DR. JAMES GRIME: So in our first
Enigma video, we left you on a bit of a cliffhanger. I was just about to
show you the flaw in the Enigma machine. Now, that video was only meant
to be a short follow-up video. But when we saw the reaction to
our first Enigma video, we decided to come in and film
again to show you how that flaw worked and how they
broke the Enigma code. Now, if you want to see the
original Enigma video-- it shows you how the Enigma
machine worked-- go check that out. We'll put the links in
the description. But now let's have a
look at that flaw. So here's the Enigma
machine again. Now, if I press the letter K-- there we go-- the letter
Q lights up this time. Now, if I keep pressing the
letter K, a different letter lights up each time. So a double-letter
would not be a double-letter in the code. So it's a very good
code indeed. But it is never K itself. So this was the flaw. A letter never becomes itself. So A is not A, B is
not B, and so on. Z is not Z. This is a clue. So the way you break the Enigma
code is, if you imagine you have an Enigma message, you
try and guess a word or a phrase that might appear
in that message. Now, every morning, 6 o'clock
in the morning, the Germans would send a weather report. Now, that was a standard form. That was always the same
every day, apart from the actual weather. It was always a standard
format. So we can pick a word that's
going to be in that weather report. We might pick the word or phrase
"weather report," or "Wetterbericht" in German. And I apologize now if I've
translated that badly. [SPEAKING GERMAN]. Now, I'm going to write
"Wetterbericht" on a piece of paper. BRADY HARAN: That's
"weather report." DR. JAMES GRIME:
That's "weather report" there in German. Here, I've got an Enigma code. And I'm going to slide my guess
underneath the code. Now, I'm going to try
and find where this phrase fits in the message. Now, I know a letter can't
become itself. So it can't fit here, because
I have a T becoming T. So that's not where it fits. Let's try this. Can it fit here? No. I've got this T matching
with T again. Let's try here. No, I've got no matching,
no matching. From what I can see, no matching
letters there. So it might fit there. If I tried that-- see, those R's match up,
so it can't fit there. So maybe it's here. Maybe this is the phrase
"weather report." Now, from this point, we can start
breaking the Enigma code. So you could use different
phrases. Try and imagine what a German
officer would send in World War II. So for example, messages would
end with "Heil Hitler." So is it "Heil Hitler" at the
end of the message? Now, if it is, we shouldn't have
any letters matching with "Heil Hitler"-- H's, E's, I's, L's. What the British code breaker
Alan Turing had to do was find a way to use this flaw to
break Enigma messages. So he built a huge machine
called the Bombe machine. It was designed by Alan Turing
and another code breaker called Gordon Welchman. It was a big machine,
noisy thing. It would rattle around. And this could help you break
the code in under 20 minutes. So you would have to break
the code every morning. So every morning, the settings
for the Enigma machine would change. So all the Enigma
machines would change stroke of midnight. So that's why a machine that
could break the code that quickly was so important. So the Bombe machine tried to
work out the plug board at the front of the Enigma machine. If we go back, at the front of
the Enigma machine, we have this thing called the plug board
that connects letters into pairs. You actually make 10
pairs of letters. When I press a letter, the
signal first goes through the plug board. It then goes through the first
rotor, through the second rotor, through the
third rotor. It then loops back, and it goes
through the machine again in reverse order. So then it goes through the
third rotor, the second rotor, the first rotor. And finally, it goes through the
plug board one more time, and it lights up one
of these bulbs. Now, I'm going to try and
draw it up for you. But I'm going to make it
as simple as I can. Let's try and do that. So first of all, it goes
through the plug board. Then it goes through
all the rotors. And I'm going to call that just
one big magic box called R for rotors. And the last thing it
does is it goes through the plug board. If we look at our weather report
here, let's look in the second place. T becomes E. Let me do that. If I press T, it goes through
the plug board, through all the rotors, through the plug
board again, and out comes E. Now, we're going to use this
to work out the plug board. I'm going to make one guess. I'm going to guess
T is connected to A on the plug board. That's a guess, but I'm
going to use it. So let's say that means that T
goes through the plug board, and out comes A. Now, A goes through
the rotors. Now, we know how the rotors
are wired up. So we know that. We pick a position and find out
what happens to A. That's not hard to do. And I don't know-- let's
make something up. Let's say it comes out as P. But
if I do that, I can deduce that P goes through the plug
board and becomes E, which means I can deduce that
P is connected to E on the plug board. Now, that's pretty cool. So you've worked out one of
the plug board settings. If that diagram works, P
must be connected to E. So I've done this a few more
times doing the same method, using my weather report crib. And I've discovered a few more
plug board settings. So the first one we discovered
was P-E. Now I've discovered K and Q are connected
on the plug board. I've discovered X and B are
connected on the plug board. And I've discovered T and G are connected on the plug board. But this last one
is a problem. I've discovered that
T and G are connected on the plug board. But I guessed that T and A were connected on the plug board. And it can't be both. This is called a
contradiction. It can't be both T-A and
T-G at the same time. This means my guess,
the T-A, was wrong. Throw it away. I got it wrong. Now I'm going to check the
next one-- what, T-B? I might check T-C, T-D. I have
to do all 26 options-- T-A, T-B, T-D, T-Z. If all the
26 options are wrong, that means your rotor position
is wrong. And what do is you go, click. You check the next rotor
position, and you go through all that again. Now, that would take
a very long time. So Alan Turing came up
with two ways to make this a bit quicker. The first one-- a really clever idea. He noticed that once you've
found one mistake, like T-A and T-G, this means that all
these other deductions are also wrong, and they don't
need to be checked. So they're all fruit
of a poisoned tree. They can all be rejected
at the same time. And you don't need to
check them again. So that really speeds it up. The other way to speed it
up is you can do this instantaneously with electrical
circuits. So that's what the Bombe
machine did. It applied an electrical current
to my assumption, T-A. The electrical current flows
through the machine. It flows through T-G,
which means wrong. But it'll also flow through all
these other deductions, which means I can find all my
deductions, which are all wrong, and I can do it
instantaneously with electrical circuits. And then it will go, click,
and check the next. And it could go through all the
rotor positions in about 20 minutes. So the main thing to remember is
the Bombe machine is built a little bit backwards. It's a process of elimination. So what you're left with
is what wasn't wrong. And you would actually
check that by hand and see if it works. The Bombe machine was named
in honor of a Polish code breaking machine,
called Bomba. Bomba was a completely different
machine, worked on a completely different
principle. It wasn't a huge machine. You could sit it on your
desk if you wanted to. And it exploited a flaw in
the German procedures. Now, they could use Bomba, the
Polish could use Bomba, to break army and air force
Enigma codes. But they couldn't break
naval Enigma codes. So what Alan Turing had to do
was find a way to break army, air force, and navy
Enigma codes. And it had to be a bit more
robust so that if the Germans choose to change their
procedures, that this method would still work. What the navy was doing
differently is the rotor starting positions were actually
sent at the beginning of each message, but they were
sent in another code entirely. So it was a completely different
code just to send the rotor starting positions. So you needed to work out how
that worked, as well, before you could even start breaking
the naval code. BRADY HARAN: Is there anything
that the makers of the Enigma machine could have done to have
avoided this problem? Was there some simple thing that
the Enigma makers could have put into that device there,
and it would have not been broken like this? DR. JAMES GRIME: Well, hindsight
is a fabulous thing. You wanted to make it so that a
letter could become itself. That was the flaw. And so the British saw Enigma. They said, that's a good idea. We'll have that. They nicked the idea. We saw Enigma, and we decided
to make one of our own. We called it the Typex
machine, except we took out the flaw. So a letter could sometimes
become itself. This made it a more
secure machine. Now, from what I've heard,
the Germans tried to break our code. But they concluded that it was
better than the Enigma machine, so they
gave up trying. At least that's what
I've heard. It's very difficult
to know for sure. It was all very secret. BRADY HARAN: So if you've
watched our original video about how the code machine works
and this one, and you still want more, I've got a
third video with all the extra material and off-cuts, which
isn't listed, but you can find the links here on the
screen and in the video description below. The bits of brown paper used
in these videos can also be found on our eBay site for
people who like to get their hands on them. And if you've watched all the
Enigma videos and all the Numberphile videos and you
still want more, can I recommend my chemistry channel,
Periodicvideos? Because recently, we got our
hands on a super high-speed camera and filmed a bunch of
reactions so we can show them in ultra slow motion. The videos are really
cool, and there's loads more to come. Go and have a look if it sounds
like something you might like. All the links are below in the
video description and here on the screen. And as usual, thanks so
much for watching. Talk to you again soon.
If you liked these videos, PBS did a documentary on it called "Decoding Nazi Secrets". It's very hard to find, unless you visit a certain Bay, but NOVA has an entire transcript of the episode for those of you who don't mind reading.
numberphile is the shit
He doesn't clarify how much work the "flaw" saves. If the flaw didn't exist then you couldn't line up the known string and the code and find legal positions. You could still do all of the other steps for every substring, instead of just the legal substring positions, right?
The first video explains how the Enigma actually works, but I never understood it nearly as clearly until I printed a paper version and played with it. That version doesn't have the plugboard swapping steps, though - just the rotors.
I'm not clear on how that chain of deduction worked. Wasn't it composed entirely of guesses?
We assumed (t,a) but then didn't we also assume (k,e) (x,b) and (t,g) or whatever?
"The Code Book" by Simon Singh is a great source for this topic.
So is the British rectified Enigma machine uncrackable (since the matching letters trick doesn't work)?
Love it. Stuff like this really interests me