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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.
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Why Build Colossus? (Bill Tutte) - Computerphile

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林宜悉 發佈於 2020 年 3 月 28 日
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