Placeholder Image

字幕表 動画を再生する

  • We've done one already I think called the ... mentioning the Tiltman break and it's

  • got to the stage, now, where somebody comes and says: "Remind us. What was the

  • Tiltman Break. Why was it so important?" and so on. The Tiltman Break exploited a

  • weakness in any cipher that's based on bitwise exclusive-OR, as indeed all the

  • Tunny traffic exactly was - just that - I suppose I could very briefly - and not

  • using too much notation to frighten computer scientists - but just as

  • a reminder. What happens with exclusive-OR, which I'll denote with a + in a

  • circle. And effectively what happens with it is that if you take a piece of

  • plaintext and you add on to it a key character, what you'll end up with is an

  • enciphered version of that plain character. And it's all done with bitwise

  • exclusive-OR. And if you say: "Well, in what code are these characters expressed?" then,

  • in what we're talking about in the middle 1940s, it was the International

  • Teleprinter Code, five-hole, which had been well known for quite a few years,

  • since the '20s I think. And it was used for telegrams, telex, transatlantic

  • communications and so on. So what happens, then, is if you take something and

  • exclusive-OR it with something else - a 5-hole tape character - you will get

  • encrypted text. If you look at that and then visit the ZigZag Decryption video,

  • where Sean and I've done an even simpler example, you'll find out how

  • zig-zag decryption works. You get a bit of Plaintext#1 one, it predicts Plaintext#2

  • The Plaintext#2 goes on a little bit further and then that predicts a bit

  • more of Plaintext#1. And you flip-flop between the two streams. That's why it's

  • called zig-zag decryption. So, using zig-zag decryption on all of

  • three thousand characters, very early on in this game,

  • the Allies really had got an absolute bonanza here. Because if you then go back

  • and say: "Well, look, we know the plaintext now, we know what ciphertext we received,

  • exclusive-OR tells us that 'plaintext' + 'ciphertext' gives 'key'. We've got

  • 3,000 characters-worth of key, So why was it called the Tiltman break? Well, it

  • was called the Tiltman break because Colonel John Tiltman, who was a

  • mathematician as well as being a military man, knew about the properties

  • and the weaknesses of exclusive-OR. And he knew that under addition, like this,

  • the key would cancel out and you could use this zig-zag techniquea. He did it and it

  • took him 10 days and he was a German expert as well.

  • He had enough mathematics knowledge but was a serious military-German expert.

  • We do make it painfully easy - and we do wave our hands and greatly oversimplify it.

  • You've got to remember that, in real life, what happens is you start zig-zagging and

  • then, suddenly, your German expert says:"Oh dear! I can't see that that's the start

  • of a new German word! Oh dear!" And, in the end, you might get blocked. But not often

  • because what you can then do is look further along the message and see if you

  • can guess another "island" [of plaintext] in the middle. It might be 'geheim'. That was another

  • good word: 'secret'. Why not drag 'geheim' through the D-stream with exclusive-OR

  • and see if you get something looking like 'geheim' at the same place below

  • it, in the other one [e.g. plaintext #2]. So, you got islands of decrypted stuff. And your job was to

  • link the islands and get everything - including the less common German words

  • that had appeared. And in the end Tiltman did it. 10 days it took him. I think it

  • would have taken him a lot less if he had to do it a second time, obviously,

  • because you get the hang of the zigzag technique. So Tiltman had done all this

  • work. But I think, for a month or two in the Research Section, nobody could

  • figure out what on earth sort of machine it was that could be generating stuff

  • that looked like this. So new recruit Bill Tutte, from Cambridge - enrolled for

  • a Chemistry degree, not Mathematics, but very keen on

  • recreational mathematics. He was given the job and he decided that having learned

  • at cipher school that if you think that there could be a periodicity in the

  • cipher then you'd better start looking for what period, what repetition rate it

  • was on . And prior to being put to work on this Tiltman Break he'd worked on a

  • similar cogs-based ciphering machine - a Swedish one called the Hagelin machine.

  • And I think it's fair to say that there's enough similarity there that is:

  • "Oh yeah! maybe it's a cogs machine? Prime numbers of [teeth on the] cogs because we've discovered

  • the prime, or relative prime, of the numbers of [teeth on the] cogs is the magic formula.

  • And he said: "OK the head of the section - Gerry Morgan - has told me that they have reason

  • to believe that one of the cogs in this machine has got 23 teeth on it". So, we've

  • covered in another video how he started looking for 23 but accidentally found 41 [teeth].

  • However there is something following on after that which is intended to

  • randomize it sufficiently well that it will disguise the 41. But it's not been

  • done well enough and occasionally the 41-icity of this is breaking through the murk

  • and convincing us that that's right. So, he announces this to the rest of the

  • Research Section and they go mad for several weeks trying to find out what

  • the [teeth numbers on the ] other streams must be. Because, don't forget, it's teleprinter code. Five

  • streams 1 2 3 4 5 but looks like some kind of two-stage mechanism. There's an

  • initial attempt to encrypt this but then there's a follow-up that's trying

  • to disguise the periodicity of all these wheels. Well after a lot of effort by all

  • the Research Section they cracked it. So here is what happens. You feed in an

  • ordinary teleprinter character into this adaptor. It goes through the first set of

  • wheels which Bill Tutte - in all the things I have read nobody explains why - he decided he

  • would call the first set of wheels the 'chi wheels' The Greek character

  • chi which is written out like that [draws character on paper] and the second set that follows on

  • afterwards, there they are look, here's the first set that is then passed on

  • into a second set of wheels which he called the psi wheels. And there's the

  • character psi. And those psi wheels were meant to give an extra element of

  • disguise as to exactly what it was the chi wheels were doing and to make

  • decryption that bit harder. Chi wheels put out a certain pattern of 1s and

  • 0s which gets exclusive-OR'd with the incoming character. They then all turn on

  • All the chi wheels always move in synchrony, together. But that doesn't get boring

  • because there's different numbers of teeth on these wheels. I mean here on

  • stream 1 there's the famous 41. Next wheel along has got 31 teeth, then 29 26

  • - not prime but relatively prime to all the rest - [then] 23. That first stage encryption

  • then travels onto the psi wheels. But the designers the machine thought it

  • would make it even harder for the Allies if we make it so that the psi wheels don't

  • always move on with every character. Let's put in a 'stutter' mechanism - or at

  • least that's what the decryptors came to call it. Sometimes they move and sometimes

  • they don't. OK that will make it harder?

  • Actually, in the end, it made it easier, as several statisticians pointed out. But that was

  • the way it was and the reason that Bill Tutte was able to prevail, and to see 41,

  • was that the psi-wheel patterns were really bad. And by 'really bad' I mean they

  • left the second set of wheels not rotating for 5. 6, 7 characters

  • on end. Y'know they didn't change the pattern at all! So, you've got this great

  • thing where very clearly it was been exclusive-OR'd in the second stage with

  • the same thing over and over and over again. And if that gets up to 6 or

  • 7 times, it's basically saying [that] it's only a single-stage machine again

  • because the second stage isn't varying fast enough. Bill Tutte

  • said: "Thank heavens for this. We were so lucky in the war. Number one the

  • Tiltman Break: that chap [the machine operator] should not have sent that message again and [thereby] given us

  • 3200 characters of key, potentially. But what really finished

  • them was that they failed to disguise the periodicity of the chi wheels

  • because they had inadequate psi wheel patterns that let great long unaltered stretches

  • come through. And that's what gave us just enough evidence that we could work

  • out that the psi wheels had got 43 47 51 53 59 and so on. So we won't go into

  • the details of precisely how that calamity occurred. Let's just say that

  • whoever was in charge of psi-wheel movements really goofed in the early

  • stages and as Tutte again says, it didn't matter that when we came back

  • later they [had] put their error right and made it better in future. By that time we

  • knew the periodicity of the wheels. So the only worry then was - and another of

  • Bill Tutte's colleagues, and later his PhD supervisor actually, a guy called

  • Shaun Wylie, who was down the hill in Hut 8, with Alan Turing and various other

  • worthies was brought up the hill, along with Jack Good and Donald Michie. People

  • were brought from Hut 8, and Naval Enigma, to help out with Tunny. And Sean Wylie, in

  • one of his writings about this, says: "Do you know the thing that panicked us

  • straight after finding out this wonderful layout of the machine [was] let's

  • hope these wheels were not interchangeable!" Could you imagine if

  • instead of having 41 31, so on, down here, it was possible to pick them out

  • and put them in different slots and permute them, like on Enigma, and he said:

  • 'Thank heavens after analyzing several weeks of traffic we were convinced these

  • things were fixed; it was always going to be 41 31 whatever. So that's one big worry

  • out of the way. So that was more or less the situation that was left then. You'd

  • got this fabulous break - the key subtracted itself out; there was

  • enough indications in there to work out what the periodicity of the wheels was -

  • and they're all relatively prime to each other - but where do we go from here?

  • Whenever somebody uses the same initial settings

  • which they shouldn't do - they're ordered not to do it - if ever this happens again and

  • gives what Bletchley Park calls a 'depth' - - and you remember the famous,

  • absolutely famous, indicator setting of the Tiltman Break was HQIBPEXEZMUG,

  • 12 characters. Yeah, well, that was how they knew it was worthwhile exclusive

  • or-ing them because the operator, the next time round when he repeated it, sent

  • out this thing [again] saying: 'my settings are HQIBPEXEZMUG'. So, you know it's

  • worthwhile exclusive or-ing them together seeing what you can find out.

  • So, they relied absolutely on the fact that in the early days - and up until mid to late

  • 1942 - the operators were told to send out the Indicator so the other end knew how

  • to set the wheels relative to one another.

  • What they didn't do except very infrequently, thank heavens, was to change

  • what's called the 'patterns' on the wheels. It's probably about time we said a

  • little bit more about that. What I've drawn out for you here on that diagram

  • is the simplest wheel of all with the fewest teeth that was 23. Here is my

  • notional starting point and you can see I've numbered them 01, 02, 03, 04.

  • So, just imagine, that after every exclusive-OR character that

  • contributes, this wheel is moving clockwise around from 6 to 7. And then it

  • moves to position 8 and so on. The dot means this is contributing a 1 when it

  • comes around to the start position. And otherwise it contributes a 0. So these

  • things, the the dots, are called the 'patterns' on the wheels.

  • Now, again, a huge stroke of luck for the Allies. It was such a pain

  • setting up all of these wheels, all 12 of them, with different patterns, and you had

  • a little slider to slide a ratchet up and down, as to whether it was 1 or 0, that

  • the Germans only changed the patterns every month. Phew! that meant that you had

  • one month to try and get depths - you know things where the person had

  • used the same Indicator twice. It may not be as a repeat of the same,

  • exactly same, message. That really was an absolute gift from on high.

  • Typically, though, an operator would say: "I've used HQIBPEXEZMUG, you know, that one

  • [that message] was about 'Parachute dispositions in Salonica' Oh! there's another one here I've got

  • to send which is about when General Katzenzinger next has his leave break.

  • Oh! what Indicator should I use there? Oh well! let's use this one again. They'll never decrypt

  • this it doesn't matter. So, very often, your zigzag was not between two similar

  • messages it was between two very different messages. But at least they'd

  • use the same settings. That, again, explains why you needed German [language] experts around to

  • say: "Oh! y'know, yes, that is the start of something or other [significant] down here".

  • So, that was the name of the game. Hope that the lazy operators give you depths by using

  • the same indicators. Then Bill Tutte came up with an extra method in late '41,

  • I think and said: "I know. Let's try and look for 'near depths' because a slightly less

  • lazy operator would say HQIBPEXEZMUG, we're not going to use

  • the same one twice. I'll only change one of them [Indicator letters]. It's such a faff.

  • Let me just change one of them. Now if only one of those settings was

  • changed and if it happened to be on a first stage chi wheel, Bill Tutte pointed

  • out that from the other four [chi settings] that you knew were the same as the last time, and

  • only one has changed, you can, with some mind-bending

  • attention to complexity and the help of German experts sitting next to you, say

  • it's not ZMUG at the end it's RMUG. So have we got any other messages, from

  • earlier on, that we've part-broken which had R in that position? Who knows?

  • That might help. So, he said, typically you might end up

  • with 20 or 30 possibilities, once you'd propagated this 'R not Z'

  • through all the morass of stuff that you've got. And he said but, yeah, with the

  • help of some really good German [linguist] guys that could work. And that was more

  • evidence, you see, because that could be backtracked into working out what the

  • wheel patterns were a bit more. So I think the feeling in the Research

  • Section was: 'This is OK so long as they keep sending out the Indicator settings'

  • But we need a lot more techniques to get us out of trouble if that isn't the case.

  • Well, everybody knows, of course, that Turing did everything at Bletchley Park.

  • Nobody else was of any importance at all :-) And I hope that one of the things that

  • this set of videos may be doing for you is to emphasize that, very important

  • though he was, he didn't do absolutely everything. One of the problems with the

  • secrecy, particularly in the late 70s and early 80s when this

  • news about Bletchley Park began to trickle out - but a lot was still under

  • the Official Secrets Act - is that some computer scientists, historians and

  • writers very incautiously started saying: "Oh well! If Turing took what the Poles

  • did for Enigma and developed it on, and then did Naval Enigma and got that

  • sorted out, he's such a genius it stands to reason it must have been him running

  • the whole Tunny / Lorentz / Colossus show". No - not true! I think our friend and

  • colleague, Jack Copeland, whose book you see up there, 'Colossus', would be the first

  • to want me to say: "No - Alan Turing had nothing to do with Colossus! Colossus was

  • purely Tommy Flowers." He [Turing] did make a contribution towards the decrypting Tunny effort

  • and it was a very very helpful one.

  • Here we are, in early '42, there's been the Tiltman break. Bill Tutte has worked back

  • from that, and the Research Section helped him to find out the disposition

  • of the wheels on this Tunny ciphering machine. What was the problem? Because

  • every message sent out on that machine had an indicator, showing the start

  • positions of all of the cogwheels. The bigger problem was the worry that the

  • patterns on the wheels - the patterns of 0s and 1s - a lot of people spent a

  • lot of brainpower working back through depths, where people had used the same, you

  • know, Indicator twice, trying to backtrack through the key text into saying: "What

  • does this mean about what the patterns are?" And, in the end, if you gathered

  • enough evidence - and certainly with the Tiltman break there was so much evidence

  • there they really did get the whole thing sorted out. They managed to work

  • out, for that month, exactly what all the wheel patterns must have been. [It] took a lot

  • of people a lot of effort, by hand. But it was done. But the worry was we're gonna

  • more and more be saying: "We want to get the patterns". At the moment we're saved

  • by the fact that we have a month to build up, and analyze, evidence before it

  • changes again. So, you know, let's say for a typical example, start of August, you

  • start collecting evidence as to what this month's patterns must be. You look

  • for depths. You've got all the indicators and by maybe August 20th, or

  • mid-August if you're very lucky, you've got enough evidence to work out

  • what the patterns on the wheels are for this month. Then you go back to all the

  • stuff that was transmitted earlier in the month, that you didn't understand. But

  • now you've got the patterns you can go back and see what the messages were. And

  • so long as the developments in the war are not happening at a breakneck pace

  • then the fact that this intelligence was two weeks old didn't matter too much.

  • Because it was high-quality intelligence. Remember this is Hitler's High Command