Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory

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Author: David Joyner

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Sturgeon, The FISH BP Never Really Caught Frode Weierud? CERN, Div. SL, CH-1211 Geneva 23, Switzerland

1

Introduction

The German armed forces employed three different types of teleprinter cipher machines during the Second World War, the Lorenz machines SZ40 and SZ42 also called Tunny by Bletchley Park (BP), the Siemens Schl¨ usselfernschreibmaschine (SFM) T52, and the one-time-tape machine T43, also manufactured by Siemens. The Lorenz machines, which existed in three different models, SZ40, SZ42a, and SZ42b, are well known as the machines that were broken at BP with the aid of Colossus. The Siemens T52 existed in four functionally distinct models, T52a/b, T52c and T52ca — which was a modified version of the T52c machine, T52d, and T52e, all going under the BP code name of Sturgeon, while the Siemens T43 probably was the unbreakable machine that BP called Thrasher. The T43 machine came into use relatively late in the war and appears to have been used only on a few selected circuits. This paper will, for the first time in the open literature, explain in detail the events that led to BP breaking the Sturgeon machines. In 1964, the Swedish Under-Secretary of State Erik Boheman first revealed that Sweden had broken the German Geheimschreiber (T52) during the Second World War. [4] In 1967, David Kahn gave further details about this achievement. [16] However, it was only in 1984, when Hinsley et al. published part one of the third volume of “British Intelligence in the Second World War,” that it was officially acknowledged that BP also had experienced some success against the Siemens T52. [13] Previously, many authors had confused the T52 with the Lorenz SZ40/42 machines and had erroneously linked the Siemens T52 to Colossus. Since 1982, Donald Davies has published detailed information about the electrical and mechanical construction of the machines. [6–8] And Wolfgang Mache has through his contacts and interviews with former Geheimschreiber operators and technicians presented the evolutionary history of the Siemens T52 machines. [17–19] Apart from Sir Harry Hinsley’s and Professor Tutte’s [22] references to BP’s attack against the T52 there has so far not been any detailed account of this part of BP’s history. It is hoped the present paper will fill this void. The first section of this paper gives a short overview of the German teleprinter cipher machines and their use, followed by a short section explaining how and when BP first encountered the Sturgeon traffic. The third ?

This article represents the views of the author but not necessarily those of his employer or any other third party.

2

F. Weierud

section explains the cryptographic principle used by the Siemens T52 machines. Here, for the first time, the “Pentagon” is introduced and an explanation is given of how important this device was for BP’s attack against the first T52 model it encountered. The following two sections continues the historical presentation of BP’s attack on the T52 and its struggle to keep abreast with the German cryptographers continuous changes to the machines. For the first time, it is revealed that BP broke the T52d, a machine with irregular code wheel movement. This was indeed a major achievement. Sections seven and eight explain what knowledge BP gained from the captured machines and the information they acquired through both FISH and Enigma decodes. The section entitled The Cryptanalytical Problem gives new and detailed cryptanalytical information about the structure of the T52 key generators and how this information was used to attack the machines. A constructed example of how to perform an attack on T52 messages in depth1 concludes this section.

2

The Machines and Their Use

All the German teleprinter cipher machines were on-line machines. This means that when an operator types his plain text message on the transmitting machine, A, the same plain text appears immediately on the receiving machine, B. Neither of the operators ever sees the cipher text. The Lorenz machines were from their inception designed to be suitable for use on high frequency radio circuits operating in the 3 to 30 MHz bands. Radio signals in this frequency range are affected by both slow and fast fading, Doppler shift and multipath propagation which can easily play havoc with the digital teleprinter signals. All these machines used the standard teleprinter speed of that time, 50 Baud, which results in an element time of 20 ms. They were asynchronous machines using a start and stop pulse for each transmitted character. The SZ40/42 machines had a better receiver design than the T52 and were therefore more successful in reconstituting severely distorted teleprinter pulses. Towards the end of the war Lorenz worked on the development of an improved machine, the SZ42c, which applied the cryptographic process directly to the radio signal itself.2 It was used in conjunction with a continuously operating, synchronous teleprinter which maintained its speed with the help of a crystal controlled oscillator. The SZ42c was an advanced design and the German engineers were clearly leading in this area. It may therefore seem that technical reasons led to the Lorenz machines being used on radio teleprinter circuits. However, the author believes that lo1

2

Two or more cipher texts or messages are said to be in depth when the texts have been aligned such that the entire texts or parts thereof have been enciphered by the same key. This process, that messages are enciphered by the same key, can occur when a cipher machine or system is used incorrectly or from the use of keys that have been constructed wrongly. “European Axis Signal Intelligence in World War II – Vol.2”, 1 May 1946, A TICOM Publication released under the US Freedom of Information Act (FOIA).

Sturgeon

3

gistics are more likely to have been the reason. The Lorenz SZ40/42 machines were a German Army development, while from an early stage the T52 machines were adopted by the Air Force and the Navy. The T52 machines were only allowed to remain on board naval ships while they were in harbour. It is evident that they would mainly be connected to the well developed telegraph line network which covered the most of German occupied territory. This was also the situation for the machines used by the German Air Force. On the other hand, a large part of the German Army tended to be continually on the move and it was relatively seldom that they could connect their machines to the fixed telegraph network. With time the T52 machines also appeared on radio circuits. Initially they were used on radio relay connections using frequencies in the VHF and UHF range, while later they would also appear on circuits in the HF (3–30 MHz) area.

3

The First Encounter

BP first observed Siemens T52 traffic in the summer and autumn of 1942. Most of the traffic passed on a radio link between Sicily and Libya, which BP called the “Sturgeon” link. [1] In the same period there was also another link from the Aegean to Sicily that BP called “Mackerel”. The operators on these links were in the habit of sending a large number of cipher text messages using the same machine settings. When using the machine, they sent a short cipher text, followed by some operator chat in clear text. They then transmitted in clear the signal “UM UM” (Umschalten — switch over) and the cipher text continued but with the machine set to its initial setting. These interruptions and operator exchanges were frequent and the cipher texts in depth would continue to accumulate. The depths allowed the BP cryptanalysts to analyse the machine in detail and they soon discovered that the machine had 10 code wheels whose patterns appeared to be fixed. At least that was their assumption based on the intercepts during September and October and the first two days of November. After that, the Sturgeon link and its traffic came to an end. In the period before September the interception was too bad to allow any of the traffic to be read.

4

The Cryptographic Principle

The analysis of the intercepts showed that the Sturgeon machine was using two operations, a modulo two addition (XOR) and a permutation of the resulting five teleprinter code elements. The modulo two key was called the subtractor and represented by the symbol Σ, while the permutation key was called the permutor and represented by Π. The cryptographic algorithm, transforming a plain text character P into its cipher text character C, is given by C = Π(P ⊕ Σ)

(1)

4

F. Weierud

where ⊕ signifies modulo two addition. The plain text character is first added to the subtractor modulo two and the permutor then permutes the result. On reception the inverse permutation took place before the addition of the subtractor, which gives P = CΠ −1 ⊕ Σ

(2)

47 53 59 61 64 65 67 69 71 73

1 0 1 1 0 0 0 1 0 1

F

1 0 1 1 0

0 1 1 0 0

I

B 1 0 0 1 1

Z 1 0 0 0 1

Figure1. SFM T52’s functional diagram.

A schematic diagram of the basic operations of all the T52 machines is given in Fig. 1. The ten rectangles of varying heights symbolize the ten code wheels whose circumference carried bit patterns of different lengths. The wheels were bakelite disks with protrusions which were sensed by one or more electrical contacts. A more modern analogy for the code wheels is shift register sequences of different lengths. In Fig. 1 the length of the code wheel sequences is written above each of the ten wheels. The code wheels were labelled A to K from right to left, omitting I. These wheel identities are used later in Fig. 4 which gives a description of the wheel stopping logic for the T52d machine. Below the wheels, the plug connections that make up the main inner key are shown connecting each of the ten wheels to the various elements of the XOR and transposition circuits. The figure is an accurate representation of

Sturgeon

5

the functioning of the T52a/b and T52d machines. In these two models each code wheel consisted of four identical cams, each fitted with a changeover contact which was used in either the XOR circuits or the transposition circuits of the transmitter and receiver part of the machine. The plugs connected to the code wheel contacts were labelled with the corresponding wheel identities A to K, each wheel being equipped with two plugs, one red and the other black. The corresponding sockets in the transposition circuit, ten in total, were labelled from 1 to 10. Sockets 1 and 2, 3 and 4, etc. were paired together but we will see later that any of the two plugs of a given wheel can be plugged into any of the transposition sockets. Further, the red/black order had no electrical significance and the two plugs could be swapped. The ten sockets in the XOR circuit were labelled with Roman numerals from I to V in pairs, where each socket in a pair carried an additional a or b label, e.g. sockets Ia and Ib. For the XOR circuit the plug order had to be strictly adhered to and the two plugs of a given wheel had to be plugged to the sockets with the same Roman numeral pair, e.g. red K would plug to IIa and black K to IIb. If the plugs of a given wheel were connected to two different Roman socket pairs a short circuit of the ± 60 volt signalling supply would be the result. The T52c/ca and T52e machines modified this relatively complex circuit by using relays with multiple contact sets for the functions in the XOR and transposition circuits. These so-called SR relays were controlled via a logic circuit driven by the cam contacts on four different code wheels. On these machines the code wheels had one single cam on each wheel; the other three cams became superfluous and were therefore removed. The relays SR1–SR5 were used in the permutation circuit, while SR6–SR10 made up the substitution circuit. The machines also did away with the flexible transposition circuit of the T52a/b and d models which allowed full freedom in the configuration of the circuit as will be explained later. The T52c/ca and T52e machines used a standard configuration of the transposition units which were wired permanently in place. Instead of changing wheel order by plugging, these machines used ten switches, one for each wheel, which could be set to one of ten positions labelled 1, 3, 5, 7, 9, I, II, II, IV, and V. There were no longer any pairs of plugs and sockets such that the previous paired designations, e.g. 1–2 and IIa–IIb would be represented simply by respectively 1 and II. The ten outputs from the wheel order selection circuit carried the same labels as the switch positions; here the outputs are called the output channels. Any of the ten wheels could be connected to any of the ten output channels via the ten switches with the restriction that a given output channel could only be selected once. If this rule was not obeyed a short circuit of the ± 60V supply would occur. Furthermore, the labels had lost their previous meaning of Arabic numerals belonging to the transposition circuit and the Roman numerals belonging to the XOR circuit. Instead the three machines, T52c, T52ca and T52e, controlled each of the SR relays via a wheel combination logic which consisted of the modulo two sum of four different output channels. The wheel combination logic for

6

F. Weierud

the T52c has previously been published by Donald Davies in his paper on the T52 machines [7] and is reproduced here in Fig. 2. The wheel combination logic was different on each of the three machines. The logic for the T52e machine has also been published by Donald Davies in his paper on the T52e machine, [6] while the logic for the T52ca machine will be presented later. The information in Fig. 2 has also been compared with information from the archives of the Swedish signal intelligence organization, FRA,3 and found to be correct.

Code Wheel Outputs 1 3 5 7 9 I II III IV V SR1 X X X X SR2 XX X X SR3 XX X X SR4 XXX X SR5 X X X X SR6 XX X X SR7 XX X X SR8 X X X X SR9 X XX X SR10 XXX X

Subtractor

Permutor

Relays

Figure2. Wheel combination logic for T52c.

The T52c and T52ca machines introduced yet another complexity, the message key unit. This unit, which consisted of 15 transposition units and which will be introduced later, was connected between the code wheel cam contacts and the wheel order selection circuit. Its function was to further permute the order of the wheels before their contacts were selected in the wheel order selection circuit which was the main inner key. As explained later, a new setting of the message key unit would be selected for each new message. This meant that even if the main inner key would remain the same the wheels would still have a different function for each new message. The T52d and e models also had irregular movement of the code wheels, a so-called stop-and-go movement. The movement of each wheel was controlled by contacts on two of the other wheels. These two machines also had a switchable autokey4 element where the third bit of each plain text character would control the movement of the wheels in addition to the control given by the wheels themselves. 3 4

FRA, F¨ orsvarets Radioanstalt. See [3, 23]. Autokey or autoclave is where a part of the key is generated from the plain text or the cipher text.

Sturgeon

7

Here is how the machine works in an example as shown in Fig. 1. First, a plain text character, B say, will be represented by its Baudot code equivalent 10011 or ×• •××5 as given in the Baudot alphabet in Fig. 5. The plain text character B is then added bitwise modulo two to the subtractor character, F say, and the result routed through the transposition circuit, which is controlled by the permutor character, I say. The resulting cipher text character is Z. The two key characters, F and I, are determined from the code wheel setting and the inner key configuration once the plain text character B enters the machine. In addition, the figure shows that an element of the transposition circuit, the transposition unit, is active when the controlling bit is 0 or, as BP said, a dot. SR1 3

1 II

SR2

SR5

III

5

I

IV

SR3

9

V

7

SR4

Figure3. The Pentagon

The analysis of the T52 key generator showed that the 10 code wheels were combined in fours. They named this circuit the “Pentagon”. The author has not been able to find any documentary information about the Pentagon, however, largely inspired by Professor William Tutte’s beautiful little book on graph theory, [21] he thinks he has found the answer. The graph in Fig. 3 is constructed from the wheel combining logic in Fig. 2. The code wheel output channels are labelled 1, 3, 5, 7, 9 and I, II, III, IV, V. A cross in the row for one of the SR relays means that the control of the relay depends on the marked output channels, e.g. the function for the SR4 relay is given by SR4 = 7 ⊕ 9 ⊕ I ⊕ IV 5

(3)

BP used the terms cross and dot to describe the Baudot code elements mark and space, logical 1 and 0.

8

F. Weierud

In the graph in Fig. 3 the SR relays are represented by the vertices and the controlling wheel output channels by the edges which join in a given vertex. The advantage of the graph is that it quickly shows the relationship between the different SR relays; it clearly shows the topology of the circuit. The symmetry of the graph is such that it is highly likely that it corresponds to what BP called the Pentagon. The Pentagon was cryptographically a weak device. Only four different subtractors could be associated with a given permutation. Furthermore, the subtractor character was always even, i.e. the 5 code impulses always summed to zero. [1] Therefore the plain text character was even whenever the cipher text character was even, and odd whenever the cipher text character was odd. For the cryptanalyst this was similar to the Enigma’s peculiarity that no letter can encipher to itself, and it was of great help in reading depths and placing cribs. The first Sturgeon message to be read was at a depth of 40, an almost incredible depth, which clearly shows that the German operators had no idea of the detailed functioning of the machine and that they must have disobeyed orders or been wrongly instructed. Eventually, with the detailed knowledge of the limitations imposed by the Pentagon device, depths of four or five could be read fairly easy. The 10 code wheels were set once a day and this initial setting remained in force during the whole day. However, the machine was equipped with a small crank which allowed the operator to easily bring the machine back to its initial code wheel settings. This was the main reason for the large number of messages in depth. With this knowledge, it was possible to read messages at depths of two or three as soon as the daily wheel settings had been recovered. When they could make a guess at a crib of about six letters even single messages could be broken with the help of the Pentagon limitations. The different messages were sent using different wheel orders. There was some form of message key device that changed the connections between the code wheels and the Pentagon. However, as the machine was brought back to its initial position, the binary streams from each of the wheels were always the same. Five letters were given as a message key, and these always came from the reduced alphabet: P S T U W X Y Z. A letter could appear more than once in the group of five — once the indicator WWWWW was even observed. BP noticed that when two indicators agreed in n positions, then usually but not always, 2n of the wheels had the same function in the Pentagon. However, this rule did not apply to indicators sent on different days. The indicator system of this machine was never broken cryptanalytically. Comparing the above description with what is known about the different Siemens T52 models it is evident that BP was confronted with the T52c machine. [6–8, 17–19] This machine had a code wheel combination logic like the one described for the Pentagon. It also had a message key unit with five levers that could be set in eight different positions indicated by the letters P S T U W X Y Z. Like the T52a/b, the c model also had the small crank that

Sturgeon

9

allowed the code wheels to be brought back to an index position. This was a conceptual error in this model as the main reason for this wheel resetting mechanism was to allow the operator to set the message key easily on the wheels. The T52a/b machines were not equipped with a message key unit like the T52c and therefore the message key was set directly on five of the code wheels. The 10 wheels were therefore brought back to the initial position and the five wheels selected as message key wheels would be set to their new position. It is debatable whether even this limited wheel resetting on the T52a/b was a good idea. However, it is evident that the complete wheel resetting used on the T52c machines was a blunder of some magnitude. The Sturgeon and Mackerel links came to an end with the second battle of El Alamein which started at the end of October 1942. One other signal transmitted on a T52c machine was intercepted later in November. It was believed to have come from the Caucasus. It consisted of the usual messages in depth and was successfully attacked. The messages dealt with the situation on the Russian front. That was the last appearance of traffic from a T52c machine.

5

The Reappearance

In the first six months of 1943 other teleprinter links appeared which also used “UM UM”. Some of the links were known to use the Tunny machine and from this moment it was often difficult to distinguish between links using the two machines. Both types of link gave only a QEP number for the indicator. The only exception to this rule was a link named Salmon where some groups of letters were sent, apparently as indicators. They were quite different from the normal Sturgeon indicator groups. Messages on Salmon, which linked K¨ onigsberg and Mariupol, were intercepted from 11 January to 6 February 1943. The machine was of a much simpler construction than the Pentagon machine and there was no combination of the wheels. Five of the wheels made up the subtractor key while the other five wheels constituted the permutor key. The messages consisted mainly of operator chat. Even though the new machine was simpler than the Pentagon machine (T52c), it was more difficult to break. The absence of the Pentagon meant that the parity of the cipher letter was no longer the same as the parity of the corresponding plain text letter. And instead of having only 60 different alphabets this new machine had 960. From this description it is evident that the machine must have been the T52a/b. In May 1943, a new link, codenamed Sardine by BP, started to operate between Sicily and Sardinia. This link was never broken. Later in the year, two operator log books were captured which contained references to the intercepted traffic on the Sardine link. Time, numbers and priority codes corresponded to those of the intercepted traffic. Also the same type Luftwaffe addresses that had earlier been used on Sturgeon appeared on this link.

10

F. Weierud

A new link codenamed Halibut by BP appeared in July 1943. The link, which operated between K¨ onigsberg and Munich,6 ceased to operate in August but reappeared in a changed form in 1944. In its first period, from July to August, a few depths of four and one of five were found. One depth of four from August was read and was found to have been enciphered in the same way as the depths that had earlier appeared on Salmon (T52a/b). Like the Salmon messages it consisted of operator chat. However, the July depth of five resisted all attempts to break it. It only succumbed a year later, in June 1944, to a sustained attack. It then turned out that it was enciphered on a new machine, the T52d.

6

A Historic Achievement

This break constituted the first break of the T52d machine, a machine similar in construction to the T52a/b but with irregular, stop-and-go, code wheel movements. The Halibut message did not use the autokey element, Klartextfunktion, of this machine but in June 1944 other Sturgeon links were suspected of using this machine with the autokey function. The break was nevertheless an outstanding achievement. The T52d was completely broken from reading a depth of five for a part of the message, while for the remainder it was only a depth of four. [12] From BP’s subsequent analysis of the machine a depth of four appeared to be the absolute minimum. How was it possible to break such a complicated machine from only one message in depth of four and five? One answer is that BP was not confronted with a completely new machine. It was mainly the stop-and-go code wheel movements which differentiated this machine from the T52a/b. The code wheels themselves had the same patterns as on the T52a/b and T52c machines. It would turn out later that all the machines in the T52 series used the same code wheel patterns. The patterns were fixed and no changes were ever made to them. This constituted a very serious weakness of these machines. The break itself was a manual operation, but assisted by a large number of catalogues which showed the possible alphabets that resulted from an assumption of a plain-cipher text pair of characters. BP did not develop a machine to assist in deciphering. All the operations were done by hand so that even developing the subtractor and permutor keys from a given wheel order and setting was a very slow and tedious process. BP also tried to use masks and inverse probability calculations, but it is not known if this was successful. As will be shown later, the permutation circuit only produced 30 out of the 120 possible permutations. Thirty-two permutations should have been possible with the five double changeover contacts used for the 6

A list of FISH links in one of the Fried reports gives the link as operating between Memel and K¨ onigsberg. [10] However, as the distance between Memel (Klaipeda) and K¨ onigsberg is only 120 km, mainly over water, the use of an HF link does not sound right.

Sturgeon

11

permutation function, but / and Z produced identical permutations, as did T and E.7 The break was a success, but it also showed the difficulty this machine presented cryptanalytically. BP launched a substantial research effort to understand the T52d machine fully and to explore possible cryptanalytical attacks against it. BP realised that solutions through depths could not be relied upon in the future because of the increasing use of the autokey function. Another problem that presented itself was how to differentiate between this traffic and ordinary Fish traffic generated by the Lorenz SZ40/42 machines. BP hoped to find statistical techniques that would allow it to identify the traffic.

ID K J H G F E D C B A a

Wheel Length 47 53 59 61 64 65 67 69 71 73

Controlled by E crosses, D dotsa K crosses, A dots K dots, J crosses J dots, H dots H crosses, G crosses G dots, F crosses F dots, E dots F dots, E dots F dots, E dots F dots, E dots

Dot and cross are BP parlance for 0 and 1, space and mark. Figure4. Wheel stopping logic for T52d.

It is not known how long the July 1943 message was but it is nevertheless an extraordinary feat to have fully deduced the “motor wheel” logic of the T52d. In contrast with the Lorenz SZ40/42, the T52d did not have separate “motor wheels.” Instead, each “motor” was formed by the modulo two addition of two other wheels, sometimes with inverted logic for one or both of the wheels. The “motor” or wheel stopping patterns were read from a different part of the code wheels than those used for the subtractor and permutor keys. And of course the movement of these wheels was again controlled by others. Four of the wheels, with the lengths 73, 71, 69 and 67, were controlled in parallel by two of the other wheels. This was presumably done to ensure a periodicity of at least 73 · 71 · 69 · 67 = 23 961 009. The wheel stopping logic as derived cryptanalytically by BP is given in Fig. 4. [11] The figure shows 7

BP replaced the six teleprinter control characters carriage return, line feed, letter and figure shift, space, and null with the special characters 3,4,8,+,9, and /. See the teleprinter alphabet in Fig. 5 and Appendix A of [23].

12

F. Weierud

how the movement of a given wheel depends on two other wheels, e.g. the K wheel, which is the leftmost wheel in the machine and with a sequence length of 47, will not move if there is a cross (1) on the E wheel and a dot (0) on the D wheel. The other wheels have similar relationships to two other wheels. The deciphered messages referred to experiments with a machine the operators called T52d, which gave BP the final proof that it had broken a new Sturgeon model. Later two captured T52d machines were found to contain the same logic as had been derived cryptanalytically from the Halibut message. In September 1943, the link named Conger appeared between Athens and Berlin. Hundreds of messages were sent and all were in depth so there was no great difficulty in reading them. However, their intelligence value was nil. The messages contained only operator chat. Conger contained references to the T52b, a machine that had previously been captured in Tunisia. By correlating the recovered code wheel sequences with those of the actual machine it was found that the initial position corresponded to that of all wheels set to one. The wheels were used in the order of their periods, while the operation of the machine corresponded to what had earlier been observed on Salmon, and in the August Halibut messages. In November, similar Conger messages in depth were sent; this time the wheels were all set to two. The description of the Conger usage is frankly amazing and shows a complete disregard for applying secure keying instructions for the machines. It would seem that the machines were used by operators who had never read the instructions and who had not been issued with operational keys for these machines. One also gets the very strong impression that the majority of these links were not operational links, but reserve channels kept open mainly with operator chat and test messages. However, their usage was cryptographically damaging to the machines. Both Conger and Halibut reappeared early in 1944 in a slightly changed form. The new Halibut messages were all short, while earlier they had often been very long. Conger, on the other hand, often contained long messages. Depths, in this case messages with the same QEP number, of up to four occurred. However, the messages had no repeats, which strongly indicated that the autokey function was being used. This hypothesis was further supported by the intercept logs which contained phrases like “Mit KTF ” and “Ohne KTF ” where KTF was the abbreviation for “Klar Text Funktion”. BP did find one depth of two without the autokey function, but a depth of two was considered to be unbreakable. Shortly afterwards it was decided to cease the interception of links using the Sturgeon machines as it was considered to be unprofitable. In the autumn of 1944 many Tunny links, which also used an autokey element, ceased to use this function and Enigma messages were found ordering the Sturgeon operators to stop using autokey on the T52d and T52e machines. During the same period, one day’s traffic on Conger was intercepted. It was found to be in depth of two and without the autokey function. However, there are no

Sturgeon

13

further indications that a lot of effort was invested in the Sturgeon machines and their traffic.

7

The Captures

The first Sturgeon machine to be captured was a T52b which was found in Tunisia. It was discovered that the code wheels on this machine moved regularly and that they did not combine. It was therefore evident to BP that it was not the Pentagon machine (the first Sturgeon type of machine to be intercepted and broken). Later a full technical description of a machine which combined the functions of the T52a/b and T52c was captured on Elba. It appeared from this description that the T52c machine was related to the Pentagon machine as it combined the code wheels in fours. However, the number of alphabets was found to be 256 instead of 60 as for the Pentagon machine. It will be shown later that this T52c machine was the modified version, T52ca. The T52a/b mode showed that the machine could have been used for the Salmon, August Halibut messages and the early Conger traffic. The Elba description also showed that the T52c machine was equipped with a wheel permuting mechanism corresponding to the message key unit described earlier. It was found that the unit consisted of five levers each of which controlled three switches out of a set of 15. Each switch interchanged two wheels in its active position and left their order unaffected in the inactive position. A switch was active or inactive depending on the position of the controlling lever, but the correlation of active switch position and lever position was different for the three switches controlled by a given lever. This circuit has been described in Donald Davies’ paper on the T52 machines. [7] In addition, it was found that all the machines were equipped with a set of switches or plugs which constituted the main inner key setting. The switches or plugs selected which of the ten code wheels controlled a given functionality in the cryptographic process. After the capture of the Elba description, an actual machine of this type was captured at Naples. This was clearly a T52c machine, but the message key unit with the five levers had been removed. It was noted that the machine was very similar to the first captured T52b machine; the T52b also had room for a message key unit although none was actually fitted. Yet another machine was captured at Naples. On this machine the original type number, T52b, had been altered to T52d. This machine was equipped with the wheel stopping logic and had a switch to enable or disable the autokey function KTF. Without KTF the code wheels had the same movement as the one derived cryptanalytically from the July Halibut message. When the KTF was active, the wheel movement logic became more symmetrical and the third impulse of the clear text governed part of the logic. Two of the wheels were controlled by a plain text cross (1), while two others were controlled by a dot (0). This logic has also been described in detail by Donald Davies. [6–8]

14

F. Weierud

Later yet another T52d machine was captured, which had been altered from a T52a. Comparing this machine with the T52b, it became obvious that the two models must have been very similar. It is known from German sources that the only real difference between the two machines was that the T52b was fitted with extra filters to reduce interference to radio installations. [18, 20] Together with the T52c machine description captured at Elba, allied forces also captured two key book pages, one for the T52d, and one for the T52a/b and T52c machine. One side of each page gave the table for 3 June 1944, while on the other side was the table for 4 June. Each table consisted of 25 rows labelled with the letters from A to Z, omitting J. A similar table for the T52d/e machine is reproduced in Appendix A. The message key QEP FF OO PP AA ZZ VV CC MM HH UU corresponded to setting the leftmost code wheel to 19, as can be found in column 1, row F. The wheel to its right is set to 11 as given in column 2, row O etc. The complete code wheel setting for this message key was: 19 11 56 31 59 33 13 46 02 25. The corresponding table for the T52c machine is reproduced in Appendix B. The same method of indicating the code wheel setting applies to this table, but in addition the lever settings for the message key unit are in the first five columns. The same QEP message as above would give the code wheel settings: 47 23 09 27 34 45 26 09 02 48 here, with the message key levers at: p t p s x. The use of these tables and the method of disguising the code wheel settings that were transmitted as QEP numbers or letters changed several times throughout the war, but the tables themselves largely retained their original structure and layout. The main instructions for the use of teleprinter cipher machines, Wehrmacht Schl¨ usselfernschreibvorschrift (SFV) [9], indicate there were three basic key tables in use, Fernschreibgrundschl¨ ussel (main inner key), Fernschreibwalzenschl¨ ussel (code wheel key), and Fernschreibspruchschl¨ ussel (message key). An example of the Fernschreibgrundschl¨ ussel for the T52d is reproduced in Appendix C.

8

Intelligence From Decodes

References to the Sturgeon machines were frequent in both Tunny and Enigma traffic. In 1942 the decodes referred only to the T52a/b and T52c machines. The Wehrmacht SFV as referred to above was issued on 1 December 1942 and also refers only to the T52a/b, T52c and SZ40 type of cipher machines. It is therefore very likely that these were the only machines available in 1942. BP also appears to have captured a copy of the Wehrmacht instructions some time before November 1944. On 17 October 1942 a message8 from C.S.O.9 Luftflotte 2 to Fliegerf¨ uhrer Afrika mentioned that T52c had inadequate security. It gave orders that 8

9

Message on the Luftwaffe’s Red (the main Air Force) key, 121-2-3, 17/10, 6610. The author has so far not been able to trace any of these messages. C.S.O. = Chief Signal Officer.

Sturgeon

15

“Secret” and “Secret Commands Only” (probably translation of Geheime Kommandosache — Top Secret) are to be enciphered on Enigma before being sent over S¨ agefisch (Sawfish) links. This message passed between stations served by the Sturgeon link using the T52c machine. Nevertheless, seemingly important messages continued to pass over this link without being previously enciphered on the Enigma. However, many Enigma messages also passed over this link before it ceased operation on 2 November 1942. This message doubting the security of the T52c stands in contrast with the Wehrmacht SFV which contains a clear instruction not to use the T52a/b over radio and radio relay connections (Richtstrahlverbindungen). The T52c was the only machine authorized for use over radio and radio relay links. However, we have seen that the Luftwaffe for some reason did not obey these instructions and that they used the T52b machine for practice messages on the Salmon, Halibut and Conger links. This shows that Luftwaffe cipher officers must have been unaware of the close links and similarities between the different T52 models and that they did not see the danger these practice transmissions were to the other machines. In February 1943, decodes show that the Germans suddenly had discovered that something was seriously wrong with their S¨ agefisch machines. A message from Madrid to Paris10 said that the T52 was very badly compromised and that enemy decipherment was possible. “Secret” and “Top Secret” messages were no longer to be sent over the T52. On 18 February 1943, a new set of instructions for using the T52 machines were issued:11 1. The indicator systems in use with the T52a/b and c are cancelled. 2. Henceforth the ten wheel settings are to be given instead and sent on a specific emergency key. 3. A new method of indicating the settings of the five message key levers is to be used. 4. The device for setting back all the wheels to the so-called zero position is to be removed. Point four of these new instructions shows that the Germans had finally discovered the faulty operator practice of sending many messages on the same key due to the facility for doing so offered by the T52 wheel resetting mechanism. Apparently they also suspected some weakness in the use of the message key procedure and therefore introduced new, temporary measures. They would later abandon the use of QEP numbers and use the QEP structure with ten bigrams that has already been presented in the previous section. It is not clear why this was considered a better procedure but it is possible it 10 11

Message on the Abwehr link Madrid–Paris, RSS 6713/2/43. Message on the Army’s Bullfinch II (Italy) key, 1735/18/2/43.

16

F. Weierud

offered more flexibility in choosing messages keys than the previous method using QEP numbers. On 19 February, yet another message12 gave further instructions: 1. T52a/b is not to be used for “Secret” and “Top Secret” messages, except when other means are not available. 2. If teleprinter links are used there must be previous encipherment on Enigma. 3. After the changes to the T52c, and after a change in the indicator system, “Secret” and “Top Secret” messages may again be forwarded without previous encipherment on Enigma. In March two messages13 said that traffic on the Aptierte (adapted) T52c no longer needed to be enciphered on the Enigma. From then on there were references to the T52ca, which probably stands for T52c Aptierte. Then finally on 14 June 1943 there was a message14 to the Naval Communications Officer in Sulina and other addressees that said: “On the completion of the adaptation to SFM T52c, the designation T52ca will no longer be used. The designation T52c only is to be used from now on.” The changes made to the T52c concerned the wheel combining logic which BP had found to be of such great help when breaking the Pentagon machine. This indicates that the Germans must have made a detailed analysis of the machine and found this part of the logic to be particularly weak. The knowledge of German security evaluations and analysis of their own cipher machines has not yet been fully declassified and released. It is therefore not yet possible to give a detailed picture of what the Germans knew and suspected with respect to the security of their crypto systems. However, it is known that Dr. Eric H¨ uttenhain, the chief of the cryptanalytic research section of OKW/Chi (Oberkommando der Wehrmacht/Chiffrierabteilung), examined the T52a/b machine in 1939.15 He found that this machine had an extraordinarily low degree of security and could be broken with about 100 letters of cipher text without a crib. This study could have resulted in the Wehrmacht SFV instruction prohibiting the use of the T52a/b on any form of radio channel. However, it is perhaps more likely the discovery by the Germans on 17 June 1942 of the Swedish success in breaking this machine led to the restriction. [23] OKW/Chi suggested changes in the machine, including ways of producing non-uniform code wheel stepping but for engineering reasons Siemens refused to accept these changes. Instead a new machine, the T52c, was produced which overcame some of the more obvious weaknesses of the earlier model. The T52c was studied by the Army cryptanalyst, Doering, 12 13 14 15

Message on the Army’s Merlin (Southern Europe) key, 19/2/43. Message on the Luftwaffe’s Red key, Nos. 322/4 and 387/7 of 6 March 1943. Naval message 14/6/43, 77, Mediterranean. “European Axis Signal Intelligence in World War II – Vol.3”, 1 May 1946, A TICOM Publication released under the FOIA.

Sturgeon

17

from OKH/Gen d Na (Oberkommando des Heeres/General der Nachrichten Aufkl¨ arung) in 1942. He showed that it could be broken on a text of 1 000 letters. This study was apparently assisted by cryptanalytical machinery in use by OKW/Chi, but it is not known how involved Dr. H¨ uttenhain and his people were in the actual study and its recommendations. The investigations resulted in the design and production of the T52d. The security analysis of the T52d was continued, mainly by Doering, and early in 1943 he showed that this machine was also insecure. This resulted in the production of the T52e. However, it was known that both the T52d and T52e machines were open to attacks through messages in depth and that at a depth of ten messages could be read without a crib. However, the cries of alarm from the German cryptographers were not heard, or at least not acted on, by the German Army and Air Force. In the summer of 1942 the totally insecure model T52a/b was still in use and the equally insecure T52c was being distributed. The Army’s position was that the teleprinter traffic went over land lines and could not be intercepted, hence there were no need to worry about inadequate security. Evidence of tapping of the teleprinter lines that appeared in Paris in 1942 and 1943 gave the Army a serious jolt and the Army’s signal authorities were forced to reconsider their views on teleprinter cipher security. However, it was too late and the newly developed T52e was only slowly being introduced at the end of 1944. The first reference to the T52d machine appeared in the decodes in October 1943.16 Subsequently, there were frequent references to all three models, T52 a/b, c, and d. From September 1944 onwards, there were also references to the newly developed machine T52e. Traffic from this machine was never observed or at least identified as such by any of the allied cryptanalytical services and the machine remained unknown to them until the end of the war.

9

The Cryptanalytical Problems

On 29 July 1944 Captain Walter J. Fried, the US Army Signal Security Agency’s (SSA)17 liaison at BP, sent his report No. 68, [12] which he devoted entirely to the Sturgeon problem, to the SSA headquarters at Arlington Hall. He started the report with the following assessment: “The problem of solving current traffic seems completely hopeless. The only feasible method of solving messages enciphered on the T52d machine seems to be through depths. Sometimes the “motor” action is switched off and this gives rise to several 16 17

Message on the Luftwaffe’s Red key, 279/0, 4/10/43. The agency went through a number of changes in both name and organization during the period 1939–1945. It was named Signal Intelligence Service, Signal Security Division, Signal Security Service, Signal Security Branch, etc. before it was redesignated Signal Security Agency on 1 July 1943, later to be changed to Army Security Agency on 15 September 1945.

18

F. Weierud

possible techniques of solution.18 For the most part, however, the problems which seem capable of solution are comparatively trivial. The fundamental difficulty of the general problem arises from the fact that that a crib does not yield key.” To give a better feeling for the fundamental cryptanalytical problems I will attempt to give an overview of what is involved in breaking the T52 machines, and how certain features of the machine hampered this task, while other features made it easier for the cryptanalyst. The basic algorithm of the machine has already been explained. To recapitulate, a five element teleprinter plain text character will first be added modulo two to a five element subtractor character and then permuted under the control of another five element permutor character as given by the encipherment formula (1).

1 2 3 4 5 a

a

0 / • • • • • #

E 4 • • • • • • • • 3 #

1 9 3 T • • • • • • • • • • • • # # 5

2 A S D Z I • • • • • • • • • • • • • • • - ’ # + 8

R L N • • • • • • • • • 4 ) ,

H O U J W • • • • • • • • • • • • * 9 7 # 2

3 F Y B C • • • • • • • • * 6 ? :

4 5 P G M K Q + X V 8 • • • • • • • • • • • 0 * . ( 1 # / = #

In the figure shift row control characters and other special functions are marked with #, while the national special characters are marked with *. Figure5. International Telegraph Alphabet No. 2 in class order

A simple way of representing the relationship between the four elements P, C, Σ and Π is through a 32 × 32 × 32 cube. One of the elements P, C or Σ can be placed in the cube and the other three elements along the three axes. Π cannot be placed inside the cube as it is not uniquely defined by P, C and Σ. The cube can then be cut by planes along any of the axes and it will then be represented by 32 squares slices each of the size 32 × 32 × 1. The choice of the representation will entirely depend on the problem to be solved. It is now easily seen that a plain text character from the 32 element teleprinter alphabet will be transformed into a cipher text character through 32 · 32 = 1024 cipher alphabets. However, this theoretical limit was seldom achieved in practice. If we analyse the basic permutation circuit used in the T52c and T52e machines we will find that / and Z produce identical permutations, as do T and E. This means that, instead of producing 32 permutations, the 18

The author’s studies of the T52d and e models have not revealed any possibility of switching off the “motor” or wheel stopping function on these machines. It is more likely the observed absence of wheel stopping was due to the use of the T52a/b machine.

Sturgeon

19

Permutor

circuit only generate 30 unique permutations. Therefore these machines only have 32 · 30 = 960 cipher alphabets. However, this was only achieved in the T52e. In the T52c and T52ca machines the wheel combination logic reduced the number of cipher alphabets even further.

/ E 4 9 3 T A S D Z I R L / ? ? E 4 9 3 T A ? ? ? ? S ? ? ? ? D Z ? ? I ? ? R ? ? L ? ? ? ? N ? ? H ? ? ? ? O U J W F Y B C P G M K Q ? ? + ? ? X ? ? V 8

Subtractor N H O U J W F Y B C P G M K Q + X V 8 ? ?

? ?

? ?

? ?

? ? ? ? ? ?

? ?

?

? ?

? ?

? ?

?

? ?

? ?

? ? ? ?

Figure6. Alphabet distribution for T52c.

Before we use the cipher squares in our analysis it is useful to introduce the concept of Baudot classes. The class of a Baudot character is defined as the number of crosses (or 1’s) that it contains. It is clear that we have six classes labelled from 0 to 5 inclusive. There are various ways of arranging these classes but the method used here is the one used at BP, and is shown in Fig. 5. The Baudot classes are indicated in the top row with the letter shift alphabet used by BP in the row below. The Baudot control characters have been given the special BP values as previously indicated in footnote 7 on page 11. Below the alphabet are the five bits of each character’s Baudot code

20

F. Weierud

value indicated by dots and crosses. The bottom row shows the corresponding figure shift characters. Using computer simulations, the T52c’s wheel combination logic has been analysed: a plot of the 32 × 32 permutor/subtractor square is given in Fig. 6. The alphabets along the permutor and subtractor axes are in the Baudot class order: an asterisk indicates the existence of an alphabet. We see that there are no alphabets in the odd classes 1, 3 and 5. All the alphabets are clustered in the even classes 0, 2 and 4. This is a confirmation of BP’s finding that the parity of the subtractor character was always even. We further see that there are 16 · 4 = 64 alphabets which, with our knowledge of the reduced permutor alphabet, gives a total number of 60 cipher alphabets. As the parity of the characters T and E is odd, the doublet T–E is not possible. Only the doublet /–Z exists, hence we get 15·4 = 60 cipher alphabets. We also see that for each permutor character there are only four possible subtractor characters as mentioned by BP. The plot clearly shows that this machine was extremely insecure.

Subtractor

Permutor

Relays SR1 SR2 SR3 SR4 SR5 SR6 SR7 SR8 SR9 SR10

Code Wheel Outputs 1 3 5 7 9 I II III IV V XXX X XXXX X XX X X X X X X X X X XX X X XX X X XX X X XX X X XX X X

Figure7. Wheel combination logic for T52ca.

The wheel combining logic of the modified T52ca machine has been reconstructed using data from the FRA archives. The truth table is given in Fig. 7 while the corresponding permutor/subtractor plot is in Fig. 9. In the plot in Fig. 9 the alphabets are in the binary order, not the Baudot class order, since such a representation shows more clearly the inherent structure of the wheel combining logic. As we can see, the alphabets are well spread out and are no longer exclusively of even parity. However, the linear structure is there and changing one single entry in the truth table will drastically change both the structure and number of possible alphabets. Each permutor character is associated with eight subtractor characters, which is twice as many as for the T52c logic. However, if we plot the permutor/subtractor square in Baudot

Sturgeon

21

class order, we find that when a permutor character is even, the alphabets have an even subtractor character, and when the permutor character is odd, so is the subtractor. This information can still be exploited by the cryptanalyst. The possible number of alphabets is 32 · 8 = 256 but, due to the reduced permutor alphabet, there are only 240 unique cipher alphabets.

2 3 4 5

1

1

10

10

8

8

9

9

6

6

7

7

4

4

5

5

2

2

3

3

A

A

B

B

1 2 3 4

Output Bits

Input Bits

1

5

Permutation Unit

Figure8. SFM T52’s transposition circuit.

The T52a/b and T52d machines use the same layout of the transposition19 circuit as the T52c and T52e, but instead of using relays for the transposition units, these machines directly use the cam contacts on each coding wheel. What distinguishes the a/b and d models from the others is that the transposition units, which consisted of double changeover contacts, were not wired permanently into the transposition circuit. Each of the five contact sets was equipped with two plug connections which were then plugged into the transposition circuit. Figure 8 shows the layout of the transposition circuit together with the circuit of a single transposition unit. The figure shows that there are two possible contact points in each Baudot bit or element branch. The connection 1–3 means that either the A or B plug of a transposition unit will connect to the socket marked with 1’s, while the other plug will go to the socket marked with 3’s. If A goes to socket one, the left part of the A plug will plug into the left-hand side of socket one, while the right part of the A plug goes to the right-hand side of the socket. In this particular case, bit one will end up in position five when the transposition unit is inactive, while 19

The terms transposition circuit and transposition unit reflect the cryptographic usage; mathematically speaking the circuit performs a permutation.

F. Weierud

Permutor

22

/ E / ? E ? 4 A 9 S I ? U ? 3 ? D ? R J N F C ? K ? T Z L ? W ? H ? Y ? P Q O B G ? + ? M ? X ? V 8

4 A 9 S I U ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

3 D R J ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Subtractor N F C K T Z L ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

W H Y P Q ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

O B G + M ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

X V 8 ? ? ? ?

?

? ?

? ?

? ? ?

? ?

?

? ?

? ? ? ?

?

? ?

Figure9. Alphabet distribution for T52ca.

in the active position bit one will leave on the branch connected to socket ten. Its final position will depend on the connection that is made from socket ten. There are 9·7·5·3·1 = 945 different ways that the five contact sets can be inserted into the transposition circuit. Computer simulations show that each of these 945 connection variants results in unique permutation sets. However, the majority of the permutation sets, a total of 561, are degenerate in the sense that each set contains only from 1 to 16 unique permutations. The set with only one single permutation is a special case — it contains the identity permutation, hence no transposition takes place. There are further variants on this where one, two or three of the Baudot character pulses will not be permuted. There are in total 300 cases where one pulse remains in place, 80 cases where two pulses are fixed and 20 instances where three pulses are unaffected. All of these cases belong to the set of the degenerate permutations. Figure 10 gives an overview of the distribution of the different

Sturgeon

23

permutation sets. The figure shows that among the remaining 384 permutation sets, 24 sets have 27 unique permutations, 240 sets have 30 permutations and 120 sets contain all the 32 permutations. Figure 10 shows that of the degenerate sets only the sets with 10 and 12 unique permutations also have normal permutations, in the sense that none of the bits remain in place. All the other degenerate sets have one or more bits that are not affected by the permutations.

Bits Stuck 1 bit 2 bits 3 bits 5 bits None Total

1

2

Number of Unique Permutations in a Set 4 5 6 10 12 14 16 27 30 60

32 Total

30 180 30 20

60

20

60

40 120

24 240 120

300 80 20 1 544

40 150 180 30

24 240 120

945

20 1 1

20

60

Figure10. Permutation distribution for T52d.

Looking at the Wehrmacht SFM T52d Key table reproduced in Appendix C, it can be shown that all the connections in this table belong to the two groups with 30 and 32 unique permutations. This means that in reality only 360 permutation sets were used by the German cryptographers during the period this key list was in use. It also means that there are not always only 960 cipher alphabets — there can be as many as 1024. This might be an indication that the Germans were aware of the fact that not all of the permutations could be used for cryptographic purposes. This knowledge may have been of a relatively recent nature. The T52a/b machine may have been used earlier with connections which resulted in degenerate permutation sets. When the Swedish cryptanalyst Lars Carlbom analysed the transposition circuit, he found four main permutation families, of which two could be divided further into three sub-groups. One of these families, he said, consisted of connections where one of the transposition units was inactive or disconnected. It is not possible to disconnect a transposition unit and still expect the machine to function, but Lars Carlbom did not know this as he had never seen a T52 machine. He based his analysis entirely on cryptanalytical evidence. In practice, what happened was that an input impulse exited the transposition circuit at the same level as it entered; hence no Baudot element permutation was taking place. The identity permutation referred to earlier is caused by such a set of connections: 1–10, 2–3, 4–5, 6–7 and 8–9, which leave all the bits in their original positions. If one or more of these special connections are combined with other more random connections, the other cases of one or more bits stuck will occur.

24

F. Weierud

Φ

/ E 4 9 3 T A S D Z I R L N H O

/ E 4 8 V X 8 32 V 9 9 X 8 8 + 4 4 Q 2 2 K 9 9 M G P C B Y F W J U

9 3 T + Q K 2 16 8 4 2

4 0 16 8 4

C A S D Z I R L N H O M G P C B Y F W J U

8 0 0 16 8 8 4 2 4 0 0 8 0 4 2

6 2 1 2 8 4 6 0 2 1

1 6 2 4 4 2 1 4 6 2

2 1 6 8 0 4 2 2 1 6

6 2 1 2 8 4 6 0 2 1

1 6 2 4 4 2 1 4 6 2

2 1 6 8 0 4 2 2 1 6

2 4 0 0 8 4 2 8 4 0

4 2 4 0 0 8 4 4 2 4

0 4 8 0 0 0 0 8 4 8

Figure11. SFM T52’s dibit distribution.

During the year when BP struggled with the July Halibut message enciphered on the T52d it developed and tried out various methods of attack. Several of them were of a statistical nature and were based on knowledge gained through the use of statistical techniques on the Lorenz SZ40/42 machines. The statistical methods BP developed only applied to the “motorless” machines and would not work on machines with wheel stopping. The T52 code wheels had an almost even distribution of dots and crosses with a slight preponderance of crosses. This meant that the modulo two addition was nearly random. However, this was not the case for the permutations, since certain impulses were more likely to go to some positions than others. Therefore the statistical techniques were based on developing statistics for certain impulse combinations of the “pseudo plain text” character, Φ, and their probability of ending up in certain positions in the cipher text character. Here the “pseudo plain text” is the real plain text transformed by the subtractor key. Φ=P ⊕Σ

(4)

The method applies to both single impulses or to pairs, dibits, but plain text characteristics are more pronounced when using a pair of impulses. For a given permutation it was possible to enumerate how often dibits of a given “pseudo plain text” character, Φ, and its inverse would be associated with dibits in different cipher text characters, C. This is shown in Fig. 11 where the permutation is generated by the transposition circuit used on the T52c and e models, and which used the connections: 1–2, 3–4, 5–6, 7–8 and 9–10.

Sturgeon 0 / A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 3 4 8 9 + /

E 4 O K 3 / N + Y U R C W X F B Q P J 9 Z I 8 L M H T D A V S G E

4 E + N J A K O P 9 D F T V C G H Y 3 U L S M Z 8 Q W R / X I B 4

1 9 U X R F S D V T 4 K J P O 3 M L W C E H A G Q B Z Y N I + / 8 9

2 3 J Z I E D S L M C A U G H 9 T V 8 4 F O K P + Y X B / R Q N W 3

T W D V B Z X R 9 P + 8 4 N M 3 I U G Y / Q C A F S E O L K H J T

A / G F R 4 C B Q S 3 N Z 8 K + Y H D I W 9 X T V P L J E M U O A

S I M J N 9 3 8 Z A C R Q B D X W L K / Y 4 + P O T H F U G E V S

D R T U / 3 9 W X K 4 I + Y S Z 8 V A N B C Q G H M O E J P F L D

Z L 3 8 O T M J S Q G V A F X D U I + H E P K 4 N 9 / B W C Y R Z

I S 8 3 K U J M L / F D H G R V T Z N A P E O Y + W Q C 9 B 4 X I

3 R D W 9 A J U T V N E S O P I L M X / K G F H B Q 8 + 4 3 Y C Z R

L Z J M + W 8 3 I H B X / C V R 9 S O Q 4 Y N E K U A G T F P D L

N K Y 4 S F E P O R U A V T / H G + I D M J L 8 Z B X 9 C W 3 Q N

H Q F G X Y B C / L 8 + I 3 O N 4 A V Z 9 W R U D E S M P J T K H

O + E P Z B Y 4 N V W Q R 9 H / C K L X 3 8 I J S F D T G U M A O

U 9 V D C I R X W E N 3 Y + J 8 Z T F 4 Q / B H G L P K S O A M U

J 3 L S 4 R I Z 8 F / 9 B Q U W X M E C + N Y O P V G A D H K T J

W T R X G L V D U Y O M E K 8 J S 9 B P A H F / C I 4 + Z N Q 3 W

F C H A 9 N / Q B J I 4 8 Z E Y + G U 3 X R W V T O M S K L D P F

Y P N + M H O K E W V G U D B F A 4 8 T S L J I 3 / 9 X Q R Z C Y

B G / Q T O H A F 8 L P J S Y E K C W M D V U R 9 N 3 Z + I X 4 B

C F Q / U K A H G 3 S E M L 4 P O B 9 J V D T X W + 8 I N Z R Y C

P Y K O 8 Q + N 4 T X B 9 R G C / E M W I Z 3 S J A U V H D L F P

G B A H W + Q / C M Z Y 3 I P 4 N F T 8 R X 9 D U K J L O S V E G

M 8 S L Y X Z I 3 G Q W C / T 9 R J P B N + 4 K E D F H V A O U M

K N P E I C 4 Y + D 9 / X W A Q B O S R 8 3 Z M L G V U F T J H K

Q H C B V P G F A Z M O S J + K E / X L U T D 9 R 4 I 8 Y 3 W N Q

4 + O 4 Y L G P E K X T H D U Q A F N Z V J M S 3 I C R W B 9 8 / +

25

X V 9 W H M T U D + P L K E Z S J R Q O F G A C / 3 N Y 8 4 B I X

V X U T Q 8 W 9 R O Y Z N 4 L I 3 D H + C B / F A J K P M E G S V

5 8 M I Z P V L S J B H T F A W U D 3 Y G K O E N 4 R C Q X / + 9 8

Figure12. Baudot XOR square in class order

The alphabets in the figure have only a length of 16, as the normal 32 element Baudot alphabet has been folded in half, with each position in the alphabet occupying a given Baudot character and its inverse, e.g. E and V, which have the Baudot vectors ×• • • • and •××××. The characters /–8 (which are all dots and all crosses) can only go to one place under all the 32 different permutation, while in all the other cases there are varying distributions. The characters belonging to classes 1 and 4 have single cross/dot distributions, while the characters in classes 2 and 3 have double cross/dot distributions. This is the reason for the clustering of the distributions in the two squares of size 5 and 10. But on the T52a/b and d models the permutations were not fixed but variable depending on the connections of the transposition units. Therefore, the permutation probabilities, and hence the statistics, depended on the given permutation set which, of course, was unknown until the machine was broken. So the statistical techniques available in 1944 were nothing more than tools

26

F. Weierud

for getting a better knowledge about the cryptanalytical problem. They were not of much use in attacking the machines. It appears that messages in depth were the only viable attack on these machines in 1944. It is far too involved to illustrate a full blown attack on a real example, but looking at a very small constructed example with a depth of two and a known crib will give a feeling for the problem. As mentioned earlier, the attacks in depths were helped by the use of tables and catalogues. One such table is the Baudot XOR or modulo two square. However, the table becomes a lot more useful when one of the alphabets is arranged in class order. This is illustrated in Fig. 12, where the plain text alphabet is in its normal order along the left hand column and the key alphabet is arranged in class order along the top row. The intersection of a plain text character and a key character will give the resulting cipher text character. However, due to the properties of modulo two addition any of the two alphabets, the one in normal order or the one in class order, can be used for any of the three elements plain, cipher or key characters. To see what is actually taking place and how one might attack two messages in depth it is of interest to return to the principal encipherment equation (1) Π(P ⊕ Σ) = C It is easily shown that permutation is distributive under modulo two addition Π(X ⊕ Y ) = ΠX ⊕ ΠY

(5)

If we apply (5) to (1) we get ΠP ⊕ ΠΣ = C

(6)

In other words, the cipher character can also be obtained by first applying the permutation on the plain text character and the subtractor before combining these two transposed elements by modulo two addition. In the case of two messages P and Q enciphered in depth by the subtractor key Σ and the permutor key Π we can write the following ΠP ⊕ ΠΣ = C

(7)

ΠQ ⊕ ΠΣ = D

(8)

Combining (7) and (8) by modulo two addition eliminates the ΠΣ term and gives at the basic equation for messages in depth Π(P ⊕ Q) = C ⊕ D

(9)

Equation 9 shows that if either P or Q is known the value of the other cannot be automatically determined, as with pure Vernam [24] encipherment where there is only a subtractor function and no permutor function. In reality

Sturgeon

27

there might be as many as ten possible solution for P or Q depending on the Baudot class in which the operation took place. If the operation takes place in class 0 or 5, P and Q are uniquely determined, while in class 1 and 4 there are five possibilities and in class 2 and 3 there are ten possible solutions. One opening for attack is the fact that the permutation only reorders the Baudot code elements: it does not change the elements themselves. Therefore if C ⊕ D contains m crosses and n dots, it must also be the same for P ⊕ Q. So if we know or can make a guess at P we will have a limited number, from 1 to 10, of choices for Q. This is the basis for an attack on messages in depths enciphered on the Siemens T52. The two messages in Fig. 13 have been enciphered with the same key on a computer simulation of the T52d machine.20 They are enciphered without the KTF and the main inner key, Fernschreibgrundschl¨ ussel, is 6–8, 1–2, 5–7, III, 4–10, IV, II, I, 3–9, V, which is the key for day one in the Norwegen Nr. 7 key table in Appendix C. The message key, Fernschreibspruchschl¨ ussel, is the same as given on page 14, QEP FF OO PP AA ZZ VV CC MM HH UU. The second message is suspected to start with “three” or “four”, since message numbers in the region of three to four hundred are expected.

1 2 3 1 P G I 2 Y N + n 2 3 4

4 + 8 1

5 L 4 1

6 X I 4

7 G P 2

8 L P 1

9 T 9 2

10 N E 3

11 E B 2

12 3 D 1

13 Y K 3

14 O W 3

15 X E 3

16 P 8 2

17 J E 2

18 3 I 3

19 B 4 4

20 V H 2

Figure13. Two messages in depth.

The class numbers appearing in the last row are found by forming the modulo two sum of the two cipher text characters and looking up in which class the resulting character belongs. Taking the first two cipher text characters T and E and combining them modulo two results in Z. This result is found by using a simple Baudot XOR square or using the class XOR square in Fig. 12. Looking up T in the vertical left hand alphabet and E in the horizontal class alphabet, we find Z at their intersection. Looking in the top row class alphabet, we find that Z belongs to class 2. The class information can also be found from the Baudot class alphabet in Fig. 5. Another, perhaps even faster, method is to look up one of the cipher text characters, say T, in the left hand vertical alphabet and then searching down the row to find the other cipher text character, E. Doing so we find E situated in one of the columns for class 2. 20

The T52 computer simulation will be made available on the Cipher Simulation Group’s (CSG) Web servers which are accessible through the author’s Cryptology Web page at URL: http://home.cern.ch/∼frode/crypto/

28

F. Weierud

Trying the word “three” with a space, here represented by 9, as a crib for the beginning of the second message gives the following possible solutions for the characters of the beginning of the first message, as shown in Fig. 14. The possible solutions for each character is given in the generatrices21 which have been obtained from the class XOR table. Looking up the first clear text letter of the crib, T, in the left hand vertical alphabet the corresponding generatrix is found further along the row in the columns for the Baudot class 2. The generatrix characters are: WYBEPG4M93 which have been entered in alphabetical order to ease the search for a possible plain text word.

1 2 T B E G M 1 P W Y 3 4 9

n 2

2 3 H B C E F G U W 3 4 8

3 4 R H Q S X Z

4 1 E A D S Z /

5 1 E A D S Z /

6 4 9 A G J W 8

Figure14. Trying the crib “three” in message no. 2.

The most prominent plain text word is the beginning of the word “MESSAGe”. We can now try to extend the plain text in the second message by using the expected “E9” (E and a space) as a further crib in the first message. This is shown in Fig. 15a. Since the beginning of the first message is suspected to contain a message number the continuation is expected to be another number. Of the numbers from one to ten the only possible solutions are “THree” or “FIve”. “ThREE” and 9 do not give any promising plain text in message number one but “fiVE” and 9 give “ONE” as shown in Fig. 15b. This is even a unique solution as none of the other characters needed for the other numbers are present in the first generatrix. The rest of the solution is left as an exercise for the reader. However, solutions are not always as straightforward as here: often it will not be possible to carry on with only two messages in depth. Very often the messages contained numbers or abbreviations which made it extremely 21

Generatrix, plural generatrices, is a decipherment or encipherment out of a set of decipherments or encipherments of the same text under a given hypothesis or cryptographic principle.

Sturgeon 7 2 E B F J T 2 U W Y 3 4 9

n 1

8 1 9 H I N S /

(a)

9 n 2 2 V H I K L 1 N O Q R X +

10 3 E H I K L N O Q R X +

29

11 2 9 C E F M P T U Y 3 4

(b)

Figure15. Continuing the cribs in messages no. 1 and no. 2.

difficult, if not impossible, to extend the messages with only a depth of two or three. It is one thing to break a number of messages in depth. However, the aim is to break the machine, so as to be able to recover the key streams and hence to break all other messages for the rest of the key period. For this purpose it is necessary to be able to uniquely determine the permutation Π for each encryption step. It can be shown that at least a depth of four is necessary, but that it is generally not sufficient. With a depth of four one has only a 20 % probability of finding a unique permutation. With a depth of seven or eight the probabilities are such that a workable key extraction can take place. As the code wheel patterns are fixed, it is possible to determine from the extracted key streams which code wheel is used where and for what purpose. From this information it is then possible to recover the plug connections and starting positions of the machine.

10

Conclusion

Not only did Bletchley Park intercept traffic enciphered on the Siemens SFM T52, but it also broke all the different models that it discovered. However, it was clear from the very beginning that the T52 was a very difficult machine to break. It probably would have remained unbroken had it not been for the German security blunders in using the machines. The blame should not be put entirely on the German teleprinter operators. The Siemens designers of the machine are equally responsible for not listening to the advice of the German cryptographic experts. The Siemens engineers appear to have been more focused on the engineering problems than on the cryptographic security of the machine. The T52a/b and the original T52c machines were basically machines with very limited security. The T52c is an extraordinary example

30

F. Weierud

of how not to go about designing cryptographic algorithms. The wheel combining logic, which clearly was meant to strengthen the machine, had exactly the opposite effect — it eased the task of breaking the machine. On the other hand, the T52d was a relatively well-designed machine. If this machine been the first to see service and the teleprinter operators had been properly instructed in using the machine, it is highly unlikely that it would have been broken. Another weakness of all of these machines is the fixed code wheel patterns. It is understandable that the designers thought that with the complexity of the machine it would not be necessary to vary the code wheel patterns. However, with variable code wheel patterns the machines would have been strengthened considerably. Due to the transposition circuit, cribs would not have led to the recovery of the key stream and even complete plain text of thousands of characters would not have resulted in recovered code wheel patterns. Sir Harry Hinsley’s statement, [13–15] that BP decided to concentrate its non-Morse interception, cryptanalytical, and decryption resources on the Army’s Tunny traffic because of a need to husband resources and the need for good intelligence on the German Army, is undoubtedly correct. However, these were probably not the only reasons why BP abandoned its efforts against the Sturgeon machines. The cryptanalytical difficulties BP faced in attacking these machines, the small number of Sturgeon links, and the very limited intelligence that could be derived from the traffic must have played important roles in the outcome of BP’s decision to concentrate on the Tunny traffic.

11

Acknowledgements

The author should like to thank Bengt Beckman who, through his friendship over the last five years, has been a constant inspiration for my research into the history of the Siemens SFM T52 machines. His help with obtaining material about the Swedish cryptanalysts and their success against these machines has been crucial to this work. As usual, Ralph Erskine has been very helpful with suggestions and improvements, not to forget his help with proof reading and archive material. David Alvarez has given generous support and supplied several documents. Special thanks go to Captain Jon Ulvensøen and The Armed Forces Museum (Forvarsmuseet) in Oslo for supplying many German documents and for giving me access to their collection of cipher machines. I should also like to thank Donald Davies for answering my questions about the T52c wheel combining logic and generally for his help over a great many years. Furthermore, I am very grateful to Geoff Sullivan who has helped me with the simulations of the permutation circuit, and whose computer simulation of the complete cipher machine in all its versions and models has been of the utmost importance to this research.

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31

References 1. Unknown Author: Sturgeon Type Ciphers (Research Section, November 1944). Addendum to Captain Walter J. Fried’s report No. 116 of 17 Nov. 1944. Henceforth called Fried reports. National Archives and Records Administration (NARA) RG 457 NSA Historical Collection Box 880 Nr. 2612 2. Unknown Author: Band-Transposition Systems. Technical Paper, Signal Security Agency, Cryptanalytic Branch, Washington, June 1944 NARA RG 457 NSA Hist. Col. Box 1029 Nr. 3304 3. Beckman, Bengt: Svenska kryptobedrifter (Swedish Crypto Achievements). In Swedish. Stockholm: Albert Bonniers F¨ orlag (1996) 4. Boheman, Erik: P˚ a Vakt. Kabinettssekreterare under andra v¨ arldskriget (On Duty. Under-Secretary of State During the Second World War). In Swedish. Stockholm (1964) 5. Campaigne, Howard: Report on British Attack on “FISH”. National Archives and Records Administration RG 457 NSA Hist. Col. Box 579 Nr. 1407 (1945) 6. Davies, Donald W.: The Siemens and Halske T52e Cipher Machine. Cryptologia 6(4) October (1982) 289–308 7. Davies, Donald W.: The Early Models of the Siemens and Halske T52 Cipher Machine. Cryptologia 7(3) July (1983) 235–253 8. Davies, Donald W.: New Information on the History of the Siemens and Halske T52 Cipher Machine. Cryptologia 18(2) April (1994) 141–146 9. Deutsche Wehrmacht: Schl¨ usselfernschreibvorschrift (SFV). H.Dv. g 422, L.Dv. g 704/3b, M.Dv. Nr. 924a Geheim, 1 Dezember 1942 10. Fried, Walter J.: Fish Notes. Fried Report No. 43 of 27 May 1944. NARA RG 457 NSA Hist. Col. Box 880 Nr. 2612 11. Fried, Walter J.: Fish Notes. Fried Report No. 46 of 12 June 1944. NARA RG 457 NSA Hist. Col. Box 880 Nr. 2612 12. Fried, Walter J.: Fish Notes (Sturgeon). Fried Report No. 68 of 29 July 1944. NARA RG 457 NSA Hist. Col. Box 880 Nr. 2612 13. Hinsley, F.H.: Geheimschreiber (Fish). In F.H. Hinsley et al. British Intelligence in the Second World War. London: HMSO Vol. 3 Part 1 Appendix 2 (1984) 477–482 14. Hinsley, F.H.: Cracking the Ciphers. Electronics & Power IEE July (1987) 453– 455 15. Hinsley, F.H.: An Introduction to Fish. In ed. F.H. Hinsley and Alan Stripp. Codebreakers, The Inside Story of Bletchley Park. Oxford: Oxford University Press (1993) 141–148 16. Kahn, David: The Codebreakers. New York: Macmillan (1967) 17. Mache, Wolfgang: Geheimschreiber. Cryptologia 10(4) October (1986) 230– 242. 18. Mache, Wolfgang: The Siemens Cipher Teletype in the History of Telecommunications. Cryptologia 13(2) April (1989) 97–117 19. Mache, Wolfgang: Der Siemens-Geheimschreiber — ein Beitrag zur Geschichte der Telekommunikation 1992: 60 Jahre Schl¨ usselfernschreibmaschine. In German. Archiv f¨ ur deutsche Postgeschichte Heft 2 (1992) 85–94 20. Oberkommando der Kriegsmarine: Die Siemens-Schl¨ usselfernschreibmaschine SFM T52d (T typ 52 d). M.Dv. Nr. 35IV, D.(Luft) T.g.Kdos. 9105d. Geheime Kommandosache, Berlin M¨ arz 1944

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21. Tutte, William T.: Graph Theory As I Have Known It. Oxford Lecture Series in Mathematics and Its Applications Vol. 11 Oxford: Oxford University Press (1998) 22. Tutte, William T.: FISH and I. In these proceedings. Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory. New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) 23. Ulfving, Lars and Weierud, Frode: The Geheimschreiber Secret: Arne Beurling and the Success of Swedish Signals Intelligence. In these proceedings. Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory. New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) 24. Vernam, Gilbert S.: Cipher Printing Telegraph Systems For Secret Wire and Radio Telegraphic Communications. Transactions A. I. E. E. Vol. XLV Feb. (1926) 295–301

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12

Appendix A

Figure16. T52d Spruchschl¨ ussel — message key.

33

34

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F. Weierud

Appendix B

Figure17. T52c Spruchschl¨ ussel — message key.

Sturgeon

14

Appendix C

Figure18. T52d Grundschl¨ ussel — main inner key.

35

Subject Index

Abwehr, 15 Autoclave, see Autokey Autokey, 6, 10–13, 27 Baudot – alphabet, 7, 25 – character, 19, 22, 25 – class, 19–21, 27, 28 – code, 7, 20, 27 – element, 21, 23 – vector, 25 – XOR square, 25–28 Bletchley Park, 1–30 – Fish, 2 – – links, 10 – – traffic, 11 – Sturgeon, see Sturgeon Boheman, Erik, 1 Code – Baudot, see Baudot – Q-codes – – QEP, 9, 12, 14–16, 27 Code wheel, 3–9, 13, 24 – combination logic, 6–8 – movement, 2, 10, 13, 16 – pattern, 3, 4, 10–12, 29, 30 – setting, 7, 8, 14 Colossus, 1 Conger, 12, 13, 15 Davies, Donald W., 1, 6, 13, 30 Dibit, 24 – distribution, 23 Doering, 17 Dots and crosses, 7, 11, 12, 20, 24, 25, 27 Enigma, 2, 8, 12, 14–16 Fish, see Bletchley Park, Fish FRA – cryptanalysts – – Carlbom, Lars, 23 Fried, Capt. Walter J., 10, 17

Generatrix, 28 H¨ uttenhain, Eric, 16, 17 Halibut, 10, 12, 13, 15, 24 Hinsley, Sir Harry, 1, 30 International Telegraph Alphabet, 19 Kahn, David, 1 Key – book, 14 – code wheel key, 14 – emergency key, 15 – generator, 2, 7 – inner key, 4, 6, 7, 13, 14, 27, 36 – instructions, 12 – message key, 2, 8, 9, 14–16, 27, 34, 35 – message key unit, 6, 8, 9, 13, 14 – message key wheels, 9 – table, 23, 27, 34–36 KTF, Klartextfunktion, see Autokey Lorenz – SZ40/42, 1–3, 11, 24 – SZ42c, 2 Luftwaffe, 9, 14–17 Mackerel, 3, 9 Modulo-two addition, 3 OKW, Wehrmacht, 14–16, 23 Pentagon, 2, 7–9, 13, 16 Permutation, 3, 8, 10, 11, 18, 21–23, 25–27 – circuit, see Transposition, circuit – distribution, 23 – identity, 22, 23 – probabilities, 25 – set, 22, 23 Permutor, 3, 4, 7, 9–11, 18, 20, 21, 26 S¨ agefisch, 15 Salmon, 9, 10, 12, 13, 15 Sardine, 9

Subject Index Sawfish, see S¨ agefisch Schl¨ ussel, see Key Shift register sequence, 4 Siemens SFM – T43, 1 – T52, 1 – T52 operation, 4 – T52a/b, 1, 9, 10, 17, 21, 25 – T52c, 1, 14, 16, 17 – T52c Aptierte, 16 – T52ca, 1, 13 – T52d, 1, 10, 14, 21, 25 – T52e, 1, 17, 19 SSA (Signal Security Agency), 17 Stop-and-go, 6, 10 Sturgeon, 1–30 – link, 3, 9, 10, 15 – machine, 3, 13 – traffic, 1, 3, 8, 9, 13 Subtractor, 3, 10, 11, 18, 20, 21, 26 Thrasher, 1 Transposition, 21 – circuit, 4, 5, 7, 10, 18, 21–24, 30 – unit, 5–7, 21, 23, 25 Tunny, 1, 9, 12, 14, 30 – , see Lorenz, SZ40/42 Tutte, William T., 1, 7 Vernam cipher, 26 Weierud, Frode, 1 XOR, see Subtractor – , see also Modulo-two addition – circuit, 4, 5 – square, see Baudot, XOR square

37

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UG|~oWu$][\§b ¤i³OS Ð0´ Bk8ªvS BPO $ ¬PORS Bk»F£F£O OR-H Q RG OpÐ_©¤§¦ Â Jµr»NBc H³²FF¸OTB R ² RBP 'Ú~´FIQ » Q$Bk² BP ~OFIBPgF£N R HF ~OFÅQ¯c².»NBPO IBPF°· ORS Ë F£OFI§S¹¬cBPNHORS J'² = FIQ$BkN$¬cBf O = OS F _ ~O F£~O¾ORS vB ¬PBPI§@ B H-O@´N F¸OT R ~OFIBPaFN§FkS~OT$L Ð_B FÊOS vB ¬ ¼ Ïª½'J NBk» H9ORS k´ORG´².» $R HÊ½ BkÄJF N Q O k´O· ® ORS ¦ $ ²4BP°JF Q F°F£ORW»k².»NF£Q$Bk² BPFkNWBP~BPFN[OvË F£ORBkF£¹L ¼ Ï¹µ ª½'JF~O F£ NQ WBcaF² ORBk~O¹OC¦ $ BP Â k~Ock² $R ¬=BPNH¾IBfO $ ORC¦ $ BP Ð0FI Sf $ ¬~F Ý kS~OF4½c²² Û 'J F B $L ¼ Ïª½'JÇWBc0BP ~OFIBPÀF£N R HF ~O_F8FF@OS ËvBfOO PxORS JWORBkcORFQkL ¦ $ ²³Bk ¼ µiËWcBfOT! $R B = Fk´ÀÄOS R BPO0O-J'£F H8SF FN¬~BPNH4Q$k´IH cR§F» SNBED Ê D cO H J² $ FQ=BP F~O $ D ~OFk FÐ_´ À LM'f D = ¬WH Q G ORF£c P §´»N²³B F ² RBP NBP» H±OS J'£F H±ÀBED~F O SG´~O³BPNHH §O B9IB ~´N².» $ k´»N-Bk@ _Bc¾OS F - = FI§SN² ~O.§SF =LgM $R ¬ ¼ Ïª½'J+SNBcHÊO » Bk´k² ~O HÉQ$B ·´£ F£OS±kOS = §c´ Q ¾kWHBPORB¬ÆF£NQ$£´ÀHF£N §FkS~OF~@BPNH HF R Q¯OFk Ý NHFÀ¬»´O'vBkWORS §F Ú~´NBkkÆOS ¼ µiËp~BfO»NBPO§O =L A Q R~ ORv k² Ð_©¤§¦ Â Jµr»NBk H² RBP v» Q$Bk² OS [OTB P0J£F H9 µ Q R O_F~O F£ NQ F£8OS ¤rORBPFIBP8Q$Bk² BPFkN_BPNH4F³OS H F£D BkQ ~ BkNQ Bf O = A'µiACB L Â RBk fDGFIH H4Q$ Fk´À_BP²³c´~OR0kÆHBfOTB@k ² H $ P¹»NBPO§O BPNHÉk O ±~BED J'F HQ¯c²²4BkNH $ @BkHDEBkNQ WB FPF² À NHFÊ¦ $ ²4BP BfO§OTBkQ =L ÊpaÙ§CÕG[_CÕ ¤_Wk´IH° Ü = OS ·c£fF£NQ$kNQ$£´NFkNvBP»k´OWORS J'² = FIQ$BkKBPÀHKJ£F H ¯®À µ F NQ F¸ORSÎ ¼ ½'ÎpÏÆÐ Â J'¦¨¤ BkNHÐ_©¤§¦ Â J ¼ Ïª½'J.¡ ªvS Ê¼ L ¢xLvk´OFk k¾OS Î ¼ ½'Î_ÏgÐ+ §O ² BkNH Ë F£OFIS ¯® kF£ORBPOFkP Ð_©'¤§¦ Â J ~BED J'£F HÉH Q¯FI§FkÊ²³B k = ¾Q¯c~OF~´Nk´N¨FN§FkS~O¾F£~ORSÀBfO¾OS ³ µ ² vBkCB F4OKF¸OT ¸[LaªvSFIC´ R Q H cO H 6 BPNHÅ§´N§ORBkF£ H 6 F£NFkS~OCF~O OS BkQORF£DGF£OF =¬ORSF£ FÀ¬BkNH9FcO ~OFkÀ'P0c´ ' ²³F Cp IHFIH BPÀH9BfOORS SF£cS §O D v~BED OS J£F 'BPFNQ$BkQ$´Bk» BcHDfBP~ORBk L ªvS Bk»F£F£O OR R BcH OS Î ¼ ½'Î_ÏgÐ+ §O ² N fDGFIH H ²-´NQTS FIH $ BkQ=Q R OSNBk ²³FkS~O8SNBED » $ ¯®À QO HaL0¤rOKPO4kN Í H´ÀQ H F· ²4BfORF£cÍcÍORS F£²³² HFIBfO ´N $ $¬kOSNBPO_FI$¬kOS Ñ~B BP HF k²4BfORFQ = DGFIQ ¬kF¸O_~BED ORS J'F _B §´ $ F k´ Q PaF£· ²³BPOFk4´N ·´NÀF8»POS8OS BfO = 0P¹vB BkNH· ²FF¸OTB R ´ R ~ _Bkp Lc¤rOW²³FkS~Op» B c´ HORSNBfOvÎ ¼ ½Î_ÏÆÐÌBfOWk² §ORBk 0vBk0²³ F£² ORBP~O¾F£ÊOS §O ´kc BP~BPFN[O@¦ $ ²4BP OSNBkÊF£O@WBcF ORS Ý kS~O@BPcBkF£À[O ÑcB BPF¸OT ¸[L ªvS Bk»F£F£O OR ¯® kF£O.ORS ½'Ð_A; §O ²vBk OS Q$BPORBP [OSFIQTSÌ ´ R H OS fvOSKP¢¤§¢4 k² B.OF Q$BcH R F~O³B-IB BPNHBkQ¯OFD cBkF£ºmBfORF£c8BPNH = B R H¨ORS ~BPFº=BPOFk¨OORB k BcHDfBP~ORBk kOS BPO = k´OFk kNÎ ¼ ½'Î_ÏgÐ'L ¤rOpBPI§@ Q F£ORBfO HORS H D ² ~O_Pa² QTSNBkFI§²4Ä· FH BkH4Q$k QOFk BPNH9HFIR ²FNBPOFk9P_¢G¤§¦¨¤[©Cª ²4BfO = FIBPI'BkNHOS HQO F ´ÀH $ SFQTSORS BkQORF£DGF£OF vWk´IHK» Q$kNH´ÀQO HaL ªvS BkQ¯ORxORSNBfO $® £cF¸OTBfORF£c¨kcORS Î ¼ ½'ÎpÏÆÐ §O ²ÇvBkx²4BP f $ µ{F~O À§FD BPNH $ H8k Q RF£-WBcWF£² $ BfOFD ¬~· Q H8OS O[W-» BkNQTS pPgOS ²³F£F£µ

Æt ³| u$eG ORB R $ DGFQ =¬ D ³SF£ OS $ $R Hk² [ORFQ F£DfBk· 0 §c´ Q =¬mO Q$~ À = BPO O H´ÀQ OSFI¾§c´ Q FÊB8OF² WB LªvSFI¨S H N = B R ORS c´NH· F£NQ Bk H°F£~O = $ DGFQ Q¯G $ BfORF£c°FKORS @ c§O§µrWB W = BNL Â c§O¨ F BPNH ²³Bk ²³FIHGµr D ²³F£F£ORB R BPNHÅQ¯FD~FFBk BkH = CF9OS vB SNBkH8k² D ÀP¹BkQ=Q R!OR Â J'¦¨¤ ÍR $ OR=LcªvS =-R OTBPF H4OS F ² ²³ F 0P ¿Ê IH¿¶B Q R~ OkkcFQ¨´NQ$Q R $¬BkNHK´ O HKOS Q$k~OFG´NBfORF£cKkÄQ G ORPµ £ckFIQ¨Q=B Bk»F£F£OF vFOS » BED c§O§µrWB W IHaL ªvS k´ORF£cNPCÎ ¼ ½'ÎpÏÆÐBkNHÌÐp©'¤§¦ Â J; $R F~O £ Q¯O´NBkvBcQ$Q$k² FSµ ² ~ORKP@OS ÝN [O» F££FIBPÀQ LvËWPORS = O Bk² ¯Ü OR°BkNH ORS ² ²-» = KP OS O Bk²³k´cS~OO8» F§O H9BP²³k³ORS F² OTBP~OCQ¯c~O F£»´O WO°D~FIQOR R F£¿¶ HK¿¶B ¤§¤L ¼ · O´NNBfO ¬Sf D $ ¬c· ²³c§OvkÆORS Q¯ccO F»´OR $¬~ORS F NBP² CBPNHÅH $ HB = Bk£ ° f9c OR8OS SB R F£~O $R §O H F£ F£~O £F ÀQ BkQ¯OFD~F£OF =L gFNBk£ ¬Æ¢G¤§¦¨¤[©Cª HFH¶kO¾FÉ¿Ê IHÊ¿¶B ¤§¤L¹ªvS vB vBk¨pcÊ» ORSc BkF£ $¬~§cHF = =¬~BkF ² ¹¬GBPÀH8²4B F£ pS OR~ OS CÝ cScOpO-OS ¨ ² BPOpORS FI BPNHa¬0k² OF² $¬0Q$c§O4P¨OS F f £FD $L0Mf D = ¬0¢GFkNBk¤i~O £F ÀQ cBED Q¯c²³²³BkNH = ³FNFH F· ²4BfORF£cBP»k´O4ORS 9 ² F£ ´NQTS H OTBPF'OSÀBfO F¸O-Bk£f H9ORS ²O9²4B k F H Q¯FI§FkN¨ORSNBfOBED H ´NNQ¯c´~O HÊORSk´NRBPÀH@P J'² $ FQ=BPBPNHË F¸ORFSKFD BkNH§S O H8ORS vB » ²4BP ²³k~ORSN$L ªvSNBfOFIvSNBfOFI ¯® QO HKP!BPF£~O £F NQ cBkFº=BfORF£c8FKvB OF² ¬BPÀHa¬ F£4¿¶ H¿ÉB ¤¤¬POS J'² $ FIQ$BP4BkNH³Ë F£OFI§S8¢G¤§¦¨¤[©Cª $ k H FD $R H-ORS F H´ÀQO'F£OSWB µiQTSNBkkF.BkNH£F£ RBEDGF£ ¯Üx Q¯OR=L

The Geheimschreiber Secret Arne Beurling and the Success of Swedish Signals Intelligence 1) Lars Ulfving1 and Frode Weierud2? 1 2

HKV/MUST, S-10786, Stockholm, Sweden CERN, Div. SL, CH-1211 Geneva 23, Switzerland

Preface The present paper appears under joint authorship, however, the responsibilities of the two authors are divided and well defined. Lars Ulfving is the sole author of the original Swedish version of The Geheimschreiber Secret 1 , while Frode Weierud alone is responsible for the translation into English, the translator’s notes, and postscript, as well as the bibliography and the appendixes. The translation has been kept as close to the original language as possible. Specialist terms and expressions have been retained where possible. Otherwise, a substitute term with the closest possible meaning has been chosen and an explanation given in the text. The original notes appear as in the original, as footnotes at the bottom of the page. Other short notes in brackets appear as in the original. Original references are marked with superscript numbers, while the references themselves are placed at the end of the text. The translator’s notes are of two types: short notes included in the text in brackets and in italic (translator’s note), and normal notes which are marked by bold, italic numbers in square brackets, e.g. [1]. The postscript, based mainly on information from Bengt Beckman’s book, fills in some of the missing personal histories and brings the account up-todate with present historical knowledge. Two appendixes and a bibliography have been added to place this account in its cryptological context and as an incentive to further study.

1

A short historical r´ esum´ e until spring 1941

2)

At the beginning of 1941 Sweden was in a situation that had drastically deteriorated during the previous year. The end of the Winter War (Russo– ?

1

This article represents the views of the author but not necessarily those of his employer or any other third party. Original Title: “Geheimschreiberns hemlighet, Arne Beurling och den svenska ¨ signalspaningens framg˚ angar” In “I Orkanens Oga, 1941 – Os¨ aker neutralitet” edited by Bo Hugemark, Probus F¨ orlag, Stockholm 1992

2

L. Ulfving, F. Weierud

Finnish war) and the signing of peace in Moscow on 13 March 1940 were traumatic events in Sweden as well as in Finland. However, the conditions were not so devastating as they could have been had the Soviet war aims been achieved. Finland survived as an independent state, but within tighter borders. The surprising and successful German attack on Denmark and Norway on 9 April 1940 brought serious consequences for Sweden. Sweden’s political freedom became seriously limited. Threats from new directions had quickly to be taken into consideration. In one area, however, the German demands on Sweden created unexpected possibilities that were exploited well. Their request to hire telegraph lines going through Sweden made great successes for Swedish signals intelligence possible. In mid-summer 1940, after the French capitulation and the Soviet occupation of the Baltic states, the Swedish intelligence service was faced with two important questions. Would Germany carry out “Operation Seel¨ owe”, a naval invasion of Great Britain, during the autumn? Would the Soviet Union again attack Finland to re-establish Russian borders on the northern shore of the Gulf of Finland while Germany was engaged on the western front? There existed no guarantees that Stalin would wait until the German air war might lead to air supremacy over the British Isles or that he would wait for the German invasion. After developments in the Baltic, Stockholm considered it likely that the Soviet Union would attack Finland at the turn of the month July-August even before, or perhaps even without, a German invasion attempt on Great Britain. Germany would then probably take the same attitude as during the Winter War, i.e. benevolent neutrality. Indications, chiefly reported by attach´es from Riga, Berlin and Moscow, showed such a development. The Finnish government was under enormous Soviet pressure, while Moscow-led communists tried to create internal trouble in the country. The pattern was the same as that before the Baltic states were occupied by the Soviet Union in June. When, on 13 August 1940, Foreign Minister G¨ unther explained the current situation to the Foreign Affairs Committee, his opinion was that there existed a real danger of such an attack. The German military attach´e in Riga was given as the source. It is remarkable that no Swedish sources or Finnish military authorities’ views were used or referred to. The Defence Staff’s intelligence department was therefore also obviously restrained in its written reports to the military command and the government. German fear of a Russian attack, however, caused Hitler to free the arms embargo against Finland shortly before 10 August. The arms’ deliveries that had stopped under the Winter War were now let through. This political change of course indicated a renewed German interest for Finland’s continued existence as an independent nation. The tension in Helsingfors was relieved. The immediate danger of a Russian attack was estimated to be over for the time being. As a result it was considered necessary that the Defence Staff’s intelligence department concerned with Finland should be strength-

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ened. Now, it was not only Finnish–Soviet relations but also German–Finnish relations that had to be watched. Since neither Finnish nor German military contacts were very communicative any longer, the task was not particularly easy. The extraordinary Swedish military contacts in Finland were evidently about to be reduced because of Finland’s German connections. The attach´e reports from Berlin also showed a clear German interest in Finland. Speculations about a German attack on the Soviet Union started to appear in the reports from Berlin. Neither the Swedish attach´es nor others could obtain any further information about Hitler’s intentions. They were reduced to making assumptions about probabilities and possibilities. A German two-front war, however, was not considered probable by the Defence Staff’s intelligence department. In autumn 1940 the situation did not seem particularly alarming to the Swedes. The concessions made, in response to German demands for troop transit and continued iron ore exports, appeared to be sufficient. The reports from the military attach´e in Moscow during the winter of 1940 no longer indicated a Russian build-up and deployment of forces against Finland. The Russian build-up of forces was instead concentrated in the border areas in the south and south-west, against Bessarabia and Bukovina. In Finland, however, they still felt that a new Russian attack was a real possibility. As a consequence of the commonly perceived threat, the military intelligence exchange between Sweden and Finland which, as already explained, had diminished after the end of the Winter War, was again improved. However, once more the Finnish interest for co-operation diminished considerably during spring 1941, principally during and after April. Attach´e von Stedingk in Helsingfors reported simultaneously that German–Finnish relations had dramatically improved. He also reported that Finnish contacts appeared to be prepared to take part in a German war against the Soviet Union, which German contacts said, with a surprising frankness, would start in early or mid-June. Colonel Carlos Adlercreutz, the chief of the Defence Staff’s intelligence department, had during a conversation with the chief of the Finnish General Staff, General Heinrichs, clearly seen the possibility of Finland joining in a German attack on the Soviet Union, or being forced to participate in such an attack. German probes about the transit of German troops from Norway to Finland through Sweden had already taken place in February. Sweden feared that these explorations would change into direct demands, but wondered if Hitler would be content with demands for transit if he intended to start a two-front war against the Soviet Union before Great Britain had been finally defeated. The uncertainty about Hitler’s intentions was brought to a head during the so-called “March crisis” that culminated in a large preparedness alert on 15 March. The alert was actually caused by a German communications error. In fact, there was no other intelligence about a German attack. However, the information obtained through signals intelligence made Swedish preparatory

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measures possible against regions where German units were positioned in Norway. The deployment and build-up at the German eastern border now started to be obvious and was difficult to conceal. However, an uncertainty still prevailed as to whether Hitler really intended to attack the Soviet Union before Great Britain was conquered. Perhaps the build-up aimed only at applying pressure — not a two-front war. How — or if — the received information was analysed at the Defence Staff and how — or if — the information in the military reports was weighed together with the rather uncertain and speculative diplomatic information, can no longer be clarified. At a presentation for the government on 21 April General Olof Th¨ ornell, the chief of the Defence Staff, judged that a German–Soviet war was probable, and that in such a conflict Finland would participate on Germany’s side. From the presentation it became clear what vague information was the basis for this judgement. The deception measures taken to protect the planning were hard for other intelligence services, including the Swedish, to penetrate. The Soviet military intelligence service was informed about the coming attack. Nevertheless, Stalin refused to believe that the attack on the Soviet Union would start before Great Britain was conquered. In one area the Swedish intelligence service was considerably in the lead. In spring 1941 the Swedish signals intelligence service furnished very interesting, extensive, accurate and unique information about German military dispositions in the vicinity of Sweden.

2

Swedish signals intelligence and intelligence service before and during the Second World War 3)

In 1936 a resolution was passed about a new defence order which came into force on 1 July 1937. The resolution included provision for the establishment of an intelligence department, a signals intelligence department and a cryptology department. However, the prerequisites for an effective intelligence service were not so good. Swedish intelligence services in the modern sense of the word had indeed been already established in the beginning of this century. The armed forces intelligence service had increased in 1905, during the Union crises, and in the First World War. The General Staff and Naval Staff of that time both had their own signals intelligence and cryptographic units. However, in the inter-war period less and less was done. The knowledge acquired in signals intelligence and cryptanalysis was lost. Politicians of that time did not understand the importance of a well-functioning intelligence service and consequently they did not grant any appropriations for this purpose. Nor did the Defence Commission, which was appointed in 1930 and on whose report the 1936 Defence Resolution was based, take any appreciable interest in the intelligence service. The General Staff’s foreign department did not

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constitute a solid enough foundation for such a service. No special agency for cryptanalysis existed before the Defence Staff was established, although the cryptographic departments at the Naval and General Staffs had some success during the First World War. The encrypted radio traffic of the Russian Baltic Fleet could be broken to some extent. The General Staff probably broke German diplomatic traffic periodically. The breaking may have taken place even earlier, but solid information about this is missing. These breaks, however, were probably quite sporadic and had a “chamber character”, i.e. rather amateurish. From the summer of 1928 signals intelligence operations were carried out fairly regularly under naval direction. In the beginning it took place from the warship Sweden (Sverige) and from the summer of 1929 from several ships in the coastal fleet. From October 1929, signals intelligence activities were also carried out from naval coastal radio stations. The first attempts to develop this branch of the intelligence service were made by the Navy. During the years 1930–31, the Naval Staff had already organized a course in cryptology and cryptanalysis. Ships in the coastal fleet started the systematic interception of foreign radio traffic in spring 1931. Later professional intercept operators were trained on the warship Queen Victoria (Drottning Victoria). The first successful attempts to break foreign cipher traffic were made in spring 1933, when they succeeded in breaking the cipher then used by the OGPU (later the KGB). These breaks into foreign military ciphers were probably the first to be made in Sweden after the First World War. The naval cryptography courses of 1930–31 were repeated in 1932–33 and 1934–35. An agreement was reached between the Naval and General Staffs to run these courses alternatively every second year. The instruction was based on theory with special exercises. The real material available was too complicated to be used in the teaching. Even if these cryptanalysis courses did not result in real breaks, they were nevertheless of great importance as they created a small cadre of trained theoretical cryptanalysts, consisting of both active and reserve officers together with conscripted students. Later on civilians from the University of Uppsala, among others, were also trained as cryptanalysts. One of these students was the mathematics professor Arne Beurling. When the future Defence Staff organization was analysed in 1935–36, cryptology-committed interest groups succeeded in pushing through the establishment of a department for cryptography and cryptanalysis — the crypto department. In some quarters a crypto department was considered unnecessary but, in spite of opposition, one was set up during the final stages of establishing the Defence Staff. Sections I to III were intended to deal with the cryptographic security of the Army, Navy and Air Force. The fourth section, crypto section IV, was intended to be a cryptanalytic section. Thus, the foundation was created for a central cryptanalytic organization. It was in crypto section IV that the Geheimschreiber traffic would later be broken.

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Radio interception was taken care of by the Defence Staff’s signals department. However, the actual signal-intercept work was completely carried out by the Navy, which was the only force with access to qualified intercept personnel.

Figure1. Dilapidated house in the back garden on Karlaplan 4.

The crypto department led an ambulatory existence during 1936–40. In the beginning, it was housed in the staff building “Gr˚ a Huset” (The Grey ¨ House) in Ostermalmsgatan 87; later in a house on L¨ utzengatan. [1] During the summer of 1939 the approaching war became more evident and the department intensified its mobilization preparations. At the outbreak of war it transferred to the premises of the Military Academy, where it had the top floor at its disposal. Soon it became overcrowded, which is why crypto section IV moved to a property on Karlaplan 4, consisting of a building facing

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the street and a dilapidated house in the back garden. The conditions were rather primitive. The furnishing was of the utmost simplicity, consisting of folding tables and simple wooden chairs. However, it was here that the crypto department was going to perform great achievements.

3

Breaking of the German encrypted telex traffic — the breaking of the Geheimschreiber 4)

At the time of the German attack on Denmark and Norway 9 April 1940, Germany demanded that there should be no interruption of their telecommunications transmitted over Swedish lines. After a positive answer, the Germans gradually hired lines in Sweden for the connections Oslo – Copenhagen – Berlin, Oslo – Trondheim, Oslo – Narvik and Oslo – Stockholm. The German embassy in Stockholm already possessed a line for their traffic to Berlin. Later on they hired a line for the connection Stockholm – Helsingfors. The interception of the German telegraph lines was the fundamental condition for the future successful breaking of the German encrypted messages. The Swedes had, by these means, access to large quantities of genuine information. Wartime arrangements allowed foreign rented telecommunication lines passing through Swedish territory to be tapped, without breaking Swedish law. We shall here for the first time in the open literature show the principles involved in the breaking of the Geheimschreiber. The Germans considered this cipher machine to be extremely secure, but their confidence resulted in an imaginary security. German carelessness and Professor Arne Beurling’s genius exposed the secret of the Geheimschreiber. 3.1

A note about teleprinters

To facilitate an understanding of the subsequent explanations we will give a short technical review of teleprinters. The first teleprinters were constructed at the end of the 19th century. The principles have remained largely unchanged since then. Every character transmitted consists of a combination of pulses of two types. The number of pulses in a character is always five, contrary to the varying number of pulses in the Morse code alphabet. All pulses are of the same length, and are indicated by positive or negative polarity or alternatively, current or no current. Five pulses taking on two different states give 32 different combinations, but that is not sufficient for all the characters that have to be transmitted. There therefore exists an arrangement with the same function as the letter/figure shift key on a typewriter. A combination of pulses causes all subsequent characters to be received as number or punctuation characters, and another combination signals in a similar way that all the following characters will be received as letters. Several teleprinter alphabets have existed. The one mostly used is called the Murray code after its inventor, or

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the International Teleprinter Code (International Telegraph Alphabet No. 2). The text is punched on paper tape which is fed into the transmitter. ‘Hole’ or ‘no hole’ in the tape corresponds to ‘current’ or ‘no current’, or to ‘positive polarity’ or ‘negative polarity’. 3.2

Teleprinter encryption

Soon after the first teleprinters were put into operation, equipment for the encryption of teleprinter signals was constructed. The method first used was simple. Two identically-punched key tapes, one for the sender, the other for the receiver, are produced. They are then glued together in a loop of manageable length, about 1000 characters. The sender punches his plain text tape and places it in a tape-reader. He then comes to an agreement with the receiver about how the key tapes will be placed in their respective tape-readers, and the transmission starts. In a simple relay circuit a modulo-two addition is performed on the characters from the sender’s two tape-readers. A character on a tape can be regarded as a binary number: a combination of ‘holes’ representing ones, and ‘no holes’ representing zeros. A modulo-two addition of two such numbers signifies an addition, without carry, of each bit in corresponding positions. The result of this addition forms the cipher character that is transmitted. The same procedure is used in the receiver. After each transmitted character all tape readers are stepped one position forward and the whole process repeats. The cipher methods gradually evolved. Instead of key tapes a number of code wheels with pins were introduced, e.g. five wheels , one for each channel in the key tape. An active pin had the same function as a hole in the corresponding channel on the tape. Thus it was no longer necessary to punch the plain text on tape and then transmit it later. The teleprinter could be directly connected to the cipher equipment, hence it was possible to transmit and receive in “real time”, so saving a lot of time. In the crypto department this encryption method, consisting of adding a key character to a plain text character, irrespective of how the key character was generated, was called “overlaying”. This term is used in the following text. 3.3

The Geheimschreiber

The German company Siemens developed a mechanical teleprinter cipher machine in the 1930s that was the first in a series of such machines. The generic name was “Der Geheimschreiber”, which the crypto department called “Gskrivare” (G-writer). In addition to the previously mentioned classical type “overlaying”, it also made a permutation2 of the pulse order as another encryption function. 2

Permutation: A permutation of a sequence of n numbers corresponds to a reordering of the sequence. Two permutations are equal when the numbers are placed in the same order. For n = 2 there are two permutations (1,2) and (2,1), for n = 3 there are six (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2) and (3,2,1). Generally it can

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The crypto department later used the expression “transposition” for this permutation. A polarity inversion was made with five relays, and five others took care of the transposition. [2] The relays were controlled by ten coding wheels which, through a set of plugs and jacks, could be connected to relays in an arbitrary way. The principle of transposition of the teleprinter pulses is not suitable for all types of teleprinters. The five pulses must be available simultaneously in the transmitter and the receiver for a permutation to take place. In the transmitter this is not so difficult to arrange, but it is much more difficult in the receiver. However, Siemens had solved the problem for the receiver even without access to modern digital technology. All functions were mechanical in the cipher machines of those days. An incoming character’s five pulses, positive or negative, charged five capacitors in sequence. When the fifth pulse was received the information stored in the capacitors was simultaneously transferred to five polarized relays. These relays were part of a circuit that selected the character to be printed. During this transfer it was possible to produce a transposition by changing the connections between the capacitors and the relays. The Geheimschreiber’s ten code wheels had the periods 47, 53, 59, 61, 64, 65, 67, 69, 71 and 73. In the first models all the wheels moved one step for each enciphered character. Since the wheel periods were relatively prime, that is they had no common factor, the total period of the machine — the number of steps the machine must make to return to its starting position — was equal to the product of all the individual wheel periods, that is 893 622 318 929 520 960 steps. This number also indicates the number of possible wheel starting positions. The “transposition circuit”, that is the insertion of the “transposition relays” between the rows, could be varied. Eight basic patterns were possible, each with 2 612 736 000 variations. [3] The combinations of connections and wheel adjustments were, before the creation of the computer, considered to be extremely large numbers. In addition there were the number of ways of connecting the code wheels to the relays. This may have given the Germans the impression that the Geheimschreiber was a very secure cipher machine. It was probably considered to be more secure than the Enigma machine which was intended for tactical use. The Enigma had, for example, a period of 17576. [4] The Geheimschreiber was gradually developed and several models were brought into service. The first machine the crypto department came in contact with was called T52a/b. Later T52c, d and e came into service. There were also variants of the different models. However, they were all based on the same basic principle. At the end of 1941, a new machine designated Z appeared in the traffic. It did not belong to the A/B-series and it was called Geheimzusatz 40 [5] and be shown that the number of permutations of n numbers is 1·2·3 · · · (n−1)·n = n! (n factorial).

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Figure2. “Geheimschreiber” or “G-skrivaren” (Schl¨ usselfernschreibmaschine T52c).

not Geheimschreiber. It was a stand-alone attachment that was connected between the teleprinter and the transmission line. It could therefore have been used together with teleprinters other than the Siemens machine that the Geheimschreiber was based on. 3.4

Arne Beurling

Who was Arne Beurling? According to Svensk Uppslagsbok (Swedish Encyclopaedia) he was “Arne Karl August Beurling, born 5 February 1905, mathematician. Beurling defended his thesis in Uppsala in 1933 (Etudes sur un probl`eme de majoration), senior lecturer same year, Ph.D in 1934, professor in 1937. Beurling is an ingenious and all-round scientist who has attained beautiful results in function theory, prime number theory, modern integration theory and in several other areas.” After the war Arne Beurling was offered an excellent position at Princeton University in USA in 1954. In 1965 he was given Albert Einstein’s office, No. 115, at The Institute for Advanced Study, a distinction granted to very few people. Arne Beurling died in 1986. It is now known that Professor Arne Beurling was the man behind the breaking of the German Geheimschreiber. David Kahn writes in “The Codebreakers”, page 482: “Quite possibly the finest feat of cryptanalysis performed

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during the Second World war was Arne Beurling’s solution of the secret of the Geheimschreiber.” Arne Beurling’s greatness is given by the fact he had at his disposal only the teleprinter tapes with the cipher text. He had no access to any machine, no plain text and no knowledge about the logical construction of the cipher machine. Everything had to be reconstructed, something which was done in a remarkably short time. It is known that he based his analysis on only 24 hours of traffic intercepted on 25 May 1940. A quick analysis showed that the first assumptions probably were correct. A check was made with the traffic intercepted for 27 May. Two weeks later the construction principles for the cipher machine were solved. On the other hand it is not known how he set about it. That secret Arne Beurling took with him in the grave. However, a reconstruction has been made by FRA (F¨ orsvarets Radioanstalt). The credit for this reconstruction goes to Carl-G¨ osta Borelius who served at the Defence Staff’s crypto section, later on FRA, from 1941 to 1985. Borelius’ description of the reconstruction work is the basis for what is shown here. 3.5

The reconstruction

There was, of course, a procedure for indicating the Geheimschreiber key settings. One setting was the inner one, that is the selective connection [6] used for the connection between the ten code wheels and the previously mentioned inversion and transposition relays. The inner setting was in force for three to nine days, starting at 9 o’clock on the first day. When a message was to be transmitted, the code wheels had first to be set to a given position. These settings had to be the same for both sender and receiver. The transmitting station would select a setting for five consecutive wheels. This setting was transmitted to the receiving station with a threecharacter so-called “QEP indicator”. The five remaining wheels were set to a predetermined key value that was valid for all messages during a 24-hour period. This setting was called “QEK”. The daily key list indicated which wheel would be “QEP-wheel” and which setting the “QEK-wheels” should have. It should be pointed out that the number 3 = letter shift, 4 = figure shift and 5 = space in this teleprinter alphabet. This has great importance in the following explanation. [7] When the transmission of a cipher message was about to start, the transmitting station would present itself with “Hier MBZ” (MBZ here) and would then ask if the message could proceed, “QRV”. If this was the case, the receiving station answered with “KK”. The transmitting station then sent “QEP” succeeded by five two-digit numbers (e.g. 12 25 18 47 52). Both operators then adjusted the wheels in their respective machines, partly the “QEK-numbers” after the key list for the current day, and partly the “QEP-numbers”. When the transmitting station was ready it would transmit “UMUM” (umschalten

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— switch over) and when the receiving station was ready it would answer “VEVE” (verstanden — understood). Then they switched over to cipher mode and the transmission of the text itself started. The cipher texts were consequently always preceded by “UMUM” and were therefore easy to retrieve in the large number of signals. It is possible that Beurling had knowledge of the Siemens & Halske patent, but this is not certain. Borelius recounts that when Beurling visited FRA on 15 November 1976, he reacted strangely to questions about the first break. He evidently did not like the questions to be put. He nevertheless said that he made use of “threes” and “fives” in the texts. Telecommunication technical problems were a great help during the breaking. The telegraph lines were long, sometimes bad, and therefore often exposed to interference, which could distort a transmitted character. The readability was nevertheless not disturbed except when the character changed to a “4” (= figure shift), because then all succeeding text became an unintelligible sequence of numbers and punctuation characters. If the distortion affected only the receiving station, the transmitting station did not notice anything, and continued the transmission. To reduce the problem, the operators normally used to write “35” (= letter shift, space) instead of only “5” (= space) between the words. Thus the consequence of a false “4” would be restored at the next space between the words. Beurling discovered that when the plain text of “3” and “5” had one pulse the same and four different, this had also to be the case in the enciphered state. For a guessed “3” there consequently existed only five possible “5” or vice versa. It was therefore relatively easy to establish spaces between words, which would have facilitated further work. It was probably this which Beurling talked about when he alluded to “threes” and “fives”. Hence a guessed “3” gave only five possibilities for Q and V in “QRV”, which asked if the message could proceed. In this way further work was greatly eased. It also seemed natural to suppose that a part of the encryption process consisted of a transposition of the five-pulse-characters pulse positions. A number of comparisons could give the transposition arrangement. Beurling tried in this case to trace back the cipher character to its appearance before the transposition. Then he made his next observation. The change from one character in the plain text to a cipher character after the “overlaying” consisted of a change in polarity for some of the pulses of the plain text character, and for all characters in a column it is always the same character that changes. We can assume that Beurling now introduced his observations on his “work sheets” (“avvecklings-papper”).3 In five rows under the examined text he placed in every column a dot for pulses with inverted polarity and a 3

Avveckling: A technical term for the elements of work that took place between the interception of a message and until the plain text could be extracted. That is, the work consisted of extracting the current cipher key.

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circle for those that did not change. When the emerging five-dot combination resembled a teleprinter character, it was called an “overlaying” character. Under this character was written the permutation order, that is the so-called transposition. Gradually it was detected that the pattern of circles and dots in the five rows of the “overlaying” repeated after a number of characters. Beurling then supposed that the pattern was produced by pin-wheels like those in the Swedish cipher machine, invented by Boris Hagelin. Subsequently he continued the work with the transposition. It turned out that if for example “pulse 2” ended up on “place 3” then the fourth circuit connection had to be open, otherwise it was not possible. If this circuit connection was controlled by a wheel with even distribution of active and inactive pins, the pulse would end up on “place 3” in half of the events, in the rest it would fall on some other place. A converse conclusion should have been possible, using an inverted argument. The complete circuit and hence the details of the remaining wheels were obtained through hypothesis tests. By these means Beurling would have got the break that revealed the Geheimschreiber secret, as Borelius’ reconstruction shows. 3.6

Imperfections, errors and laziness

It has been mentioned earlier that the telecommunication connections were bad. But it was not only single characters that were distorted and therefore gave an opening for breaking. The abundant number of “parallel texts”, that is an enciphered text sent several times with the same key setting on the cipher machine, were a big help in breaking the Geheimschreiber. In extreme cases the same message was sent 20 to 40 times with the same setting. How could this happen? One of the basic rules of cryptological security is never to send the same or a different message with the same key setting. Bad connections and distortions together with laziness gave many openings of this type. The keying procedures have already been described. It takes a certain time to adjust the wheels by hand. To facilitate the adjustment of the “QEKwheels”, that is the current key for the day, there existed a cursor that easily could be moved around on the wheel and positioned on an arbitrary key number. The wheels could be freed with a locking arm. All the wheels could be turned backwards with a handle until their cursors came to a home position when the wheel stopped. This handle sat on the right on the front of the machine under a plate with the inscription “LANGSAM DREHEN” (turn slowly). The idea was that every morning the cursors would be set on the five wheels that were intended for the daily key (the QEK-wheels). Later these wheels could quickly be returned to their agreed positions before every new transmission. Unfortunately it became a habit that even when the “QEP-numbers” were set, the cursors were set to the key values and then

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the wheels were cranked back. This was against the existing rules, as new “QEP-numbers” should be selected for every new message. Since the lines were long and sometimes poor there were often distortions. These sometimes caused one of the machines to interpret the distortion as a character. The operator of the other machine would not notice anything. One of the machines would then be one step ahead of the other. The cipher machines were no longer in phase and the message became unintelligible. When this happened, it was necessary to break the transmission, switch over to plain text, choose a new message key and continue the transmission.

Figure3. Decryption unit for German line traffic, ex. “APP”.

Now the big mistake was made. For each break in the transmission of a message due to continuous distortions on the line, the operators chose the easy solution of simply cranking back the wheels to the previous setting. In this way the cryptanalysts got their parallel texts with all their errors and flaws which gave a large number of opportunities for breaking it. The high security of the Geheimschreiber became therefore in many ways simply illusory. 3.7

Interception and preparation

As mentioned earlier, the traffic on the German hired telecommunication lines through Sweden was intercepted. It was quickly discovered that apart from plain text, encrypted text was also transmitted. When Beurling found how the Geheimschreiber functioned, Swedish technicians under the leadership of

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Viggo Bergstr¨ om started to construct special machines for decryption after directions from Beurling. [8] These machines very soon made it possible to follow the frequent changes in cipher keys and subsequently quickly extract the plain text. The machines were later built in quite large numbers in L.M. Ericson’s workshop for precision mechanics.

Figure4. The decryption units, “APPARNA”, at their working places.

The German Geheimschreiber traffic was broken and deciphered from June 1940 until May 1943. This went on even when new models were introduced and the key procedures were gradually changed. The intercepts came from a number of teleprinters in a room in Karlaplan 4 which were connected to the different lines between Germany – Norway, Sweden and Finland. The machines, which were very noisy, were supervised 24 hours a day. The texts came out in a never-ending stream of paper tapes, which were then glued on to big sheets of paper. The daily routine was the following: In the morning (after 9 o’clock, when the daily key was changed) the cryptanalysts examined the incoming traffic, waiting for a case with sufficiently many “parallel texts” to occur. As soon as possible, the cipher key extraction (“avvecklingen”) took place. When the new key settings were produced they were given to the staff who worked with the deciphering machines, and the deciphering of the day’s harvest could start. Subsequently the plain texts were cleaned up and typed. They were later given to the various consumers of intelligence. As mentioned above, two types of traffic were observed and studied. The most extensive were the military traffic and the traffic between Berlin and

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Figure5. In the machine room. (Room with teleprinter-receiving machines connected to the intercepted lines.)

the embassy in Stockholm. The diplomatic traffic had the highest priority, as this concerned Swedish–German relations. At least two key settings therefore had to be determined every day. At first, the teleprinters used in Karlaplan 4 were machines from the American firm Teletype. Teleprinters were, however, in short supply as importing them was difficult during the war. However, the Royal Telecommunication Administration (Kgl. Telegrafverket) were persuaded to surrender a number of their teleprinters, which resulted in a return to Morse telegraphy on some lines. When the crypto department later succeeded in obtaining a batch of Siemens teleprinters, these replaced the Teletype machines, which was certainly reasonable considering their use. As mentioned earlier, when newer versions of the Geheimschreiber were later introduced, attachment units were constructed and connected to some of the deciphering machines that were used for the C model traffic. For the Z-traffic only one deciphering machine was built. [9] Large quantities of messages were decrypted and distributed. This extensive traffic resulted in an increase in the number of staff. The number of teleprinters and deciphering machines also increased until they reached a total of 32. The decryption of the Geheimschreiber traffic developed gradually into a real industry needing a lot of people. In 1941 the staff increased to 500 people and later on it became even bigger from time to time.

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Table1. Number of distributed messages. Year 1940 1941 1942 1943 1944 Total

Encrypted Unspecified Unencrypted Total 7100 7100 41400 41400 101000 19800 120800 86600 13000 99600 29000 29000 187600 77500 32800 297900

The highest number of messages distributed in one day (October 1943): 678.

The breaking of the Geheimschreiber was a large contributory factor to the establishment of FRA (formed from the Defence Staff’s signals and crypto departments) as an independent authority on 1 July 1942. In May 1943 the keying principle was changed with the result that further deciphering became impossible. A small group stayed on to handle those messages that for different reasons had not been deciphered earlier.

Figure6. View from the rack room. (Room with equipment racks where the intercepted telecommunication lines entered.)

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On the eve of Operation Barbarossa: How was the intelligence used? 5)

What has just been described, it must be emphasised, was a spectacular performance even on an international scale. As far as known the Siemens Geheimschreiber was not broken in any other country. [10] It was also an extraordinary yield based on a relatively limited investment. Beurling’s reluctance to explain how he did it could be due to the fact that he solved the problem so easily and quickly that he found it too easy to arrive at the solution. But in reality genius shows itself in simplicity and its accompanying excellence.

Figure7. Another view from the rack room.

In 1940 the crypto department had been developed with mostly rather new staff. Its technical and organizational achievements were therefore considerable, since during autumn that year it began to distribute German messages in ever-increasing numbers. German unit compositions and their position, together with military and political deliberations and directives were in this way known to the Swedish authorities, sometimes almost at the same time as the real addressee. The German traffic was not particularly alarming during the autumn of 1940. Hitler was hardly interested in Sweden politically. The planning for the attack on the Soviet Union was still in its infancy. The directives for Operation Barbarossa were first drawn up in December 1940. This gave

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19

the crypto department a respite that was used to build up and render more effective the breaking, analysis and delivery routines. The Defence Staff could therefore prepare methods for handling the decrypted material at a time when it was not under any particular pressure. Texts “of strategic importance or of an obviously secret nature” were delivered directly to Adlercreutz, as chief of the intelligence department, who normally submitted them to his superiors Commander-in-Chief General Olof Th¨ ornell and the chief of the Defence Staff Major-General Axel Rappe. Then the texts went to the intelligence department’s own sections. Routine messages went there directly. Afterwards the messages were burned, apart from those judged to have long-term value or that were of great strategic importance. Otherwise, distribution within the Defence Staff was very restricted. A distribution list was never established. The material was delivered to the recipient after an assessment in each particular case. (Comment: Destruction of the decrypted original texts has probably created problems for modern historical research.) Distribution outside the Defence Staff, to the Foreign Office and the Security Service, took place in the beginning through Adlercreutz’s personal service. The distribution to UD (Utrikesdepartementet = Foreign Office) was very restricted as Adlercreutz doubted the Foreign Office’s security consciousness. However, that the co-operation between the Foreign Office and the crypto department was as good as it became, was due to the fact that foreign minister Richard Sandler (1932–1939, later governor of G¨ avle) was a very keen amateur cryptologist although, as a cryptanalyst he had no real success. His great services consisted of arranging for UD to inform the crypto department when important events were under way and when encrypted messages might be sent to Germany. This could assist the cryptanalysts, by allowing them to check that the decrypts were correct. [11] Different considerations contrasted with each other here. The necessity to deliver information to suitable Swedish authorities conflicted with the requirements for secrecy in order to minimize the risk of betrayal of this unique intelligence source. As the decryption work was done by a department of the Defence Staff, Adlercreutz wanted the intelligence department to be the first to receive all information and even to have a right to direct the work in the crypto department. However the crypto department successfully resisted these attempts to boost the intelligence department’s power. In the beginning, few objections were raised against Adlercreutz’s control over distribution. But when the German preparations for Operation Barbarossa eventually came to their final stage, the Foreign Office started to feel that they did not get all the intelligence that they needed. The chief of the crypto department then decided to change the distribution routines after consultation with the Foreign Office, who also suspected that they did not get all the information in time.

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L. Ulfving, F. Weierud

During the winter of 1941 the incoming information became more and more alarming for Sweden, much more so than during the autumn and winter of 1940. However, it was now possible to get a continuously clear view from the decrypts of the groups, composition and combat readiness of the German forces in Norway and therefore also of changes in the situation. A lengthy force enumeration, intercepted on 21 April 1941, indicated a general movement of troops towards the north. Nevertheless, as on previous occasions no concentrations or deployment could be shown to be directed against Sweden. Nor was there any indication in the numerous reports from military border patrols, customs officers, police commissioners and officials interrogating Norwegian refugees that a German offensive against Sweden was imminent. The decrypted diplomatic traffic gave no special reason for alarm. The repeated German threatening warnings to Swedish contacts were reflected neither in the incoming intelligence nor in their own signals. During a period when German–Soviet tensions increased rapidly, it was nevertheless impossible to ignore the warnings. The government, principally the prime minister and the foreign minister, as well as the military command, were not prepared to cause trouble and accordingly create German irritation. It was not therefore apparent that they reckoned with a German–Soviet war. Many analysts consider that war preparations serve only as instruments of pressure during negotiations. However, that ignore the dynamics of future military developments which are created by a deployment as large as that which occurred here. Economic factors and military logistics make it almost impossible to keep large, inactive troop concentrations in place as a trump card during long negotiations, just as it is damaging for the units’ fighting spirit. It is too expensive not to use the troops, therefore they must either be used in combat or be demobilized and returned to civilian life. Only victory justifies the price — even if it is high. For example, consider the collapse of the economic, political and ecological systems now affecting the states of the former Soviet Union as a consequence, during a long period, of a highly forced “war economy” that did not result in any gains. On 4 June a message was received indicating that strong German forces would in the near future be transferred east of Rovaniemi in northern Finland. Units would come from Germany as well as from Norway. The deployment was to be ready for 15 June. However, no demands on Sweden for the transit of troops could be gathered from the messages. Two divisions would be transferred by sea to Stettin, then in turn to Oslo and on to Rovaniemi. The information in the decrypted messages clearly indicated a German attack on the Soviet Union. On 11 June three further messages came which showed that this assumption was probably correct, as well as other intelligence revealing that Finland could not avoid becoming involved in the war. On 16 June came a teleprinter message that AOK (Armeeoberkommando) Norwegen had taken military command of Finnish Lappland and that the troop transports were going as planned. The same day, 16 June, the teleprinter connection Berlin

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– Helsingfors via Stockholm was established following an earlier request. In spite of different speculations about a negotiated agreement, the incoming messages in the week before 27 June increasingly pointed towards an imminent outbreak of war. Despite the intelligence, the Defence Staff did not cancel leave for the mid-summer weekend. An assessment that there would be a negotiated settlement, which would not require a high military preparedness, clearly had some validity. However, it is also possible that when the assessment was made that the war would not affect Sweden, it was more important to conceal the possession of this extraordinary source, which consisted of access to the Geheimschreiber traffic. Perhaps, therefore, they took it easy and allowed themselves to be “taken by surprise”.

5

What happened later? When and how was the unique source exposed?

6)

The decrypted German messages had, as mentioned earlier, been the most valuable sources during the weeks before the German attack on the Soviet Union on 22 June 1941. This would remain the position for a few years. With the attack, the teleprinter traffic to the German commands in Oslo and Rovaniemi, as well as the diplomatic traffic Stockholm – Berlin increased. The information received by the Swedish authorities became more detailed than before. During the first year, from summer 1941 to summer 1942, when the German campaign against the Soviet Union took place, the decryption of the German teleprinter traffic provided extraordinary intelligence. German military plans and German politics towards Sweden could be clarified with the utmost certainty. However, no reliable knowledge was obtained about Adolf Hitler’s political and strategic intentions. Intelligence throwing any light on the innermost reasoning of the people close to Hitler rarely or never existed. The supreme army commands in Oslo and Rovaniemi did not command any of the decisive operations of German warfare. Hitler therefore seldom interfered in what went on in these theatres of operations. Nevertheless, even if the embassy in Stockholm and the commands in Norway and northern Finland were on the periphery of German interests, the intercepted internal German briefings and compilations had a great intelligence value for Sweden. Adlercreutz’s restrictions on distributing the decrypts to external recipients, except for the senior officers of the Defence Staff and the Intelligence Department, were mainly aimed at not exposing this exclusive source. Special instructions about other aspects of handling the material were issued in September 1941 by Samuel ˚ Akerhielm in his capacity as deputy chief of the Defence Staff. The purpose was, of course, not to reveal the source. The decrypted messages had to be communicated and handled in secure ways. It was not permitted to refer to this material in conversations, and even less so

22

L. Ulfving, F. Weierud

on the telephone or in writing. When the messages were no longer needed, they had to be burned in controlled conditions. The German confidence in the Geheimschreiber’s security was, as explained earlier, an illusion. However, even the Swedish belief that the Geheimschreiber’s secret still was a secret, except in Sweden, soon also became an illusion. Some time in August 1941 the Soviet Union obtained access to the decrypted material. The courier Allan Emanuel Nyblad had the task of transporting the decrypted messages from Karlaplan 4 to the Staff building “Gr˚ a ¨ Huset” on Ostermalmsgatan 87. He was a rather quiet man. He had been recruited as an agent, on ideological grounds, by the Soviet Union. The espionage was carried out in the following manner. On his way to the Gr˚ a Huset, Nyblad went to a rented flat situated along his usual route and photographed the messages he carried. The photos were given to the Soviet representatives, who had promised Nyblad a prominent position in a future communistic Sweden. He is not likely either to have received or demanded any money worth mentioning. It is a reasonable assumption that the Soviet intelligence services (the NKVD and GRU) followed the Swedish success with interest. Moscow must have welcomed the likelihood that Sweden, with the aid of the intelligence, would take as strong as possible a position against Germany. But at the same time, the decrypted texts could also create doubts about Swedish power and will to withstand the German pressure. Here we may reflect that the Soviet Union was taken by total surprise in 1941. During spring 1941 information about the coming German attack was leaked from Sweden to Great Britain (via the naval attach´e) who passed on the information to the Soviet Union. However, General Golikov, then the chief of the GRU (the military intelligence service), actively contributed to the surprise by playing down the warnings from western sources, especially British, for reasons of political expediency. (The British intelligence service, SIS or MI 6, had until the Second World War primarily been working against the Soviet Union. Distrust can therefore be considered to be the explanation.) Nyblad’s spying was exposed in January 1942. It could not be exactly established which messages came into Russian hands through Nyblad, as he could not remember clearly on which days he had copied the material (T. Thor´en) [12]. It is not known whether the Soviet Union derived any benefit from the information. Less than six months after Nyblad’s spying stopped, the Defence Staff discovered a new leak about the successful Swedish codebreaking activities. This time the leak soon had devastating consequences. On 22 June 1942, Colonel Carl Bj¨ ornstjerna, chief of the newly created foreign affairs section, which was directly subordinated to the chief of the Defence Staff, wrote to Major-General von Stedingk, the military attach´e in Helsingfors, “A serious mishap has taken place. The Germans have been

The Geheimschreiber Secret

23

warned by the Finns that we have succeeded in breaking their G-schreiber. For this reason they are changing keys, message channels and everything . . . ”. No contemporary information exists about how “the serious mishap” happened. However, one need not be surprised. Swedish service personnel had been so open towards their Finnish colleagues that a leak was made possible. The openness shown during the winter of 1941, when it was conceivable that both Sweden and Finland could have common defence interests, continued after the summer of 1941. The Finnish military attach´e, Colonel Stewen, was even treated like an insider in the higher Swedish staffs, and the Germans suspected him of communicating sensitive information to Sweden, who they presumed then passed it on to the USA and Great Britain. However, it was equally possible that both of these great powers were capable of acquiring the alleged “leaked information” themselves. When the Germans criticized their Finnish colleagues for gossiping, the latter defended themselves by revealing that the Swedes had intercepted the teleprinter connections and were breaking the messages. It is even possible that Colonel Stewen had seen decrypted messages; at least he knew about them. The Finnish intelligence about the Swedish codebreaking activity probably reached the Germans some days before 17 June 1942, when the big alert hit the German communications. In the beginning, the counter-measures were quite incoherent, but they were soon concentrated in two directions. One consisted of introducing new cipher machines or attachments to them. On 21 July 1942 a new machine appeared in the traffic, T52c, “C¨ asar”. In the beginning it appeared on only a few lines, while on the others the old machine remained in use. As time went, more and more C-machines were put into operation. At first inspection the C-machine appeared to be completely normal. When the crypto department received parallel texts it could attack these as before, but the texts no longer fitted the previously known patterns. The sequences were no longer periodic or they had at least no short periods. Was this a new encryption method? At last the crypto department hit upon the solution. Two texts had been solved and it appeared that two “pin series” were identical in the long sequences. They had already earlier worked on the hypothesis that the seemingly infinite sequences were generated by addition, modulo-two, of the results of two wheels and hence obtained very long periods. The identical sequences allowed this hypothesis to be tested. This had failed earlier. Was it true that the old A/B-machines’ QEK-settings also were used in the C-machine? It was known that the C-machine could be used like the A/B-machine. For the A/B-machine they knew which five code-wheels were QEK-wheels, and also the settings. They then combined the wheels two by two in the ten combinations, but that did not work. However, when this procedure was repeated by leaving out four of the wheels it turned out to be correct. In this way it was possible to reveal the functioning of the C-machine.

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The Germans had in a hurry made the mistake of keeping an element from an older, simpler system in a new cipher system. In the C-machine they used the same wheel-lengths and pin-patterns as in the A/B-machine and the keying principle was the same. They should have made the new machine completely independent of the old one, but it is likely that production difficulties created obstacles. The A/B-machine could be connected to the C-machine. Therefore the quick change of machines did not have any appreciable effect. The other counter-measure taken by the Germans consisted in avoiding transmitting particularly important messages over Swedish telecommunication lines. It was therefore no longer possible to maintain the excellent intelligence about the German armed forces in Norway and Finland. A further deterioration occurred in October 1942 when all teleprinter traffic to and from Oslo and Rovaniemi was sent over Danish–Norwegian, or Finnish–Baltic cables. In certain cases cables were laid specially for this purpose. However, the teleprinter traffic to and from the German Embassy in Stockholm could still be intercepted and broken. In October 1942 the Germans ordered the introduction of so-called “Wahlw¨ orter” (randomly chosen words). The idea was actually sound. It is a good cryptological practice to avoid stereotype beginnings, which are usually where the codebreaker starts to look for an entry. The “QET-texts” were of course necessarily monotonous. Now the text would begin with a “Wahlwort” and in this way move the stereotype, fixed text further on to an undefined place in the message. However, the good intention failed. Many people follow instructions to the letter. Most people used the word given as an example in the instruction, which probably was SONNENSCHEIN (sunshine), as it occurred very often at first. Some managed to produce the word MONDSCHEIN (moonlight). The record was the word DONAUDAMPFSCHIFFSFARTSGE¨ SELLSCHAFTSKAPITAN (Danubesteamshipcompanycaptain). When the procedure with Wahlw¨ orter was used correctly it became more difficult, but not impossible, to decrypt the incoming messages. In May 1943 such radical changes in the keying procedures were introduced that codebreaking became almost impossible. The breaking of the Geheimschreiber’s teleprinter messages therefore diminished considerably. A smaller group was left on the task to try, if possible, to do something with the current material. Otherwise they were engaged in decrypting older material that had not been dealt with earlier, and in following the traffic. During 1944 the Geheimschreiber appeared in versions D and E and a mysterious machine called Y. The crypto department never succeeded in breaking these machines. Models D and E were further developments of the machines that carried the designations A, B and C. The Y-machine [13] could perhaps have been a further development of the Z-(Zusatz)ger¨ at (Z(additional)device = Z-attachment). But, as just mentioned, the traffic transmitted with these machines could never be decrypted, only followed.

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Other leaks also occurred, but were never of any significance. It was the Finnish military attach´e in Stockholm, Colonel Stewen, who exposed the secret.

6

Experiences and lessons

7)

When the new Defence Staff started functioning on 1 July 1937 the conditions were not the best for the intelligence and crypto departments. They did not have a solid foundation to build on. The procedures applied in the intelligence department were rather simple: namely, they were suited to producing compilations of open material and to making glossaries. Incoming messages from signals intelligence and e.g. attach´es were passed on “in extenso” to the concerned parties without making any overall assessments and conclusions. This was left to the individual reader. The information was therefore not turned into intelligence. The crypto department worked under very frugal conditions during its first development phase. However, through considerable efforts, where limited means were used in the best possible way, impressive results were achieved. Swedish military intelligence collection deserves very good marks for the period just before Operation Barbarossa and during its opening phase. The Swedish military attach´e in Helsingfors had given a warning in good time about a German attack on the Soviet Union in which Finnish participation was highly probable. The continuous decryption of the Geheimschreiber’s messages also indicated clearly and unambiguously an imminent outbreak of war. No inquiry will probably ever be conducted to see if the organization was a pure military endeavour, or a common one for the foreign department and the military commands to study and analyse the incoming information jointly. At least no documents exist showing this to be the position. Evidently it was considered adequate to circulate attach´e reports and decrypted messages without any attached intelligence evaluation. However, the most essential messages were probably discussed by representatives from the Foreign Office and the military commands at their weekly meetings which they started in the beginning of April 1941. Yet the incoming information gave the impression that Sweden would not be pulled into the war on the German side. The Swedish government and the commander-in-chief were therefore not surprised on 22 June 1941 as they had been on 9 April 1940. Nor was it necessary for Sweden to take any precipitate measures. They could afford to lie low and show surprise in order not to expose the exclusive source of the decrypted German teleprinter messages. No information exists about this, but the view is not unreasonable. As mentioned, no organization existed for compilation, study, analysis and synthesis in preparing intelligence evaluations. Nor was the establishment of such an organization considered. The assessment of the circulating messages’

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intelligence value and the conclusions were left to the individual readers, whether with good or bad results. Any long-term analysis and assessment of the war’s course and end was never carried out, but considering the turbulent developments ahead that was perhaps best. When one looks back to see whether it is possible to learn from that time’s events one must also take into consideration the classical dilemma of a professional intelligence service. Incoming intelligence rarely or never gives information about planning prerequisites, considerations and objectives of the supreme command’s inner circles, and even less about chosen alternatives. For this to be possible one must have access to a traitor or a planted spy in the enemy’s supreme command (e.g. the CIA’s Oleg Penkovski in the Soviet Union or Mossad’s Eli Cohen in Syria). Normally one is simply reduced to using information which can give intelligence about possible actions and when they are likely to be realized. When different readers, each studying from varying positions, preconceived opinions and needs to assert his preserve, draws intelligent conclusions from raw information which will be the basis for decisions, the result can be disastrous. The lonely decision-maker may very well take non-optimal, irrational decisions. However, if the decision is made in full session, the delay caused by the decision-making process can produce catastrophic consequences before everybody agrees after a long discussion. These are two of the conditions for a strategic attack to succeed, like the German attack on Denmark and Norway. A third risk also exists. A joint, balanced intelligence estimate, which is carried out by a whole organization, can in the end be so diluted that it has no value for the decision-maker. The balance between the different extremes demands a lot from those carrying out intelligence work, irrespective of grade or service rank. It should also be pointed out that it is nearly impossible to assess all undercurrents influencing a historic event so as to make a forecast. Unknown as well as known events, which an intelligence service will not be able to interpret and describe, can create unknown forms of interference in a chain of events so that they can hardly be predicted.

7

Conclusion

On New Year’s Eve 1941, Sweden was seemingly in the same geostrategic situation as the year before. However, a change in the wind was under way. In front of Moscow’s gates, the Germans’ storm wave had collapsed when Marshal Zhukov’s Siberian troops launched a violent counter-attack on 6 December 1941. The Red Army had good help from “General Winter”, who would assist in several winters to come. But in reality the strategic initiative was on its way to slipping out of German hands. However, it would take a whole year before this became evident for the world, when a complete German army was annihilated near Volga.

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On 7 December 1941, the day after the counter-attack outside Moscow, Japan attacked the American fleet in Pearl Harbor. With that an industrial giant arose in terrible anger — an anger that in the end would turn the fortunes of war. In the Second World War, the breaking of the cipher from the German Enigma machines and the Japanese Purple machines [14] was of crucial importance. The considerably greater intellectual effort needed to break the Geheimschreiber messages, which was accomplished in Sweden, did not in any way have the same decisive significance for the war. Therefore this accomplishment has not been so well known. However, from a Swedish perspective, it was of considerable importance as it actively contributed to keep Sweden out of the war.

8

Bibliography

Unpublished documents Documents of various types concerning the breaking of the Geheimschreiber in FRA’s secret archives. Published works Carlgren, Wilhelm M, Svensk underr¨ attelsetj¨ anst 1939–1945, Stockholm 1985. Kahn, David, The Codebreakers, New York 1967. Annotation The publication of information from FRA’s archives has taken place with due permission.

9

Notes

1. Where no other source is given, the account is based on information from F¨ orsvarets Radioanstalt’s (FRA) documents. 2. Carlgren, p. 32. 3. Resum´e of experts in FRA’s documents, compare with Kahn, p. 478. 4. After Carl G¨ osta Borelius’ unpublished documents in FRA’s archive. 5. Carlgren, p. 68. 6. Carlgren, p. 80, compare with Borelius’ documents. 7. Carlgren, p. 179.

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10

Translator’s Notes

1. Both of these addresses are in Stockholm. The majority of the FRA installations were in or around Stockholm, many of them adopting names with the ending “bo” which means room or house. On Liding¨ o, a small island on the eastern side of Stockholm, there were altogether five different FRA installations. Krybo and Rabo where FRA intercepted radio traffic and did cryptanalytical work, Petsamo which intercepted radio teleprinter traffic, Utbo for training intercept operators, and Matbo (“the food house”) where there was a restaurant and housing quarters. In Stockholm city were Karlbo, Karlaplan 4, and Lebo on Strandv¨ agen 57 which housed the FRA administration. Elsewhere in the country there were a few intercept stations and other installations. Sydbo intercepted Baltic radio traffic, while Norbo covered the Arctic radio traffic and traffic on the Finnish–German–Russian fronts. Ostbo covered the eastern parts of the Baltic Sea, the Baltic States and Poland. 2. The author refers to the use of relays for the inversion and the transposition circuits, which is how Carl-G¨ osta Borelius describes the circuits in his manuscript. However, only the T52c and T52e machines used relays for these circuits. The other machines, T52a/b and T52d, used the cam contacts on each coding wheel. The term “transposition circuit” reflects the cryptographic usage; mathematically speaking the circuit performs a permutation. 3. The number of combinations given by the author, 2 612 736 000 = 10!·720, is presumably the number of ways the 10 coding wheels can be selected and the number of permutation sets that can be obtained from the transposition circuit. This circuit has five double changeover contacts or transposition units which will give a total number of 25 permutations, which we call a permutation set, for a given set of connections. Furthermore, there are 9 · 7 · 5 · 3 · 1 = 945 ways that the five contact sets, each equipped with two plug connections, can be inserted into the transposition circuit. Computer simulations show that each of these 945 connection variants results in unique permutation sets. However, the majority of the permutation sets, a total of 561, are degenerate in the sense that each set contains only from 1 to 16 unique permutations. The case of the set with only one single permutation is special because it is the identity permutation. Of the remaining 384 sets, 24 sets have 27 unique permutations, 240 sets 30 permutations and 120 sets contain all the 32 permutations. Inspection of a Wehrmacht SFM T52d Key table from May 1945 shows that all of the permutation connections belong to the two groups with 30 and 32 unique permutations, which means that in reality only 360 permutation sets were used by the German cryptographers during this period. The given number of 720 permutation sets probably is the result of a too superficial analysis of the T52 transposition circuit. The pluggable permutation units are only available on the T52a/b and T52d machines. On the T52c and T52e machines the transposition cir-

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4.

5.

6.

7.

4

29

cuit uses relays instead of directly using the code wheel contacts. The five relays are permanently wired in one of the most basic permutation configurations. Therefore the only selection available on these machines is which code wheel controls the different transposition relays. Due to an anomaly of the rotor movement in the Enigma machine, the middle rotor will step twice every time the left rotor advances. Therefore the period is 26 × 25 × 26 = 16900 instead of 26 × 26 × 26 = 17576, but the machine has a total of 17576 starting positions. The translator previously believed that FRA had confused the terminology. The early Siemens T52a/b machine (1937) was called Geheimzusatz while the Lorenz SZ40 and SZ42 machines were called Schl¨ usselzusatz (cipher attachment). However, recent archive research has shown that the German teleprinter operators used the term G-Zusatz for the SZ 40/42 machines.4 The following communication was decoded by Bletchley Park on the link they named Stickleback (Berlin – H.Gr. S¨ udukraine) on 13 September 1944: ”Do you have a G-Zusatz 40 available? Fundament 40? . . . So you have no 40 G-Zusatz any longer . . . good . . . many thanks . . . a Fundament . . . So you have a forty’er after all . . . good . . . good.” Fundament 40 and 42 were used by the operators to refer to the SZ40 and SZ42 machines. Later this usage would cease and instead would appear Fundament A and Fundament B. These two terms would refer to the SZ42A and SZ42B variants. The dialogue above shows nevertheless that all these cryptic terms for the different machines were not understood by all. The use of the Z designation for the SZ40 machine probably comes from the German use of the letter Z to describe this machine while setting up an encrypted communication circuit. To set up encrypted communication with the T52a/b they would transmit in clear the Q-code “QEK”, while for communication with the T52c and the SZ40 machines they would transmit “QEK C” and “QEK Z” respectively. The author uses the term “transposition connection”, which is correct in the sense that it transposes the function of a given code wheel, but it is a term likely to be confused with the machine’s permutation circuit or the transposition unit. The translator has therefore decided to call this part the selective or programmable connection. Because the enciphered text can contain any of the 32 possible teleprinter combinations, including the six control signals, the teleprinters used for interception had to be modified. In these specially modified teleprinters the signals carriage return, line feed, letters, figures, space and null were replaced with the numbers 1,2,3,4,5 and 6. All the other combinations were represented by their corresponding letter as normal. The British codebreakers at Bletchley Park (BP) used a similar arrangement where

“Log Procedure Relating to The Use of “Limitation” on Non-Morse Army Links”, addendum to Captain Walter J. Fried’s report No. 118 of 21 Nov. 1944. NARA RG 457, NSA Historical Collection, Box 880, Nr. 2612.

30

8.

9.

10.

11. 12.

13.

14.

11

L. Ulfving, F. Weierud

they replaced the six control signals by the characters 4, 3, 8 or -, 5 or +, 9 or . and /. See Appendix A. The construction of the decryption units, Apparna, was led by engineer Vigo Lindstein of L.M. Ericson’s cash register department. He would later join Hagelin’s Cryptoteknik as technical chief and eventually end up as deputy director of AB Transvertex, another Swedish cipher manufacturer. The breaking of the SZ40 machine was based on intercepted cable traffic, while intercepted radio transmissions later allowed the Swedish cryptanalysts to break the more modern SZ42. The cable traffic covered the period from 26 November 1941 until March 1943 and the first Swedish break into the SZ40 took place on 9 April 1943. The codebreakers at Bletchley Park made a break into the Siemens T52 machine during the summer of 1942. They had followed the use of this machine that BP called Sturgeon for some time. The T52 machine was mainly used on radio teleprinter links belonging to the German Air Force and the German Navy. Due to a question of priorities BP allocated their resources on the German Army links that used the Lorenz SZ40 and SZ42 machines. However, the Swedish codebreakers were the first to break the Siemens T52 machines. It is more likely that the crypto department was looking for probable words or “cribs” than testing for correct decryption. The author refers here to Commodore Torgil Thor´en, the chief of the Defence Staff’s crypto department. The review of the Nyblad case is part of Thor´en’s analysis, which is included as Appendix 6 in the 1946 report “Investigation into the Defence Staff’s handling of decrypted messages from FRA”. In his book, Bengt Beckman explains that the Y or QEKY machine was the Siemens one-time-tape machine T-43 which towards the end of the war was used on radio communication circuits that also used the SZ40/42. The Japanese machines, Purple, Coral and Jade, were used for high-level diplomatic communications and therefore never carried the same kind of tactically important traffic that was the case for the Enigma. Nevertheless, intelligence from these machines was important for the conduct of the war, and the reports from Japan’s ambassador in Germany, Hiroshi ¯ Oshima, contained much information of great strategic value.

Translator’s Postscript

Lars Ulfving’s account of Swedish codebreaking during the Second World War has largely been superseded by Bengt Beckman’s book Svenska kryptobedrifter (Swedish Crypto Achievements), [5,41] as Lars Ulfving himself acknowledges. Ulfving’s account, which is largely based on Carl-G¨ osta Borelius’ internal FRA history, cannot be compared with Beckman’s complete historical treatment of Swedish cryptography. Bengt Beckman, who is the former chief of FRA’s cryptanalytical department, interviewed many people who

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were directly or indirectly involved in FRA’s work during the war and had full access to the archives. He did not participate in FRA’s wartime work, since he joined the organisation in 1946. However, he personally knows most, if not all, of those who took part. Although, Lars Ulfving had limited access to the FRA archives and sources he did a good job with the material at his disposal. A strong point in his presentation is the setting of the cryptological exploits in their true historical context, which shows their importance for Swedish defence and foreign policy. However, it lacks a more profound explanation of the cryptanalytical problems and the personal histories of those who were involved. Arne Beurling has a central place in both Lars Ulfving’s presentation and Bengt Beckman’s book, which he clearly merits. Arne Beurling was in many ways Sweden’s and FRA’s Alan Turing. Like Turing he was a genius who always worked from first principles and received great pleasure in seeking simple solutions to problems. However, unlike Turing, he was not socially awkward. He liked an enjoyable evening in town, while his good looks and great personal charm made him very attractive to women. He was also a typical outdoors man who liked trekking, sailing and hunting. However, he had a darker side. He could be stubborn and difficult. Throughout his life he had many conflicts with other people and could then be physically violent. He is known to have settled one argument with the famous Swedish cryptographer Yves Gyld´en with his fists. Bengt Beckman dedicates three full chapters to Arne Beurling. The picture that emerges is of a person with a complex character, but who is full of life and nevertheless inspires both trust and friendliness. Like Turing, Arne Beurling would make the initial breaks into a problem and lead the way, but afterwards he would take on other tasks, allowing others to continue the work. Before Beurling decided to attack the Geheimschreiber problem, he had worked together with ˚ Ake Lundqvist, botanist and chess Grandmaster,5 on superenciphered Russian codes. The Swedish cryptanalysts made great inroads into the Russian code and cipher systems. Olle Sydow and G¨ osta Wollbeck were two of the major cryptanalysts working on the Russian problems, but there were many others. They made up a variegated group of professors in Slavic languages and literature, mathematics and astronomy including a few art historians. Not to forget all the young women of “good” families who, as at Bletchley Park, attended to the more humdrum tasks. Another of Beurling’s great achievements at FRA was his solution together with Robert Themptander, an actuarial mathematician, of a very difficult double transposition problem. These ciphers had made their first appearance in the autumn of 1940. They were sent by two spy transmitters, with the callsigns CDU and MCI, which were located on the continent and communicated with a station in England. In June 1941 the same traffic, which 5

˚ Ake Lundqvist received the title of Grandmaster in correspondence chess in 1962.

32

L. Ulfving, F. Weierud

always started with the indicator CXG, appeared in the transmissions of the British embassy in Stockholm. Double transposition can be a difficult cipher to break. In this case it was made even more difficult by applying a monoalphabetic substitution before the double transposition. By analysing the cipher texts they discovered that the digits 0,1,2,3 and 4 had a higher frequency than expected, something which indicated a substitution alphabet in the range 01–45. In October 1941, when Arne Beurling struggled with this problem, he finally succeeded in breaking six messages enciphered with the same key. He discovered that double transposition was indeed used with keys of different length for each transposition. However, his greatest difficulty was not the transpositions but rather to reconstruct the substitution alphabet. He apparently guessed that the alphabet would be in its ordered sequence, but the plain text that emerged did not fit the English language as expected. After many trials Beurling finally succeeded in extracting one word that made sense: “Baltik”. However, the rest was mainly incomprehensible. Arne Beurling then brought the text to his good friend Richard Ekblom, professor in Russian at the University of Uppsala. After slightly rearranging the text, Ekblom said: “This looks like Czech”. And it turned out to be telegrams from Vladimir Vanek who was the Czech Exile Government’s representative in Stockholm. As the telegrams showed that Vanek was involved in espionage against both Germany and Sweden, he was arrested in his home on 27 March 1942. A search resulted in the identification of the book used as the base for the transposition keys. It was Jan Masaryk’s Sv˘etov´ a Revoluce (World Revolution). The meaning of the indicator CXG escaped the FRA cryptanalysts during the war but now, more than 50 years later, Robert Themptander says it must have stood for Czech Exile Government. It is said that Arne Beurling himself considered this solution of a double transposition cipher with a monoalphabetic substitution and in an unknown language to be a greater feat than his solution of the Geheimschreiber cipher. Arne Beurling was not the only master cryptanalyst at FRA during the war. He was perhaps the only genius, but there were also other excellent cryptanalysts, who performed great achievements. A group of three people, Carl-G¨ osta Borelius, Tufve Ljunggren and Bo Kjellberg, under the leadership of Lars Carlbom succeeded in breaking the Lorenz SZ40 and SZ42 machines. The SZ40 traffic had been observed on the German cable connections in November 1941 and in January 1943 FRA also observed the same traffic on radio circuits. Their first break occurred on 9 April 1943, based on the cable traffic, while they also succeeded in breaking the SZ42, which was then used on radio, in September 1943. The solution of the SZ40 came later than the first British solution of the same machine in January 1942. However, Arne Beurling’s solution of the T52a/b machine in June 1940, based on a set of messages in depth intercepted on 25 and 27 May, constituted the first break of a modern, on-line teleprinter cipher. As with the Siemens T52 solutions the Lorenz machines were also

The Geheimschreiber Secret

33

broken by hand methods. The only tool was a SZ40 “replica” which was constructed using bicycle chains of different length to simulate the action of the twelve coding wheels. FRA’s resources were very limited. With a peak staff of 384 people in 1942 it was a tiny organization compared with Bletchley Park (BP) and Arlington Hall. It is therefore of interest to compare FRA’s Geheimschreiber group with the corresponding Fish6 sections at Bletchley Park. FRA’s Geheimschreiber group, which consisted of the sections 31f, 31g, 31m, and 31n, saw its peak performance in November 1942 while the Fish sections at BP had their peak in the autumn of 1944. In November 1942, 31f, which was responsible for tidying up the texts and typing the final results, provided 10638 messages. It was staffed by 56 people handling the tidying up process and 18 typists. At the same time, the line intercept section, 31n, had nine technician and eight young women who glued the printed teleprinter tapes on sheets of paper. The Post Office supplied up to three maintenance people on demand who would tend to the 72 line receivers and the 36 teleprinters. The cryptanalytic section, 31g, had 14 cryptanalysts and 60 women who manned the decoding machines, the “Apps”. There were a total of 32 “Apps” of which 22 had the special T52c adapter and 26 specially connected teleprinters. Finally, in the translation and compilation section, 31m, there were seven compilers and 13 translators including a few persons taking care of the odd jobs. In total the Geheimschreiber group had about 185 people. In September 1944,7 at the inauguration of BP’s new Block H which was built to house Max Newman’s section and his machines, there were a total of 345 people working on the Tunny problem in the two sections, the Newmanry and the Testery. The Newmanry comprised 20 male civilians, at least 10 of them with honours degrees in mathematics, one US Navy officer, 2 US Army officers, and 186 Wrens from the Women’s Royal Naval Service, a total of 209 people. In Major Tester’s section, the Testery, there were at this time 21 officers, including two US Army officers, 77 other ranks, 25 ATS (Auxiliary Territorial Service) women, and 26 male civilians, a total of 136 people. They included six mechanics and 37 machine operators, while 30 people were working on registration of traffic and 20 others were engaged on breaking “dechis”8 and anagramming depths. In addition there were 34 “setters” whose job it was to carry a break back to the beginning of a message and compute the settings for the machine operators. The remaining nine people were taking care of a variety of jobs. 6

7

8

Fish was the BP codename for the non-morse, teleprinter, transmissions and the ciphers they employed. The Lorenz SZ40/42 was labelled Tunny while the Siemens T52 machines were known as Sturgeon. Captain Walter J. Fried’s report No. 96 of 29 Sep. 1944. National Archives and Records Administration (NARA), RG 457, NSA Hist. Col. Box 880, Nr. 2612. Dechi is a kind of “pseudo plain text” as given by the expression D = Z + X = P + Ψ . The dechi is part of the method used to strip off the influence of the Chi wheels of the Lorenz SZ40/42 machine.

34

L. Ulfving, F. Weierud

At the end of September 1944, Colossus 5 had been installed in the new Block H and was fully operational, while Colossus 6 had also been installed but was not yet connected. A total of 12 Colossi were planned and ten machines were in operation at the end of the war. The sections also had up to 16 Tunny machines to decode messages on already broken keys. Tunny was also used for the “dechi” process and the Newmanry was equipped with three of these machines. During September over 2.5 million plain text characters were produced by the two Fish sections from a total of 40 million intercepted characters.9 This is only 6.25 %, however, the majority of the intercepted signals, 82 %, consisted of transmissions of fewer than 2000 characters, which were too short to be broken. What is immediately apparent in this comparison is the difference in approach. The FRA group appears more like a production unit where the daily cryptanalytical problem was well in hand and was solved with a minimum of specialist staff and without any machines. In BP’s Tunny sections the cryptanalytical problem clearly demanded the biggest resources both in cryptanalysts and machine operators who attended to the Colossi and other specialised machines. One reason for this is due to the differences in the two cipher machines. In the Siemens T52 the code wheel patterns remained fixed while for the Lorenz SZ40/42 they had to be broken every day for some of the links. This required a major effort from the cryptanalysts. FRA also had the advantage of working with intercepted transmission that were as good as the intended German recipient. This was never the case for BP who very often had to work with marginal material due to the difficulty of receiving and transcribing the very faint Fish signals. However, the T52’s cryptographic algorithm, which used permutation together with modulo two addition, was more difficult than the principle used for the SZ40/42 machines. Seen in this light, FRA’s results are astounding, which can only partly be explained by the dedication of the people and their leadership. One important factor must have been the quality, professionalism and experience of those involved. The majority were highly educated and those who lacked formal education were extremely talented. One person who comes to mind is G¨ osta Wollbeck, then G¨ osta Eriksson, who, when he joined FRA, lacked formal academic education but had a good knowledge of Russian acquired through self-study. He would, over the years, assimilate one language after the other and undertake whatever translations were needed. However, there is yet another factor. Even though there appear to have been tensions within the organisation, something that probably can be explained by the close proximity of so many strong and somewhat eccentric personalities, most of them clearly loved the work they were doing. As Arne Beurling’s student and very good friend over many years, Bo Kjellberg, said 9

Captain Walter J. Fried’s report No. 101 of 14 Oct. 1944. NARA, RG 457, NSA Hist. Col. Box 880, Nr. 2612.

The Geheimschreiber Secret

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recently at a meeting of FRA veterans: “That was the most wonderful time of my life. To have all those unsolved problems in front of me.”

12

Acknowledgements

The translator should like thank Dipl. Ing. Wolfgang Mache for his request for help in translating parts of Lars Ulfving’s paper into German or English. This request, from an old friend, started the process which has resulted in the paper finally being published here. I should also like to thank Alan Stripp and Ralph Erskine for proof reading earlier versions of the translation and their many suggestions. I am further indebted to the author, Lars Ulfving, and Lieutenant-Colonel Bo Kjellander of Probus F¨ orlag, Stockholm, for their friendliness and courtesy in granting permission to publish the translation together with the original illustrations. Geoff Sullivan has helped me with the T52 simulations and I am very grateful for his assistance. Finally I wish to thank Bengt Beckman for permission to quote from his book and FRA monograph and for helping me to obtain photos from the FRA archives.

13

Translator’s Bibliography

References 1. Ahlfors, Lars: The Story of a Friendship: Recollections of Arne Beurling. Mathematical Intelligencer Vol. 15 No. 3 (1993) 25–27 2. Banks, David L.: A Conversation with I. J. Good. Statistical Science Vol. 11 No. 1 (1996) 1–19 3. Bauer, Friedrich L.: Entzifferte Geheimnisse, Methoden und Maximen der Kryptologie. In German. Berlin: Springer Verlag (1995) 4. Bauer, Friedrich L.: Decrypted Secrets, Methods und Maxims of Cryptology. Berlin: Springer Verlag (1996) 5. Beckman, Bengt: Svenska kryptobedrifter (Swedish Crypto Achievements). In Swedish. Stockholm: Albert Bonniers F¨ orlag (1996) 6. Beckman, Bengt: A Swedish Success: Breaking the German Geheimschreiber during WW2. Monograph produced by F¨ orsvarets Radioanstalt, Stockholm, Sweden (1997) 7. Beckman, Bengt: Svenska Kryptotriumfer Under Andra V¨ arldskriget (Swedish Crypto Triumphs During the Second World War). In Swedish. Monograph produced by F¨ orsvarets Radioanstalt, Stockholm, Sweden (1999) 8. Beckman, Bengt: S˚ a Kn¨ acktes Z-Maskinen (This is how the Z-Machine was broken). In Swedish. Monograph produced by F¨ orsvarets Radioanstalt, Stockholm, Sweden (1999) 9. Carter, Frank: Codebreaking with the Colossus Computer. The Bletchley Park Trust Reports No. 1 November (1996) 10. Carter, Frank: Codebreaking with the Colossus Computer: An Account of the Methods Used for Finding the K-wheel Settings. The Bletchley Park Trust Reports No. 3 May (1997)

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11. Carter, Frank: Codebreaking with the Colossus Computer: Finding the K-wheel Patterns. An Account of Some of the Techniques Used. The Bletchley Park Trust Reports No. 4 June (1997) 12. Chandler, W.W.: The Installation and Maintenance of Colossus. Annals of the History of Computing 5(3) July (1983) 260–262 13. Coombs, Allen W.M.: The Making of Colossus. Annals of the History of Computing 5(3) July (1983) 253–259 14. Davies, Donald W.: The Siemens and Halske T52e Cipher Machine. Cryptologia 6(4) October (1982) 289–308 15. Davies, Donald W.: The Early Models of the Siemens and Halske T52 Cipher Machine. Cryptologia 7(3) July (1983) 235–253 16. Davies, Donald W.: New Information on the History of the Siemens and Halske T52 Cipher Machine. Cryptologia 18(2) April (1994) 141–146 17. Davies, Donald W.: The Lorenz Cipher Machine SZ42. Cryptologia 19(1) January (1995) 39–61 18. Deavours, Cipher A. and Kruh, Louis: Mechanics of the German Telecipher Machine. Cryptologia 10(4) October (1986) 243–247 19. Flowers, Thomas H.: The Design of Colossus. Annals of the History of Computing 5(3) July (1983) 239–252 20. Gl¨ under, Georg: Als Funker und “Geheimschreiber” im Krieg 1941–1945. In German. Pionier Nr. 11/12 (1989) and Nr. 2 (1990) Translated into English by Paul K. Whitaker. Unpublished. 21. Gollman, Dieter and Chambers, W.G.: Clock-Controlled Shift Registers: A Review. IEEE Journal on Selected Areas in Communications 7(4) May (1989) 525–533 22. Good, I.J.: Enigma and Fish. In ed. F.H. Hinsley and Alan Stripp. Codebreakers, The Inside Story of Bletchley Park. Oxford: Oxford University Press (1993) 149–166 23. Halton, Ken: The Tunny Machine. In ed. Hinsley and Stripp. Codebreakers. (1993) 167–174 24. Hayward, Gil: Operation Tunny. In ed. Hinsley and Stripp. Codebreakers. (1993) 175–192 25. Heider, Franz-Peter: A Colossal Fish. Cryptologia 22(1) January (1988) 69–95 26. Hilton, Peter: Reminiscences and Reflections of a Codebreaker. In these proceedings. Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory. New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) 27. Hinsley, F.H.: Geheimschreiber (Fish). In F.H. Hinsley et al. British Intelligence in the Second World War. London: HMSO Vol. 3 Part 1 Appendix 2 (1984) 477–482 28. Hinsley, F.H.: Cracking the Ciphers. Electronics & Power IEE July (1987) 453– 455 29. Hinsley, F.H.: An Introduction to Fish. In ed. Hinsley and Stripp. 1993. Codebreakers. (1993) 141–148 30. Kahn, David: The Geheimschreiber. Cryptologia 3(4) October (1979) 210–214 31. Kjellberg, Bo: Memories of Arne Beurling. Mathematical Intelligencer Vol. 15 No. 3 (1993) 28–31 32. Mache, Wolfgang: Geheimschreiber. Cryptologia 10(4) October (1986) 230–242 33. Mache, Wolfgang: The Siemens Cipher Teletype in the History of Telecommunications. Cryptologia 13(2) April (1989) 97–117

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34. Mache, Wolfgang: Der Siemens-Geheimschreiber — ein Beitrag zur Geschichte der Telekommunikation 1992: 60 Jahre Schl¨ usselfernschreibmaschine. In German. Archiv f¨ ur deutsche Postgeschichte Heft 2 (1992) 85–94 35. Mache, Wolfgang: Lexikon der Text- und Daten-Kommunikation. In German. M¨ unchen: R. Oldenbourg Verlag 3rd. revised edition (1993) 36. Randell, Brian: The Colossus. In ed. N. Metropolis et al. A History of Computing in the Twentieth Century. New York: Academic Press (1980) 47–92 37. Sale, Tony: The Colossus Computer 1943–1996. Kidderminster UK: M & M Baldwin (1998) 38. Selmer, Ernst S.: From the Memoirs of a Norwegian Cryptologist. In ed. Tor Helleseth. Advances in Cryptology — EUROCRYPT ’93. New York: Springer Verlag, Lecture Notes in Computer Science 765 (1993) 142–150 39. Selmer, Ernst S.: The Norwegian Modification of the Siemens and Halske T52e Cipher Machines. Cryptologia 18(2) April (1994) 147–149 40. Tutte, William T.: FISH and I. In these proceedings. Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory. New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) 41. Weierud, Frode: Sweden, Cryptographic Superpower. A Book Review. Cryptologia 22(1) January (1998) 25–28 42. Weierud, Frode: Sturgeon, The FISH BP Never Really Caught. In these proceedings. Coding Theory and Cryptology: From Enigma and Geheimschreiber to Quantum Theory. New York: Springer Verlag, Lecture Notes in Computational Science and Engineering (1999) 43. Wermer, John: Recollections of Arne Beurling. Mathematical Intelligencer Vol. 15 No. 3 (1993) 44. Zorpette, Glenn: Breaking the enemy’s code. IEEE Spectrum 24(9) September (1987) 47–51

Documents 45. Oberkommando der Kriegsmarine: Der Geheimzusatz der Siemens-Fernschreibmaschine T.typ.52. M.Dv. Nr. 35 Geheim, Berlin Oktober 1937 46. Deutsche Wehrmacht: Schl¨ usselfernschreibvorschrift (SFV). H.Dv. g 422, L.Dv. g 704/3b, M.Dv. Nr. 924a Geheim, 1 Dezember 1942 47. Oberkommando der Kriegsmarine: Die Siemens-Schl¨ usselfernschreibmaschine SFM T52d (T typ 52 d). M.Dv. Nr. 35IV, D.(Luft) T.g.Kdos. 9105d Geheime Kommandosache, Berlin M¨ arz 1944 48. Small, Albert W.: Special Fish Report. National Archives and Records Administration RG 457 NSA Historical Collection Box 1417 Nr. 4628 (1944) 49. Campaigne, Howard: Report on British Attack on “FISH”. National Archives and Records Administration RG 457 NSA Historical Collection Box 579 Nr. 1407 (1945)

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14

Appendix A

Modified teleprinters with International Telegraph Alphabet No.2 Lower Case Code elements Upper Case (letters) 12345 (figures) A 11000 – B 10011 ? C 01110 : D 10010 ”Who are you” E 10000 3 F 10110 *) G 01011 *) H 00101 *) I 01100 8 J 11010 Bell K 11110 ( L 01001 ) M 00111 . N 00110 , O 00011 9 P 01101 0 Q 11101 1 R 01010 4 S 10100 ’ T 00001 5 U 11100 7 V 01111 = W 11001 2 X 10111 / Y 10101 6 Z 10001 + 1 00010 Carriage Return (BP 2 01000 Line Feed (BP 3 11111 Letters (BP 4 11011 Figures (BP 5 00100 Space (BP 6 00000 No Action (BP

code: code: code: code: code: code:

3) 4) 8 or –) 5 or +) 9 or .) /)

Note: *) Unassigned, reserved for domestic use.

The Geheimschreiber Secret

15

39

Appendix B Chronological List of Swedish Geheimschreiber Events ††

1940 Apr

T52a/b, first observations, to/from Norway

Jun

T52a/b, first solutions

Sep

T52a/b, first routine production

May

T52a/b, to/from German Legation in Stockholm

Jun

T52a/b, to/from Finland

Nov

SZ40 observed on cables

Jun Jul

Rumours in Berlin about Swedish breaks T52c, first observations

Sep

T52c, first solutions

Dec Jan Feb Mar Apr May Jun

New key system SZ40 on radio, first observations T52ca, first observations T52ca, first solutions SZ40 on cables, first solutions New key system SZ40 on radio, first solutions

Sep

SZ42 on radio, first solutions

Dec

T52d, first observations

Feb

No more solutions of cable traffic

Sep

T52e, first observations

Dec 40: 7100 msgs 20–30 staff 1–2 “apps”

1941

Dec 41: 41400 msgs 94 staff 10 “apps”

1942

1943

Dec 42: 120000 msgs 185 staff 32 “apps”

Dec 43: 71000 msgs 51 staff

1944

††

Reproduced with permission from FRA’s Monograph A Swedish Success [6]

Subject Index

APP, Appar, see Decoding machines, Appar Beurling, Arne, 1, 5, 7, 10–15, 18, 31, 32, 34 – Geheimschreiber, 11–13 Bit inversion, see Modulo-two addition Bletchley Park, 29–31, 33, 34 – Fish, 33, 34 – Major Tester, 33 – Newman, Max, 33 – Siemens T52, 30 Borelius, Carl-G¨ osta, 11–13, 28, 30, 32 BP, see Bletchley Park Cipher machines – Enigma, see Enigma – Geheimschreiber, see Siemens SFM, T52 – Hagelin, 13 – Japanese, 27, 30 – SZ40/42, see Lorenz SZ40/42 – T43, see Siemens SFM, T43 – T52, see Siemens SFM, T52 Ciphers – KGB, 5 – military, 5 – Russian, 31 – substitution, 32 – transposition, 31, 32 Code – Morse, 7 – Murray, 7 – Q-codes – – QEK, 11, 13, 23, 29, 30 – – QEP, 11, 13, 23 – – QRV, 11 Codes – Russian, 31 Decoding machines – Appar, 14, 15, 30 – Tunny, 33, 34 Enigma, 9, 27, 29, 30

F¨ orsvarets Radioanstalt, see FRA FRA, 11, 12, 17, 29–32, 34, 35 – cryptanalysts – – Beckman, Bengt, 30, 31 – – Beurling, see Beurling, Arne – – Borelius, see Borelius, Carl-G¨ osta – – Carlbom, Lars, 32 – – Eriksson, G¨ osta, see Wollbeck, G¨ osta – – Gyld´en, Yves, 31 – – Kjellberg, Bo, 32, 34 – – Ljunggren, Tufve, 32 – – Lundqvist, ˚ Ake, 31 – – Sydow, Olle, 31 – – Themptander, Robert, 31, 32 – – Wollbeck, G¨ osta, 31, 34 – installations, 28 – – Gr˚ a Huset, 6, 22 – – Karlbo, 6, 15, 16, 22, 28 – resources, 33 – section IV, 5, 6, 11 G-Zusatz, 29 – , see also Lorenz SZ40/42 Geheimschreiber, see Siemens SFM, T52 Geheimzusatz, see Lorenz SZ40/42 Hagelin, Boris, 13, 30 L.M. Ericson, 15 – Lindstein, Vigo, 30 Lorenz – SZ40/42, 9, 16, 24, 29, 30, 32–34, 39 Modulo-two addition, 8, 23, 34 – , see also Overlaying Nyblad, Allan Emanuel, 22, 30 Overlaying, 8, 9, 11–13, 28 Permutation, 8, 9, 11–13, 28, 29, 34 Purple, see Cipher machines, Japanese

Subject Index QEK, see Code, Q-codes QEP, see Code, Q-codes Schl¨ usselzusatz, see Lorenz SZ40/42 Siemens SFM – T43, 24, 30 – T52, 8–13, 24, 28, 34 – T52a/b, 9, 23, 24, 28, 29, 32, 39 – T52c, 9, 23, 24, 28, 29, 33, 39 – T52d, 9, 28, 39 – T52e, 9, 28, 39 Soviet intelligence, see Nyblad Sturgeon, 30, 33 – , see also Siemens SFM, T52 SZ40/42, see Lorenz SZ40/42 T52, see Siemens SFM, T52 Teleprinter, 7–8, 15, 16 Transposition – , see Permutation Tunny – , see also Decoding machines, Tunny Turing, Alan, 31 Ulfving, Lars, 1 Wahlw¨ orter, 24 Weierud, Frode, 1 Y-machine, see Siemens SFM, T43 Z-(Zusatz)ger¨ at, see Lorenz SZ40/42 Z-machine, see Lorenz SZ40/42 Z-traffic, see Lorenz SZ40/42

41

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