Here I would like to mention Bill Tutte. He was handed intercepts by frustrated code breakers taken from a machine that could generate 1.6 billion difference combinations and employed 12 wheels with 41 settings on each wheel, and based on teleprinter code and binary. With a pencil and rectangular sheets of paper he soon realised that the magic number was 41, the prime number of 574. He had arrived at the conclusion that there was a 574 line 'refresh rate' but knew that was too long and narrowed it to 41. In November 1942 he successfully cracked the Lorenze Machine. One of the early successes of Bill was he learnt of the impending major push against the Red Army near a place called Kursk. Not only times, but dispositions and directions of attack. England was able to warn Russia of this and they were ready when Germany attacked.  Kursk went down as the biggest tank battle in history and also the biggest aerial battle. I also mention a man, a GPO engineer called Tommy Fellows, who not long after this invented the worlds first computer.

Regarding Collossus, the first computer. After the war Churchill said that Collossus had been dismantled. But 2 survived and were then installed in GCHQ and were used into the 1960s. In 1946 the Americans claimed to have invented the computer. The fact they we already had TWO in operation seems to have escaped their attention. Tommy Fellows is the name of the man who invented the computer. Read and weep Americans!!!

Bletchley Park, remarkably, never saw a Lorenz machine until after the war. All was done by hand and by the 'tunny machine'. Bill Tutte must never be forgotten for his monumental expertise and achievements. Bill Fellows was decorated by the Canadians for his work, but has never been recognised here in the UK, a very dismal state of affairs. In June 1993 he went to a local college to learn how to use a computer and was awarded a certificate!! Tommy died in 1998.

Tunny Machine

As the number of intercepts, now being made at Knockholt in Kent, increased a section was formed in Bletchley Park headed by Major Ralph Tester and known as the Testery. To understand Lorenz the team needed something known as depths, when 2 or more messages were intercepted using the same key at source. This was realised when a tired operator in Greece was asked to re-transmit a large message as part of it had not been received. He did this, but failed the change the key. This was what we had been waiting for. The unknown German operator also abbreviated some words in the second transmission, giving a small but obvious change in the 'order'.

After nearly 4,000 characters had been keyed in at the sending end, by hand, the operator at the receiving end sent back by radio the equivalent, in German, of "didn't get that — send it again".

They now both put their Lorenz machines back to the same start position. Absolutely forbidden, but they did it. The operator at the sending end then began to key in the message again, by hand. If he had been an automaton and used exactly the same key strokes as the first time then all the interceptors would have got would have been two identical copies of the cipher text. Input the same — machines generating the same obscuring characters — same cipher text. But being only human and being thoroughly disgusted at having to key it all again, the sending operator began to make differences in the second message compared to the first.

The message began with that well known German phrase SPRUCHNUMMER — "message number" in English. The first time the operator keyed in S P R U C H N U M M E R. The second time he keyed in S P R U C H N R and then the rest of the message text. Now NR means the same as NUMMER, so what difference did that make? It meant that immediately following the N the two texts were different. But the machines were generating the same obscuring sequence, therefore the cipher texts were different from that point on.

The interceptors at Knockholt realised the possible importance of these two messages because the twelve letter indicators were the same. They were sent post-haste to John Tiltman at Bletchley Park. Tiltman applied the same additive technique to this pair as he had to previous Depths. But this time he was able to get much further with working out the actual message texts because when he tried SPRUCHNUMMER at the start he immediately spotted that the second message was nearly identical to the first. Thus the combined errors of having the machines back to the same start position and the text being re-keyed with just slight differences enabled Tiltman to recover completely both texts. The second one was about 500 characters shorter than the first where the German operator had been saving his fingers. This fact also allowed Tiltman to assign the correct message to its original cipher text.

Now Tiltman could add together, character by character, the corresponding cipher and message texts revealing for the first time a long stretch of the obscuring character sequence being generated by this German cipher machine. He did not know how the machine did it, but he knew that this was what it was generating! This is but a minute sprinkle of information. For a more detailed study please visit the excellent site linked below.

http://www.codesandciphers.org.uk/lorenz/fish.htm

The logical functioning of the Tunny system was worked out well before the Bletchley Park cryptanalysts saw one of the machines—which only happened in 1945, shortly before the allied victory in Europe.

The Lorenz SZ machines had 12 wheels each with a different number of cams (or "pins").

Wheel number 1 2 3 4 5 6 7 8 9 10 11 12
BP wheel name[10] 1 2 3 4 5 37 61 1 2 3 4 5
Number of cams (pins) 43 47 51 53 59 37 61 41 31 29 26 23


The SZ machine served as an in-line attachment to a standard Lorenz teleprinter. It had a metal base 19 in (48 cm) × 15.5 in (39 cm) and was 17 in (43 cm) high.[8] The teleprinter characters consisted of five data bits, encoded in the International Telegraphy Alphabet No. 2 (ITA2). The enciphering machine generated a pseudorandom character-by-character key that was XOR-ed with the input characters to form the output characters.

Each of the five bits (or "impulses") of the key for each character was generated by the relevant wheels in two parts of the machine. The Bletchley Park analysts called these the ("chi") wheels, and the ("psi") wheels. Each wheel had a series of cams (or "pins") around them. These cams could be set in a raised (active) or lowered (inactive) position. In the raised position they generated a '1', in the lowered position they generated a '0'.

The chi wheels all moved on one position for each character. The psi wheels also all moved together, but not after each character. Their movement was controlled by the two ("mu") or "motor" wheels. The SZ40 61 wheel moved one position with each character, but the 37 wheel moved on only when the cam on the 61 wheel was in the active position. If the cam on the 37 wheel was in the active position, all five psi wheels then moved. The SZ42A and SZ42B models had additional complexity to this mechanism, known at Bletchley Park as Limitations.

The key stream generated by the SZ machines thus had a chi component and a psi component that were combined together with the XOR function. Symbolically, the key that was combined with the plaintext for enciphering—or with the ciphertext for deciphering—can be represented as follows.
 

Key = Chi-Key Psi-Key

The number of cams on each wheel equalled the number of impulses needed to cause them to complete a full rotation. It should be noted that these numbers are all co-prime with each other, giving the longest possible time before the pattern repeated. With a total of 501 cams this equals 2501 which is approximately 10151, an astronomically large number. However, if the five impulses are considered independently, the numbers are much more manageable. The product of the rotation period of any pair of chi wheels gives numbers between 41×31=1271 and 26×23=598.

Operation

Each "Tunny" link had four SZ machines with a transmitting and a receiving teleprinter at each end. For enciphering and deciphering to work, the transmitting and receiving machines had to be set up identically. There were two components to this, setting the patterns of cams on the wheels and rotating the wheels for the start of enciphering a message. The cam settings were changed less frequently before the Summer of 1944. The psi wheel cams were initially only changed quarterly, but later monthly, the chi wheels were changed monthly but the motor wheel patterns were changed daily. From 1 August 1944, all wheel patterns were changed daily.

Initially the wheel settings for a message were sent to the receiving end by means of a 12-letter indicator sent un-enciphered, the letters being associated with wheel positions in a book. In October 1942 this was changed to the use of a book of single-use settings in what was known as the QEP book. The last two digits of the QEP book entry were sent for the receiving operator to look up in his copy of the QEP book and set his machine's wheels. Each book contained one hundred or more combinations. Once all the combinations in a QEP book had been used it was replaced by a new one. The message settings should never have been re-used, but on occasion they were, providing a "depth", which could be utilised by a cryptanalyst.

As was normal telegraphy practice, messages of any length were keyed into a teleprinter with a paper tape perforator. The typical sequence of operations would be that the sending operator would punch up the message, make contact with the receiving operator, use the EIN / AUS switch on the SZ machine to connect it into the circuit, and then run the tape through the reader. At the receiving end, the operator would similarly connect his SZ machine into the circuit and the output would be printed up on a continuous sticky tape. Because this was the practice, the plaintext did not contain the characters for "carriage return", "line feed" or the null (blank tape, 00000) character.

British cryptographers at Bletchley Park had deduced the operation of the machine by January 1942 without ever having seen a Lorenz machine, made possible because of a mistake made by a German operator.  https://secure.wikimedia.org/wikipedia/en/wiki/Lorenz_Cipher - I always state, when qutonig from Wikipedia, that you should not take every word as gospel. There are errors in every version I have read. I have on my virginmedia tv 'tivo' box a program saved from on code breakers, some of which is quoted in my first paragraphs above. As the information in this tv programme is given to us by Bletchley Park themselves I prefer to trust their details.

Interesting footnote to Tommy Fowler. In 1993, he bought his first desktop computer but could not work out how to use it, so he enrolled in an evening class and was awarded a certificate!! Tommy died in 1998.

Enigma Code Machine