained.

  (j) An element of surprise was the discovery that the carry is cyclometric, a fact which suggests that we may be ready to decode before the machine. To decode such carries except on the machine would need an enormous staff.

  (k) There are snags ahead. To get the first key onto the messages we still need much fortune and a complete study of all parallel material. All subsequent keys up to the fourth and fifth will be very hard; after that they will more probably prove laborious.

  (l) Since the old rod system cannot be used an alternative method is being provided. It cannot be ready for three weeks.

  (m) Meantime staff must be collected or adjusted and it is necessary to consider this carefully.

  II. Staff

  It is obvious that a most careful and immediate study of our output will sooner or later be necessary. This cannot be done except on the system of supervising the outgoing traffic as is done in Hut 8, and on the Italian Enigma. It is more necessary for us than for Hut 8 since we must always solve by trial and error at least one position of message for every key.

  The linguistic (German) staff at present consists of three, Miss Lever, Miss Rock and myself. As we shall also have to direct all the solutions and may have to work shifts, at least two more linguists must be chosen and have time to learn (a) what we know we want, (b) what might be useful. All hunters must know all the tricks of the machine.

  The existing system of crib-hunting by proxy has yielded the Italian Enigma in two years the total of 0 (nought) cribs. I should add that I am using ‘cribs’ in the widest sense of the term. A long ‘crib’ in the ordinary sense is no longer necessary. We must proceed as with the Italian Enigma by the careful study and correction of messages before they leave us. Any other system of arbitrary correction by those who do not understand machine plans and cannot avail themselves of Morse corrections is repugnant and unthinkable.

  We need, therefore:

  (a) Two more scholars for watch, the watch probably proceed to message solution.

  (b) A certain increase of general staff at the earlier possible moment.

  (c) Three or four machines and relays of decoders, cannot watch results off machines in another Hut.

  With regard to (b) I suggest the gradual return from the Naval Hut of the Cottage staff. They were first loaned intermittently and are now really on a continuous loan. They are not doing work up to their capacity and should, in my opinion, be replaced by a Wren section. Return could be gradual. Some could be spared for (c), the machines. There would then remain (a) which is a matter of urgent moment. I would welcome a private discussion.

  A. D. Knox

  (I shall be away tomorrow, ADK)

  28 October 1941

  APPENDIX 5

  Abwehr and SD cipher machines attacked by the ISK section

  1. Group II Enigma Called the Zählwerk (counter) Enigma by the Germans; also called the Lobster Enigma by ISK Solved by Dilly Knox in October 1941. The principal Abwehr Enigma, with multi-notched rotors (11, 15 and 17 notches), used until the end of 1944 for European communications.

  Called ‘Group II’ after the Radio Security Service name for the radio circuits carrying its traffic.

  The Abwehr became aware that the Zählwerk Enigma could be broken by a 10-letter crib. Users were then instructed to encipher messages twice, but appear not to have done so.

  The machine was withdrawn from German military attachés in 1943. It ceased to be supplied to the Abwehr after 23 November 1943, and was largely replaced by the KD Enigma and Cipher Machine 41 (see below) towards the end of 1944.

  2. GGG Enigma Solved by Mavis Batey (née Lever) in February 1942. An Enigma used by the Abwehr solely for communications between Madrid and several outstations situated round the Strait of Gibraltar.

  There were about 500 signals a month from February 1942 onwards, of which 90 per cent were readable.

  3. KK Enigma Captured in November 1942 at Blida in Algeria. An Enigma with multi-notched rotors (11, 15 and 17 notches) used by the German Armistice Commission in Vichy France and north Africa.

  4. ‘Green’ South American Enigma Solved in December 1942. An Enigma with multi-notched rotors (11, 15 and 17 notches) used by the Abwehr for communications between Germany and South America.

  5. Canary Islands Enigma Solved by Margaret Rock in May 1943. Used for maintaining a weather ship reporting service between Berlin and the Canaries.

  6. SD Enigma Solved by Keith Batey in August 1943. Used by the Sicherheitsdienst for European communications, including Berlin–Turkey.

  7. ‘Red’ South American Enigma Solved in January 1944. An Enigma with multi-notched rotors (11, 15 and 17 notches) used from November 1943 by the Abwehr and Sicherheitsdien
st for communicating with South America.

  The first two groups and last two groups in its traffic were identical to make it look like Naval Enigma, although signals were also sometimes sent in 5-letter groups.

  8. KD Enigma Solved in January 1945. Used between Berlin and Madrid and Lisbon. A machine with multi-notched rotors (nine on each rotor) and a rewirable reflector. The ‘D’ reference suggests that the rewirable reflector was the same as the ‘D’ reflector introduced by the German air force in January 1944.

  Replaced the Group II Enigma for security reasons (see above).

  9. Cipher Machine 41 (Schlüsselgerät 41 (SG 41)) Introduced on 12 October 1944.

  A Hagelin-type machine, with six pin wheels whose motion was very irregular – the wheels sometimes moved backwards. Even when pure key was available, the wheel settings and pin patterns could not be reconstructed.