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.

Flaw in the Enigma Code – Numberphile
Tagged on:                                                     

100 thoughts on “Flaw in the Enigma Code – Numberphile

  • December 7, 2018 at 6:31 am
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    Apparently it takes around a minute for an average home computer to break the 3 rotor setup (with the exploit, not through brute force). I'm very impressed that the Bomb machine from the 1940s was only 20 times slower than what exists today.

    Reply
  • December 19, 2018 at 11:15 am
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    And how long would take a modern PC to brute-force enigma code? 🙂

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  • December 21, 2018 at 4:30 pm
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    Polish codebreakers crack enigma code. NOT TURING!!! (to uneducated people)

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  • December 22, 2018 at 5:02 am
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    oh bee-have

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  • December 23, 2018 at 10:18 pm
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    Analysis by exception: very powerful.

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  • December 28, 2018 at 9:19 pm
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    Enigma MAchine EM 33.
    100% Fakery

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  • January 2, 2019 at 12:20 pm
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    So there are 10 pairs and 26 letters. What if lets say B is not plugged to any other letter. Can B become itself in this case?

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  • January 2, 2019 at 8:09 pm
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    Could modern computers break the enigma code easily?

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  • January 4, 2019 at 12:33 pm
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    Demonetized.

    Reply
  • January 6, 2019 at 12:11 am
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    Why didn't the allies figure out the surprise of the battle of the bulge offensive?

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  • January 12, 2019 at 3:16 pm
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    6:33 listen closely.

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  • January 16, 2019 at 9:34 pm
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    so advanced back then, third grade science now lol

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  • January 29, 2019 at 6:05 pm
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    Did the Germans think that the rule that a letter could not become itself strengthened rather than weakened the code?

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  • February 2, 2019 at 11:23 am
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    6:48 20 million years circa.

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  • February 5, 2019 at 12:07 am
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    Why only ten pairs there are 26 Ietters

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  • February 5, 2019 at 8:15 pm
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    well..i am 35 and i acumulated enough information here and there,i know stuff.but for a young boy,like between 10 and 20 this channel is AMAZING .the amount of info you can find here and how well is explained.oh i wish we had teachers like this and youtube vids to complement school.keep doing this stuff forever

    Reply
  • February 6, 2019 at 4:29 pm
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    Please also do WPA2 decryption…

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  • February 7, 2019 at 8:54 am
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    Nothing against Alan Turing, but it would not have taken me a year to break the Enigma machine…

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  • February 10, 2019 at 9:13 pm
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    Another flaw was the rotors were in numerical order according to the movie.

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  • February 11, 2019 at 12:58 am
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    I heard it was the Poles who originally designed the bombs.

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  • February 12, 2019 at 3:47 pm
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    Imagine the responsibility on those code breakers and the folks who make use of the info contained. They couldn't just show up where some secret attack was to take place because very quickly it would give away that we've broken their code. The dogs of war.

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  • February 14, 2019 at 12:37 am
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    How things have changed. Everyone has access to algorithms now like AES that when implemented correctly can't be broken yet by anyone, not even by the military.

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  • February 15, 2019 at 8:31 pm
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    Just something: I don't really care for math usually but the excitement and fascination that Dr Grimes delivers the information with is contagious. I find myself engaged in a manner that doesnt usually happen when math is involved and thats something special. I try to remember that when I'm teaching my own children….that excitement, curiosity and fascination can be inspired in others.

    A sincere thank you from me to all of you! Very well done!

    I'm not new to Brady's work or numberphile but it still amazes me how effective these videos are at teaching concepts. I went too long without saying thanks, imho.

    Reply
  • February 17, 2019 at 11:18 pm
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    That's not wang it's number Wang!

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  • February 18, 2019 at 1:27 am
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    I've come up with an unbreakable cypher.
    So the Enigma Machine was cracked because of its flaw of no letter returning itself, right?
    If you make letters be able to return themselves, as the British did, then it's harder to crack, right?
    What's better than sometimes? Always.
    Make every letter always return itself.
    Uncrackable.

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  • February 18, 2019 at 6:00 pm
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    1:37 jojo reference

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  • February 18, 2019 at 6:15 pm
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    The University of Manchester has a building named after Alan Turing. It would an honour to study mathematics there

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  • February 18, 2019 at 8:06 pm
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    '"this is called a contradiction" wow I'm learning so much

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  • February 19, 2019 at 12:05 am
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    8:42 what was that?

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  • February 19, 2019 at 3:26 am
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    you made me like maths and I hate my self for liking maths

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  • February 19, 2019 at 10:06 pm
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    Fantastic overview of Enigma, I didn't know about the plugboard ramping up the permutations!
    On a tangential; how USA treated Alan Turing after his HUGE contribution, was abominable.

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  • February 19, 2019 at 10:06 pm
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    "What could you put in to make it more secure?" An ssl certificate.

    Reply
  • February 19, 2019 at 10:32 pm
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    Well, two hours at Bletchley Park museum and left with a blank cortex. Think…I have at least the basic concept thanks to the Doc! How fortunate we are in Europe to have our innovation culture.

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  • February 20, 2019 at 2:26 pm
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    It's always the little things that get ya!

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  • February 20, 2019 at 4:03 pm
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    (late) Question: that any letter never translated to itself – was enigma designed that way or was it a mathematical consequence out of the setting itself? I Mman in theory if all circuits were really kind of random, then shouldn't once in a while a letter k translate to itself? And if it was designed that way: how did the germans made sure this never happened? and why did they designed enigma that way, when it should be no weak point, if once in a while a latter translated to itself? (because: why not. You can never be sure which letter translated to itself, so in the end it doesn't matter anyway..)

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  • February 20, 2019 at 11:05 pm
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    Simple solution to the Enigma flaw. [1] push key [2] push key corresponding to the letter that lights up [3] write down the 2nd letter down
    now a letter can represent itself because you double encrypted.

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  • February 21, 2019 at 6:53 pm
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    Thing is, if letter can be itself, in THEORY there is possibility that Enigma actually codes the message to same as original

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  • February 21, 2019 at 9:00 pm
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    So basically, if you went back in time and made it so the enigma machine can make letters be themselves, whilst avoiding the chance of a message just straight up not being encrypted because of random chance, the enigma code would most likely never have been cracked.
    But then again, maybe it would still have been cracked, since there were cycles of letters. We may never know unless we try (under heavily regulated restrictions for safety and in a proper environment like a simulation obviously) Maybe add some nice additions like numbers as well as cables that connect 3 character and have them switch amongst eachother every now and again based on rotation inside the machine and what characters were changed previously, with previously being ever changing depending on rotation among other things.

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  • February 21, 2019 at 11:13 pm
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    You should have given a little more credit to the Polish who encoded the first Enigmas and were the fundemental to break the military Enigma.

    Reply
  • February 22, 2019 at 12:12 pm
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    at 8:45 – something is encoded to the audio track of this video. can any body tell what?

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  • February 22, 2019 at 8:48 pm
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    Absolutely brilliant! Love content like this!
    Amazing videos, mate! The way he is presenting it, it's pretty clear that he loves the stuff and loves presenting it as well. His energy make sit even better…

    Reply
  • February 23, 2019 at 8:56 am
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    0:39

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  • February 24, 2019 at 6:22 am
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    I am going to download both of these videos go back in time and show it to the Fuhrer.

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  • February 24, 2019 at 5:14 pm
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    i think my brain is dripping out of my ear.

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  • February 24, 2019 at 5:58 pm
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    when does the american english version comes out

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  • February 24, 2019 at 6:15 pm
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    How did they figure out that a letter couldn't become itself?

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  • February 25, 2019 at 4:30 pm
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    how did the germans compare both the machines if they didnt know about the flaw and if they did y did they not fix it in their own..

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  • February 25, 2019 at 7:07 pm
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    This makes no sense to me.

    Reply
  • February 25, 2019 at 11:45 pm
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    The British should have called it the X-Box instead of the X-Machine, they would have made a fortune.

    Reply
  • February 26, 2019 at 8:15 am
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    no such thing as clever or win or find or not, think any nmw and any be perfect

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  • February 26, 2019 at 5:14 pm
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    Now I want to write a program and see how long it would take modern household computer to break the code the clever way, and then the bruteforce way.

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  • February 26, 2019 at 6:47 pm
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    I thought type X was developed in Camp X in Canadia with coop of Americans and brits

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  • February 27, 2019 at 2:02 am
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    I understand how (pe) can be deduced from (ta). But I don’t understand the 3 further deductions. I suppose if you keep inputting t, via an understanding of the rotor settings, you can work out that you’ll get k, then x, then t. But how do you deduce that k then becomes q? Or that x then becomes b / t becomes g? As the first one was because we knew that t must lead to e based on the code vs ‘german weather report’ phrase but i’m not sure how we subsequently know t overall goes to q and then b and then g. Would appreciate an explanation! Thanks!

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  • February 27, 2019 at 10:18 am
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    A shot for every time he says "plugboard"

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  • February 27, 2019 at 11:50 am
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    So the flaw is. German compound words. Appearing frequently in military terminology.

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  • February 28, 2019 at 11:46 am
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    Another big Enigma's flaw whas that it's commercial version could be bought without much problem.

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  • March 1, 2019 at 12:12 am
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    I'd love to hear something about how this flaw was discovered.

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  • March 1, 2019 at 8:39 pm
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    please remember that three Polish gus broke enigma code before the WW2 has started, and later during the war they give codes to brithish etc

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  • March 1, 2019 at 9:13 pm
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    The Bombes were designed by the Poles, not the British. The Poles cracked Enigma and then gave the intelligence on how to their French and British counterparts.

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  • March 2, 2019 at 7:13 pm
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    Ya know the best part about Enigma?
    You can just add more rotors and some misc symbols (like @, #, or %) to increase the amount of combinations.
    It can still be broken, but it'd be extra difficult.

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  • March 7, 2019 at 7:12 am
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    Youre a pos for cutting that vid off like that imma block ur channel after this 😂

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  • March 10, 2019 at 5:14 am
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    Grey does not have this flaw

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  • March 11, 2019 at 12:53 am
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    What the heck do you do for a living ??
    I am a machinist by trade and can't imagine what field of…. you are in just a curiosity

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  • March 11, 2019 at 7:34 am
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    i love this guy

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  • March 12, 2019 at 10:50 pm
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    That moment when the fake is better than the original. Happens rarely.

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  • March 16, 2019 at 1:30 am
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    leave it to the Brits to just sorta touch on the Polish who did 99% of the work

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  • March 17, 2019 at 11:02 pm
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    There was another flaw in that the rotors were numbered chronologically instead of randomly, this also proved to be an Achilles heel when breaking Enigma. 🐵🤓🤡

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  • March 18, 2019 at 12:51 pm
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    I wonder how they found out a letter could not be itself?

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  • March 21, 2019 at 8:17 am
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    Why dont british capture a german radio operator and ask him how its work

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  • March 22, 2019 at 9:16 am
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    My question is assuming the machine had initially made a wrong assumption about a letter and found a contradiction later, how could Turing eliminate the intermediate encryptions ?

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  • March 27, 2019 at 5:47 pm
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    To learn true history always check the sources first. Three Polish matematicians: Marian Rejewski, Jerzy Różycki and Henryk Zygalski cracked the Enigma in the first place. Greetingd fae Scotland!

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  • March 28, 2019 at 12:06 pm
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    Just great! I love this type of stuff, thank you so much for explaining it.

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  • March 31, 2019 at 3:20 pm
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    Why doesn’t it have the letter ß

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  • March 31, 2019 at 7:51 pm
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    Absolutely mind blowing.
    Showing the kind of exceptional mind that Turing had.
    Such a shame that the prejudices of the day, led to the destruction of that same mind.

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  • April 15, 2019 at 11:51 am
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    I think thats a solid "Wetterbericht"^^ unless you pronounced the ch a little bit wrong.
    I guess its because this element does not appear in english.
    Its more like a hiss than a sharp k, but the sound is made in the same area as the k.

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  • April 15, 2019 at 11:40 pm
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    I am German, and I think your German is perfect

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  • April 22, 2019 at 3:54 am
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    to be honest this isnt hard to understand 😉

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  • April 23, 2019 at 4:28 am
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    The Enigma code had no flaw, the problem was the users.

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  • April 23, 2019 at 10:19 pm
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    but why nobody tought of this option well a human mistake i dont want to know what would happened when this mistake wouldn't be made

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  • May 5, 2019 at 5:41 pm
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    When you say built the bomb you have overlooked Tommy Flower? Tommy played a very important role

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  • May 10, 2019 at 8:27 pm
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    I wonder how big a bomb would have to be to break SHA-3

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  • May 12, 2019 at 10:17 am
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    Poles built the bomb first!

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  • May 16, 2019 at 12:06 am
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    How do you know typing T all those times after should result in q, b and then g? Help me Numberphile please this is for a project.

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  • May 19, 2019 at 6:37 pm
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    How did the British know a letter would not translate onto itself once put through the code?

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  • May 25, 2019 at 7:34 am
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    Did he say "My German is very bad" in German, or did he say something else?

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  • May 27, 2019 at 10:10 pm
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    +1+00500+1+1+

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  • June 11, 2019 at 2:32 pm
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    Ah, so they were sending their messages in German so we couldn't read them… Sneaky Germany, very sneaky!

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  • June 29, 2019 at 8:26 pm
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    1:40 "Mein Deutsch ist sehr schlecht, entschuldige"

    Reply
  • June 30, 2019 at 12:06 pm
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    JAMES IS SO CUTE

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  • July 8, 2019 at 12:06 am
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    I wish numberphile taught all my maths

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  • July 8, 2019 at 1:57 am
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    Alan Turing didn’t break the Enigma first.

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  • July 25, 2019 at 2:20 am
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    1:20 why would you encrypt weather report?

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  • August 9, 2019 at 2:38 pm
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    So the Polish were the first ones to break the code and the British take credit for it. Sounds about right

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  • August 11, 2019 at 12:15 pm
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    Why wouldn't a letter become itself?

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  • August 13, 2019 at 4:24 pm
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    If you always keep the rotors set to AAA does each key always produce the same letter?

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  • August 20, 2019 at 1:43 am
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    wouldn't the flaw be really easy to fix? At the reflector portion of the machine, couldn't they just have two letters loop
    back to themselves so it would sometimes be the same letter?

    Reply
  • August 20, 2019 at 1:53 am
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    wait so if the only flaw in enigma was that a letter could map back to itself then wouldn't the typeX machine be unbreakable?

    Reply
  • August 20, 2019 at 6:49 pm
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    so glad the decided to do a bigger follow up video, so interesting.

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  • August 21, 2019 at 12:07 am
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    Can anyone tell me why the Enigma machine used the English alphabet instead of the German alphabet? It doesn't have the extra 4 letters from the German alphabet

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  • August 21, 2019 at 12:34 am
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    Side note: I laughed out loud in The Imitation Game when Denniston was interviewing Turing and asked how old he is and he said 27, meanwhile Benedict Cumberbatch is clearly in his 40's 😂😂

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