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  • >> Sean: You've got this guy, Bill Tutte, with his team of people - or the team of people who

  • he was working with - and they have cracked this code. Why do they need computers?

  • Where did Colossus come in? >> DFB: Colossus came in because the sheer amount of counting

  • that you had to do was enormous. You were basically, in the end, looking for the

  • occurrences of dots (or zeros) in, well 41 * 31 * 5 times whatever [settings to try out] ...

  • You know, you might be able to afford to get the whole Research Section doing just one

  • little bit of it, but day in day out? All you wanted to do was to look for

  • patterns and count out the number of zeros within them. And you need a

  • computer! It doesn't matter if it's a special-purpose computer - which Colossus was.

  • When they first realized this they tried to go back to Enigma-type

  • technology: "Oh! we understand about relays and uniselectors. let's build something

  • electromechanical". It was called Heath Robinson, and for those of you in North

  • America Heath Robinson is the direct [UK] equivalent of Rube Goldberg.

  • They were both cartoonists that drew impossibly complicated electromechanical

  • machines, and made cartoons, out of them So, there's this huge amount of stuff to

  • be counted up but electro-mechanically, when they tried to do it, it couldn't go

  • fast enough. It would take days. And they tried to speed the machines up and they

  • just went up in blue smoke. And eventually I think Alan Turing had

  • worked with Tommy Flowers from Dollis Hill GPO [General Post Office]. He'd worked

  • with them for some aspects of the Enigma decode but as we know [for] Enigma

  • electromechanical was just about OK. But Turing said: "Why not let's get

  • in Flowers for an opinion and Max Newman who was by then head of Research Section, said:

  • "All right, bring him in and we'll have a chat. And Flowers took one look at it and said: "You will

  • never get it fast enough to do what you want electromechanically. Forget it!

  • We've got to go electronic and use valves". And of course there was a huge [outcry]: "Flowers

  • are you off your head?! We all know valves, they go 'bang'

  • every few minutes! They're not reliable." I think I've said this before [but] I'll say it

  • again: Tommy said to them "I've been doing research on use of thermionic valves in

  • telephone exchanges and I can tell you they can be remarkably reliable so long

  • as you never turn them off". And it's particularly the heaters on the cathodes.

  • If you bring those up to voltage very quickly so they instantly go red or

  • white hot the filament will [often] go 'bang', but if you bring them up very carefully, from

  • dull red to bright red, and all that... And then, at the end of the day, don't switch

  • them all off. Lower the voltage and do that very very carefully. You will

  • minimize the number of thermionic valve blowouts you get and so, basically, the

  • message was 'Never ever turn them off and it'll be fine'. And in the end it was. And

  • the electronic speeds were just about enough. But it still took ... a typical run

  • on Colossus to discover Initial Settings on a pair of wheels might take 10

  • minutes, something like that. And you've got to do that for five different pairs.

  • So, y'know you're taking about an hour to work out settings, if you didn't know

  • them alread. Standing Orders said: 'You must never take more than two hours'. If

  • you haven't got it sorted by then, on the settings, give up [and] go to another message.

  • But then, if you knew the settings but didn't know the wheel patterns that was

  • a huge amount of effort [that] was needed. In fact Frank Carter reckons 10 hours of

  • Colossus time to establish what the patterns of 1s and 0s were on the

  • wheels. Now you've realized why they ended up with 10 Colossi at Bletchley Park.

  • They got a huge amount of work to do. And you mustn't also run away with the idea

  • that Colossus could do absolutely everything. It couldn't. The great

  • majority it could, but it relied on this slight statistical disparity, there were

  • always more 0s than 1s. And look for what [wheel] setting make that happen.

  • But just occasionally a rogue message would come in where it just happened to

  • be 50:50, and there wasn't a skew or a bias.

  • And then you have to throw that one away and say: "We'll come back to that later".

  • So it wasn't 100% but it was good enough to make a decisive difference to

  • the war. Yes, it seems weird doesn't it that it's not 50:50 between 0s and 1s?,

  • in a regime where we're doing exclusive-ORs. Well, what you've got to

  • remember is if you exclusive-OR something with itself you get a bunch of

  • 0s. But whatever it is, if you exclusive-OR all those together, if they're identical

  • the exclusive-OR, on a character basis, will be five 0s and to make those

  • show up at Bletchley they denoted it with a /, if you remember.

  • OK, well, that's all very well but that ... so how would that lead to a bias, a skew ?

  • Answer: in many many languages, not the least German and not the least

  • English which, as we must remember is a Germanic language, you get doubled

  • letters, OK? So, Sean, if I say to you - I'm guessing - the probability of 'z' in English

  • is 1/100 what's the probability of getting two z's? 1/100 times 1/100?

  • >> Sean: Well, hat would be the mathematical answer >> DFB: Yeah! Yeah! if they're all independent it will

  • be 1/10000. But they're not! Double 'z'' is far more common, even in

  • English let alone in German. than one in 10,000. Really, you know, 'dazzle, 'puzzle', all

  • these kind of things. It's not massively common, as a bigram,

  • but it's more common than the base probabilities would indicate. Double p's

  • as well: "happy, slapping, flappy". All these kind of things. So character doubling was

  • one of the vital components of saying that if you look on a certain stream and

  • it's a 0, and you look on the adjacent streams from 2 to 5 and it's a 0 as

  • well, then it's a null character. And that could have been generated by having one

  • thing exclusive-ORd with it's identical thing. So, on a bitstream basis they

  • adapted that and said the reason we are seeing

  • more 0s is that if you slide these bitstreams over each other by one bit

  • and exclusive-OR, them you'll find that double-letter occurrences lead

  • eventually to more 0s coming out than 1s, because on the nature of exclusive-OR,

  • - if something is the same as something else and you exclusive-OR it - it gives

  • 0s not 1s. So, it's a bit rough and ready and hand-wavy, there's more to it

  • than that but that is just one example of how the language structure itself can

  • do you in. And it's reported that the German cryptanalysts realized that this

  • would be a weakness of the Lorenz cipher but they said: "We're not to worry, it

  • would need you to build a machine and they'll never be able to do that. There'd be

  • so much data it will kill 'em! You'd need roomfuls of people and even

  • within a month they wouldn't do it. But what they didn't foresee was the advent

  • of machines with electronic speeds, not just electromechanical ones, and that

  • could just about get on top of it.

>> Sean: You've got this guy, Bill Tutte, with his team of people - or the team of people who

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