To study and encourage popular interest in all branches of Science.

Newsletter August 2002

Dear Member,

I enclose a copy of the Society's lecture programme for the 2002/2003 session.

The first lecture will be on Thursday 19th September at 8.15 pm in the Crypt Room at St John's Church, Church Row, NW3. It will be on Death after Life in Ancient Nubia and our speaker is Dr Margaret Judd, a Canadian who has been working for the past year in the Department of Ancient Egypt and Sudan at the British Museum.

Diary Date. Science Week 2003 will be March 7th - 16th.


P R Wallis

The earliest known cryptographic machine was invented by Leon Alberti, an Italian architect in the 15th century. He arranged the alphabet around the circumferences of two concentric discs, one smaller than the other. This provided a convenient tool for the encryption and decipherment of messages using the simple 'Caesar' substitution cipher which is mentioned in Julius Caesar's Gallic Wars and described later by Suetonius. Having only 25 possibilities, it is easy to decode. However, Alberti showed that his cipher disc could be used to generate a 'polyalphabetic' by changing the setting of the discs after each letter according to a known key-word. It becomes then a mechanized version of the 'Vigenère Cipher', more difficult to break. It came to light that Babbage broke it in 1854, though the first publication of the method was by F W Kasinski in 1863.

In 1918 the German inventor Arthur Scherbius and his friend Richard Ritter set up an innovative engineering company. One of their developments was a piece of cryptographic machinery, essentially an electrical version of Alberti's cipher disc. Called 'Enigma', Scherbius' invention would become the most fearsome encryption machine in history.

The machine has three parts: a keyboard, a scrambler and a lamp display board. In the simplest form the scrambler is a rubber disc (the 'rotor') riddled irregularly with wires which changes the plain-text letter to the cipher-text letter. Scherbius' idea was for the scrambler rotor to rotate for each letter encrypted, achieving a polyalphabetic cipher with 26 different alphabets. However, every 26th letter uses the same alphabet, which would be a serious weakness once discovered. Scherbius therefore used three rotors, clocking round as in a mileometer, giving a total of 26 x 26 x 26 = 17,576 distinct scrambler arrangements. He also added a 'reflector', to send the electrical signal back through the rotors. This doesn't increase the number of alphabets, but it makes the procedure for decryption identical to that for encryption. All signalmen have the same machine, but need to know the initial settings of the rotors to use each day, the 'day-key'. He went further. He made the three rotors interchangeable, increasing the number of possible initial settings by a factor of 6. He also added a 'plug-board' to swap 6 pairs of letters out of the 26; this multiplied the number of keys by 100,391,791,500! Overall there were some
10,000,000,000,000,000 keys.

Such an encryption system cannot be broken by the technique of frequency analysis. He believed it to be impregnable.

His patent was filed in 1918, but did not meet with immediate commercial success. However the German military were shocked into appreciating the importance of such a machine by the revelations in 1923 by Winston Churchill (in his book 'The World Crisis') and the Royal Navy's 'Official History' of the first world war that their ciphered messages had been broken. So, in 1925, enigma went into service in the German military; they bought over 30,000.

Cracking the Enigma

The Allies, secure in their victory, made very little effort to break the new cipher but Poland, squeezed between the Soviet Union's ambition to spread communism and Germany's desire to regain the territories ceded to Poland, were desperate for intelligence information. They were able to determine the design of the enigma machine, with the help of the French intelligence authorities and a disaffected German. But that was only a first step which the Germans expected anyway. The real security lies in the key: the scrambler sequence, the scrambler initial orientations and the plug-board arrangement for each day.

The breakthrough at the Polish Biuro Szyfrow was made by the young mathematician Marian Rejewski. He realized that a weak point lay in a repetition occurring in the German messages. They had appreciated that the more messages they sent using a single key, the easier it would be for cryptanalysts to break the system by statistical techniques. They therefore changed their key everyday. But in addition, they provided a different individual key for every individual message. At the beginning of every message they sent three letters for new initial orientations of the three rotors, but not changing the rotor arrangement or the plug-board; this was the 'message key', as distinct from the 'day key'. It ensured that only a limited amount of text had a particular key. But they sent it twice to ensure it was safely received. It was of course protected by the day key encryption, but the repetition was a weak point. Rejewski saw that the 1st and 4th letters of the cipher text originated from the same letter, ditto for the 2nd and 5th, 3rd and 6th . He discovered that there was one very abstruse pattern* which was dependent on the scrambler settings alone. Having access to a replica Enigma machine, he was able to catalogue all possible patterns for the 105,456 settings; it took a year to do this. As the number of messages built up each day, he was able to deduce the settings for the day key. Establishing the plug-board settings, though larger in number, was less difficult. The Poles were able to read Enigma for most of the 30's!

By 1938, German cryptographers increased the Enigma security. The operators were given two additional rotors, so the number of arrangements, 3 out of 5, increased to 60.They also increased the plug-board cables from 6 to 10. The number of possible keys became:

The Poles recognized that they did not have the facilities to crack this improved Enigma system and, with Germany withdrawing on 27th April 1939 from its non-aggression treaty with Poland, they sought the help of the British and French . On 24th July, British and French cryptanalysts visited the Polish Biuro to see their feats; two spare Enigma replicas were offered, one of which reached London on the 16th August in the baggage of Sacha Guitry and his wife. Two weeks later, Germany invaded Poland.

Bletchley Park, which the HSS visited in 2000, became the center of burgeoning activity, with more staff and resources than the Poles could have found. They were able to find other weaknesses in the practical use of Enigma. Operators were liable to pick obvious rather than random keys for the message keys, eg QWE from the keyboard or their girlfriend's initials. They also discovered that the system deliberately avoided a rotor being in the same position on consecutive days; this reduced the number of options by a factor of 2. Enigma kept changing and the team of cryptographers at Bletchley were "like a pack of hounds trying to pick up the scent"(Gordon Welchman in charge of Hut 6). If any is to be singled out, it is Alan Turing, who identified Enigma's greatest weakness and ruthlessly exploited it.

He followed Rejewski's strategy of separating the search for rotor settings from the determination of plug-board settings. He ignored the message keys as he expected the Germans to cease the repetition. Instead he used 'cribs', guesses at plain text words and phrases, such as 'wetter' appearing in regular weather reports. He also mechanized the use of loops by connecting three enigma replicas in series and wiring them to cancel the effect of the plug-board. He produced, at a cost of £100,000, an emulator with 12 sets of linked Enigma scramblers, which he called 'bombes' after the earlier Polish machines. The first arrived on 14th March 1940 but was too slow. Four months were to go by before an improved design was available and, in the meantime, the Germans dropped the message key repetition. Within 18 months there were15 more bombes in operation and by the end of 1942, 49. Even if the code-breakers guessed a plain text crib, they had to associate it with the correct bit of cipher text before the bombes could be used. Fortunately there was another characteristic of the Enigma machine that could be used to provide a check. The presence of the reflector meant that no plain text letter could be translated into itself. Thus the crib could be slid along the cipher text until no letter was the same in both; the longer the crib, the better it worked.

There were several different Enigma networks. The Naval one was the most difficult, having a choice of 8 rotors and a reflector variable in 26 positions. More techniques were required if the U-boat was to be beaten in the battle of the Atlantic. In one, mines were sown by the RAF so that German messages would report the map reference for use as a crib. Raids were made to capture German code books.

Overall, Bletchley Park was able to obtain vital information which avoided defeat in the U-boat war and many other operations. Sir Harry Hinsley wrote, "The war, instead of finishing in 1945, would have ended in 1948 had the Government Code and Cipher School not been able to read the Enigma ciphers and produce the Ultra intelligence".

Hitler used an even more impressive machine, the Lorenz SZ 40, to communicate with his generals. Though based on Enigma it set Bletchley a task beyond the capability of Turing's bombes. Eventually Max Newman designed a more flexible and powerful machine drawing heavily upon Turing's concept of the universal machine. It was shelved at first on the grounds of impossibility, but taken forward by Tommy Flowers in the Post Office Research Station at Dollis Hill. Colossus, the world's first computer, was delivered to Bletchley Park on 8th December 1943. But that, and the whole future story of encryption and electronic security is another story.

Finally, I must reveal my source. It is Simon Singh's book The Code Book- the secret history of codes and code-breaking, 2000, Fourth Estate. He also wrote Fermat's Last Theorem and lectured for our Science Week this Spring. Many thanks.

Selected References

*: He constructed 26-letter rows comparing the 1st and 3rd letters. He then followed a chain using the rows alternately until the original letter appeared again. His great insight was that the pattern of the lengths of the loops was independent of the plug-board settings. Back

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Last updated by Julie Atkinson   28-Jan-2018