Editing Colossus computer (section)

==Purpose and origins==
{{See also|Cryptanalysis of the Lorenz cipher}}
[[File:LorenzSZ42at TNMOC.jpg|thumb|left|upright=1.5|A Lorenz SZ42 cipher machine with its covers removed at [[The National Museum of Computing]] on [[Bletchley Park]]]]
[[File:SZ42-6-wheels-lightened.jpg|right|upright=1.8|thumbnail|The [[Lorenz cipher|Lorenz SZ machines]] had 12 wheels, each with a different number of [[Cam (mechanism)|cam]]s (or "pins").
{|class="wikitable" style="margin: auto auto auto auto"
|-
! Wheel number
|1||2||3||4||5||6||7||8||9||10||11||12
|-
! BP wheel name{{sfn|Good|Michie|Timms|1945|loc = 1 Introduction: 11 German Tunny, 11B The Tunny Cipher Machine, p. 6}}
| style="text-align:center;"| ''ψ''<sub>1</sub>
| style="text-align:center;"| ''ψ''<sub>2</sub>
| style="text-align:center;"| ''ψ''<sub>3</sub>
| style="text-align:center;"| ''ψ''<sub>4</sub>
| style="text-align:center;"| ''ψ''<sub>5</sub>
| style="text-align:center;"| ''μ''<sub>37</sub>
| style="text-align:center;"| ''μ''<sub>61</sub>
| style="text-align:center;"| ''χ''<sub>1</sub>
| style="text-align:center;"| ''χ''<sub>2</sub>
| style="text-align:center;"| ''χ''<sub>3</sub>
| style="text-align:center;"| ''χ''<sub>4</sub>
| style="text-align:center;"| ''χ''<sub>5</sub>
|-
! Number of cams (pins)
|43||47||51||53||59||37||61||41||31||29||26||23
|}
]]

The Colossus computers were used to help decipher intercepted radio [[teleprinter]] messages that had been [[encryption|encrypted]] using an unknown device. Intelligence information revealed that the Germans called the wireless teleprinter transmission systems ''"Sägefisch"'' (sawfish). This led the British to call encrypted German teleprinter traffic "[[Fish (cryptography)|Fish]]",{{sfn|Good|Michie|Timms|1945|loc = 1 Introduction: 11 German Tunny, 11A Fish Machines, (c) The German Ciphered Teleprinter, p. 4}} and the unknown machine and its intercepted messages "[[Lorenz cipher|Tunny]]" (tunafish).<ref>{{cite book |chapter=PART THREE: Fish |chapter-url=https://books.google.com/books?id=j1MC2d2LPAcC&pg=PA139 |title=Codebreakers: The Inside Story of Bletchley Park |first1=F. H. |last1=Hinsley |first2=Alan |last2=Stripp |date=2001 |publisher=Oxford University Press |access-date=26 October 2017 |via=Google Books |isbn=978-0-19-280132-6}}</ref>

Before the Germans increased the security of their operating procedures, British cryptanalysts [[Cryptanalysis of the Lorenz cipher#Diagnosis|diagnosed]] how the unseen machine functioned and built an imitation of it called "[[Cryptanalysis of the Lorenz cipher#British Tunny|British Tunny]]".{{sfn|Hayward|1993|pp=175–192}}

It was deduced that the machine had twelve wheels and used a [[Vernam cipher]]ing technique on message characters in the standard 5-bit [[ITA2]] telegraph code. It did this by combining the [[plaintext]] characters with a stream of [[Key (cryptography)|key]] characters using the [[XOR]] [[Boolean function]] to produce the [[ciphertext]].{{fact|date=March 2025}}

In August 1941, a blunder by German operators led to the transmission of two versions of the same message with identical machine settings. These were intercepted and worked on at Bletchley Park. First, [[John Tiltman]], a very talented GC&CS cryptanalyst, derived a [[keystream]] of almost 4000 characters.{{sfn|Budiansky|2006|pp=55–56}} Then [[Bill Tutte]], a newly arrived member of the Research Section, used this keystream to work out the logical structure of the Lorenz machine. He deduced that the twelve wheels consisted of two groups of five, which he named the χ (''[[chi (letter)|chi]]'') and ψ (''[[psi (letter)|psi]]'') wheels, the remaining two he called μ (''[[Mu (letter)|mu]]'') or "motor" wheels. The ''chi'' wheels stepped regularly with each letter that was encrypted, while the ''psi'' wheels stepped irregularly, under the control of the motor wheels.{{sfn|Tutte|2006|p=357}}

[[File:Lorenz Cams.jpg|left|upright=1.5|thumbnail|Cams on wheels 9 and 10 showing their raised (active) and lowered (inactive) positions. An active cam reversed the value of a bit (0→1 and 1→0).]]
With a sufficiently random keystream, a Vernam cipher removes the natural language property of a plaintext message of having an uneven [[frequency distribution]] of the different characters, to produce a uniform distribution in the ciphertext. The Tunny machine did this well. However, the cryptanalysts worked out that by examining the frequency distribution of the character-to-character changes in the ciphertext, instead of the plain characters, there was a departure from uniformity which provided a way into the system. This was achieved by [[Cryptanalysis of the Lorenz cipher#Differencing|"differencing"]] in which each bit or character was XOR-ed with its successor.{{sfn|Good|Michie|Timms|1945|loc = 1 Introduction: 11 German Tunny, 11C Wheel Patterns, (b) Differenced and Undifferenced Wheels, p. 11}} After Germany surrendered, allied forces captured a Tunny machine and discovered that it was the [[electromechanical]] [[Lorenz cipher|Lorenz SZ]] (''Schlüsselzusatzgerät'', cipher attachment) in-line cipher machine.{{sfn|Good|Michie|Timms|1945|loc = 1 Introduction: 11 German Tunny, 11A Fish Machines, (c) The German Ciphered Teleprinter, p. 4}}

In order to decrypt the transmitted messages, two tasks had to be performed. The first was "wheel breaking", which was the discovery of the cam patterns for all the wheels. These patterns were set up on the Lorenz machine and then used for a fixed period of time for a succession of different messages. Each transmission, which often contained more than one message, was enciphered with a different start position of the wheels. Alan Turing invented a method of wheel-breaking that became known as [[Turingery]].{{sfn|Copeland "Turingery"|2006|pp=378–385}} Turing's technique was further developed into "Rectangling", for which Colossus could produce tables for manual analysis. Colossi 2, 4, 6, 7 and 9 had a "gadget" to aid this process.{{sfn|Good|Michie|Timms|1945|loc = 24 – Rectangling: 24B Making and Entering Rectangles pp. 114–115, 119–120}}

The second task was [[Cryptanalysis of the Lorenz cipher#Steps in Wheel Setting|"wheel setting"]], which worked out the start positions of the wheels for a particular message and could only be attempted once the cam patterns were known.{{sfn|Good|Michie|Timms|1945|loc = 1 Introduction: 11 German Tunny, 11E The Tunny Network, (b) Wheel-breaking and Setting, p. 15}} It was this task for which Colossus was initially designed. To discover the start position of the ''chi'' wheels for a message, Colossus compared two character streams, counting statistics from the evaluation of programmable Boolean functions. The two streams were the ciphertext, which was read at high speed from a paper tape, and the keystream, which was generated internally, in a simulation of the unknown German machine. After a succession of different Colossus runs to discover the likely ''chi''-wheel settings, they were checked by examining the frequency distribution of the characters in the processed ciphertext.{{sfn|Small|1944|p=15}} Colossus produced these frequency counts.