[00:02.140 --> 00:04.820]  We'll start with the part everybody knows.
[00:05.100 --> 00:06.120]  This is Alan Turing, of course.
[00:06.340 --> 00:09.420]  He's the father of modern computer science.
[00:09.640 --> 00:15.000]  And he was the mastermind behind the German Enigma cipher in Bletchley Park in World War II.
[00:15.800 --> 00:20.940]  This is his famous machine, the bomb machine, first installed in March 1940.
[00:21.900 --> 00:26.480]  And it helped the team at Bletchley Park decrypt Enigma messages much faster.
[00:28.700 --> 00:39.120]  And his work and his team's work at Bletchley Park helped shorten the war by two to four years and saved 15 to 20 million lives, according to historians.
[00:40.040 --> 00:41.940]  So, let's start at the beginning.
[00:42.840 --> 00:45.160]  The Enigma machine was invented in 1918.
[00:46.360 --> 00:54.880]  It was first invented for commercial use for banks or diplomats, not as a military invention.
[00:56.220 --> 01:05.420]  It was first invented by the Schifferer Maschinen, Acting Gesellschaft Company, which is German for the Cypher Machines Corporation.
[01:05.860 --> 01:14.980]  Keep in mind, I'm going to be saying a few words in languages I don't speak, so please allow my mispronunciations.
[01:17.120 --> 01:19.400]  This is the Enigma model C here.
[01:19.560 --> 01:20.520]  It's an original photo.
[01:22.380 --> 01:27.640]  It's an original photo taken by that company because there are no surviving models.
[01:27.940 --> 01:32.960]  It is the commercial Enigma that is most similar to the Nazi Enigma 1.
[01:35.260 --> 01:36.600]  So, let's move on.
[01:38.420 --> 01:41.660]  So, the Enigma machines were simple circuits.
[01:41.660 --> 01:51.960]  They simply took a key press on the keyboard and connected the signal from that key through a circuit to a certain lamp.
[01:52.920 --> 01:58.720]  What made them special was their ability to scramble the lamp that the key connected to.
[01:59.700 --> 02:17.240]  So, when one presses a key on the keyboard on the Enigma, the signal goes from the keys to the rotors, where each rotor has a carefully constructed scramble of wires in it.
[02:17.240 --> 02:21.160]  So, the rotors are labeled 1, 2, and 3.
[02:21.800 --> 02:22.960]  Disregard these labels here.
[02:23.900 --> 02:28.780]  The rotors are labeled 1, 2, and 3 with an actual label on the outside.
[02:30.700 --> 02:35.180]  And so, the order of these rotors could be changed.
[02:35.320 --> 02:43.760]  It could be hot swapped by the operators of the Enigma as a setting used in the machine.
[02:44.240 --> 02:48.200]  So, every rotor 1 was the same between all the different Enigma machines.
[02:48.980 --> 02:50.660]  Every rotor 2 was the same, and so on.
[02:51.360 --> 02:53.720]  So, the signal would go from the keyboard to the rotors.
[02:54.880 --> 02:56.980]  It would go into one of the contacts on the rotors.
[02:57.020 --> 02:59.660]  It would go to the other side, its position scrambled.
[03:00.480 --> 03:03.520]  Then it would happen the same for rotor 2 and rotor 3.
[03:03.920 --> 03:09.880]  It would reach the reflector, which pairs the 26 letters of the alphabet into 13 pairs.
[03:10.440 --> 03:19.480]  That means that when a letter goes in, let's say A, it could be paired to letter Z, and it would be returned back through the rotors backwards.
[03:20.060 --> 03:22.440]  Then that signal would finally go to the keyboard.
[03:27.660 --> 03:35.720]  So, importantly, what this does is, for every setting on the Enigma machine, for example, right now it's set to 25, 23, and 7.
[03:36.260 --> 03:41.960]  For every setting, the keys are paired into 13 pairs.
[03:41.960 --> 03:46.980]  That is, if you press the letter A at a certain setting, and it output as G.
[03:46.980 --> 03:50.340]  If you press G at that same setting, it would output as A.
[03:51.420 --> 04:08.180]  That also means that a letter cannot be encrypted as itself, which, while famously was a cryptographic blunder, it was known and it was allowed because of the ease of use for the Enigma machine it allowed for.
[04:08.180 --> 04:21.720]  Which is that, on two ends, if there's Operator A and Operator B, if Operator A sends a message with some starting settings, Operator B, as long as they have those same starting settings, they can decrypt the message.
[04:21.880 --> 04:22.840]  They don't need to change anything.
[04:26.220 --> 04:34.380]  So, this is the Nazi Enigma one, first introduced in 1930, and became widespread across the military in 1932.
[04:34.920 --> 04:41.640]  It is very similar to the Enigma Model C, except for this addition of a plug board at the front of the machine.
[04:43.600 --> 04:50.400]  The plug board is very important to the actual encryption of the Enigma, and what made it so difficult to solve.
[04:51.440 --> 05:04.680]  The way it works is, a signal will go from the keyboard, the plug board would intercept it, then the signal will go to the rotors and back through, and then the plug board would intercept it once again, and then that would go to the lamp board.
[05:05.700 --> 05:10.720]  On the plug board, you could pair any two letters with an actual physical plug.
[05:11.080 --> 05:25.920]  And so what that does, if you have X and Y paired, and A and B paired, if you press the letter X, it will go into the rotors as if you had pressed Y, And then if we got an output of A from the rotors, it would go through the plug board and go to the BLAMP.
[05:29.720 --> 05:40.920]  So, this allowed for significantly more difficult encryption.
[05:41.300 --> 05:48.760]  So, with only three cables on the plug board, there are 3.5 million different pairings you can do.
[05:48.760 --> 05:50.820]  With five, it turns into 5 billion.
[05:51.540 --> 05:53.160]  With five cables, it's 5 billion.
[05:55.000 --> 05:59.840]  Now, with all these settings, there's only four settings each Enigma operator needs to know.
[06:00.220 --> 06:02.460]  They would need to know the pairings on the plug board.
[06:02.960 --> 06:06.180]  They would need to know the actual rotor rotations.
[06:07.140 --> 06:11.100]  They would need to know the order of the rotors, what order you put them in.
[06:11.980 --> 06:14.700]  And they would need to know what's called the ring setting.
[06:15.820 --> 06:20.040]  Each rotor on the Enigma had a letter ring on it.
[06:20.620 --> 06:24.380]  For the Army and Air Force Enigmas, it would be numbers.
[06:24.800 --> 06:26.620]  For the Naval Enigmas, it was letters.
[06:27.920 --> 06:32.120]  This letter ring could be turned with respect to the internal wiring.
[06:32.460 --> 06:33.580]  That's called the ring setting.
[06:34.060 --> 06:42.400]  What that does is the ring itself isn't doing anything, but it changes the point at which a rotor can turn over the next rotor.
[06:42.400 --> 06:54.920]  So the rotors are normally counting in base 26, but if you change the ring setting, the next rotor could cycle when this rotor is at position 8, for example, instead of position 1.
[06:57.900 --> 07:05.740]  Now, to encrypt and decrypt messages, as long as both senders have those settings correct, then everything will work.
[07:06.300 --> 07:09.580]  And they'll both be able to encrypt and decrypt the message sent.
[07:11.700 --> 07:16.640]  Let's look at the first decryption attempt at Enigma.
[07:17.960 --> 07:25.580]  So, importantly, military Enigmas had different wirings within the actual rotors than the commercial Enigmas.
[07:25.580 --> 07:32.060]  So this would be something that a codebreaker would need to know.
[07:32.220 --> 07:38.500]  They would need to deduce the internal wirings of the reflector and of the actual rotors.
[07:40.000 --> 07:45.160]  So, the Polish were actually the first working on Enigma, not Alan Turing.
[07:45.160 --> 07:47.960]  They started work in 1932.
[07:49.640 --> 08:05.780]  And through just looking at the actual sent ciphertexts and with their own commercial Enigma they had bought previously, they were able to deduce all the internal wirings of the rotors and the reflector, even without a military Enigma of their own.
[08:06.500 --> 08:13.640]  With this intelligence, they were able to create their first copy of a military Enigma machine in 1933.
[08:16.780 --> 08:20.240]  The first step to solving the messages have been solved.
[08:20.380 --> 08:24.100]  They had their own Enigma machine with the correct internal wirings.
[08:24.100 --> 08:26.780]  Now, they just needed the four settings used.
[08:28.600 --> 08:32.900]  Let's look at how messages were sent between two Nazi operators.
[08:35.140 --> 08:38.280]  They would randomly generate what's called a ground setting.
[08:38.480 --> 08:39.740]  That's the starting rotor settings.
[08:40.340 --> 08:42.280]  They would randomly generate the starting rotor settings.
[08:42.820 --> 08:45.560]  Let's say X, Y, and Z were the starting settings.
[08:46.100 --> 08:50.280]  Keep in mind, I'm going to be solving this as if it was a naval enigma.
[08:50.280 --> 08:54.600]  That means I'm going to be using letters as if those were the settings.
[08:55.820 --> 09:01.000]  But they were only solving actually the army and air force enigmas.
[09:01.300 --> 09:05.380]  So, they would actually be using numbers, but it's easier to explain with letters.
[09:06.140 --> 09:10.280]  So, an operator would randomly generate a ground setting.
[09:10.460 --> 09:11.540]  Let's say X, Y, Z.
[09:12.000 --> 09:17.940]  They would type this twice and encrypt it using the daily ground setting in their settings book.
[09:19.020 --> 09:21.000]  And this turns into A, B, C, D, E, F.
[09:22.320 --> 09:26.260]  So, in their book, they had a starting setting they were supposed to use.
[09:26.660 --> 09:28.780]  They would randomly generate a different setting.
[09:29.280 --> 09:35.180]  And that's what they would use to actually encrypt the rest of their message as the starting rotor settings.
[09:36.660 --> 09:43.100]  To send that randomly generated string, they would type it twice and encrypt that using the daily start settings in their book.
[09:44.560 --> 09:47.860]  This output string of letters is called the message indicator.
[09:48.120 --> 09:51.500]  That would be sent as a preamble to every single message sent.
[09:53.260 --> 09:55.720]  Now, the Polish, they could deduce this.
[09:55.900 --> 10:03.520]  But what's difficult is they can't decrypt it because they don't know any of the settings used.
[10:03.520 --> 10:07.400]  They don't know the daily start settings because they don't have a settings book from the Nazis.
[10:08.140 --> 10:09.960]  And so, they can't really do much.
[10:10.400 --> 10:13.100]  But they do know a few clues.
[10:14.240 --> 10:18.480]  So, they know that the letter X was in positions one and four.
[10:18.700 --> 10:21.900]  Or they know that some letter was in positions one and four.
[10:22.060 --> 10:23.980]  And they encrypted that to A and D.
[10:23.980 --> 10:28.200]  So, the same letter became A and D and rotor positions one and four.
[10:29.680 --> 10:30.580]  That's shown here.
[10:30.760 --> 10:32.340]  Question mark at rotor position one.
[10:32.740 --> 10:35.580]  That goes to A and the same for D at rotor position four.
[10:36.340 --> 10:38.500]  But because these operations are reversible.
[10:38.800 --> 10:48.780]  Because the letters are paired, That means if you put A at rotor position one it would become that mystery letter And if you put that mystery letter at the rotor position forward, that would become D.
[10:50.480 --> 10:59.420]  So, what the Polish codebreakers could do with this was they could find a ton of message indicators sent on that same day.
[10:59.740 --> 11:01.880]  Those would all be made with the same settings.
[11:02.960 --> 11:06.980]  And they knew that A would become D with this operation.
[11:07.240 --> 11:07.920]  A would become D.
[11:08.320 --> 11:09.920]  They knew that D would become G.
[11:10.280 --> 11:11.960]  And that G would become A.
[11:13.380 --> 11:14.460]  That's a cycle now.
[11:14.780 --> 11:15.340]  A becomes D.
[11:15.500 --> 11:16.080]  D becomes G.
[11:16.280 --> 11:17.320]  G becomes A again.
[11:17.820 --> 11:18.780]  So, that's a cycle.
[11:18.940 --> 11:19.740]  It's called ADG.
[11:20.220 --> 11:27.000]  If you get enough message indicators, you can create cycles that make up the entire alphabet as shown here.
[11:27.860 --> 11:31.040]  And these are like fingerprints for certain rotor settings.
[11:32.540 --> 11:35.500]  Because you can mark the lengths of all these.
[11:35.620 --> 11:36.760]  11, 9, 3, 2, 1.
[11:36.760 --> 11:42.840]  And every single rotor position and rotor order has a different characteristic.
[11:43.180 --> 11:45.240]  Which is what these string of numbers would be called.
[11:46.020 --> 11:49.360]  So, the Polish created this machine called a cyclometer.
[11:49.360 --> 11:53.720]  It would have one set of rotors.
[11:54.080 --> 11:56.220]  And then it would have another set of rotors.
[11:56.360 --> 11:57.580]  Three steps advanced.
[11:58.480 --> 12:07.660]  And what you could do is you could put in any random letter at position one.
[12:08.540 --> 12:09.520]  Run that through.
[12:09.900 --> 12:10.960]  And then the output doesn't matter.
[12:11.160 --> 12:14.240]  And you can run that through at the second set of rotors.
[12:14.240 --> 12:21.680]  And whatever output you get, you can start creating a database of all of these characteristics.
[12:22.420 --> 12:24.520]  And the rotor settings that were used to create it.
[12:25.080 --> 12:28.820]  There are 17,000 different rotor rotations.
[12:29.280 --> 12:30.720]  And six rotor orders.
[12:30.960 --> 12:33.380]  Meaning there's 105,000 different characteristics.
[12:34.000 --> 12:39.260]  And with the cyclometer, in just over a year, the Polish actually made a database of all the characteristics.
[12:40.480 --> 12:44.440]  And they also did that again for positions two and five and three and six.
[12:44.940 --> 12:48.920]  So, that's almost... that's over 300,000 different characteristics marked.
[12:49.360 --> 12:53.300]  And they successfully decrypted Enigma in 1934.
[12:54.340 --> 12:57.180]  This worked until November 1st, 1937.
[12:57.500 --> 13:02.900]  They were able to decrypt Enigma messages with a little bit of effort finding out what the characteristics were.
[13:02.900 --> 13:09.780]  Then, on November 1st, 1937, the Germans changed the wirings of the internal reflector.
[13:09.900 --> 13:12.200]  So, all the work had to be done again over a year.
[13:13.060 --> 13:15.060]  And that... they did that and it worked.
[13:15.500 --> 13:24.000]  And... but shortly after, they changed how they... the Nazis changed how they made the message indicator.
[13:24.000 --> 13:26.520]  So, that... it was... that was the end of that.
[13:28.560 --> 13:30.060]  Uh... this is Marian Rajewski.
[13:30.180 --> 13:32.800]  He was the person who actually first solved Enigma using this method.
[13:34.220 --> 13:36.180]  Can you back up Jamie's second question?
[13:40.720 --> 13:43.860]  So, the Polish solved it again after that.
[13:44.740 --> 13:47.360]  The new message indicator was created as follows.
[13:48.420 --> 13:53.800]  There will be a randomly generated starting setting the... uh... an operator would make.
[13:54.260 --> 13:57.020]  Instead of a daily start settings that all operators have.
[13:58.040 --> 14:03.700]  Then, in the same way as before, they would randomly generate a ground setting and type that twice.
[14:03.860 --> 14:07.500]  And encrypt it using that randomly generated start setting.
[14:08.840 --> 14:13.500]  And then, that ground setting they generated would be used as the encryption for the rest of the message.
[14:15.120 --> 14:15.660]  So...
[14:16.720 --> 14:21.340]  Uh... again, the... uh... Polish operators, they knew that...
[14:21.840 --> 14:28.260]  uh... they knew that... um... the first and fourth... um... positions had the same input letter.
[14:28.580 --> 14:30.420]  The same for the second and fifth and third and sixth.
[14:30.580 --> 14:34.040]  They all had the same input at the... at those different rotor positions.
[14:34.780 --> 14:40.560]  And so... when they found a message indicator that had the same letter in those two positions as well.
[14:40.560 --> 14:42.080]  That would be called the female.
[14:43.380 --> 14:49.760]  If... as long as they found... uh... they... as long as they found three message indicators with a female of the same letter.
[14:50.100 --> 14:53.420]  In the first and fourth, second and fifth, and third and sixth position.
[14:53.640 --> 14:54.400]  Here it's I.
[14:55.320 --> 14:57.280]  If they found three message indicators like that.
[14:57.520 --> 14:58.580]  With their new machine.
[14:58.580 --> 15:00.220]  The BOMBA Cryptologichna.
[15:00.440 --> 15:01.820]  Or the Cryptological Bomb.
[15:02.280 --> 15:04.180]  They could decrypt those messages.
[15:05.940 --> 15:06.500]  So...
[15:06.500 --> 15:07.900]  The BOMBA...
[15:07.900 --> 15:10.020]  had six rotor stacks on top.
[15:11.520 --> 15:13.920]  Uh... the first... there would be three pairs.
[15:14.080 --> 15:14.460]  One and two.
[15:14.620 --> 15:15.020]  Three and four.
[15:15.160 --> 15:15.800]  And five and six.
[15:16.360 --> 15:19.000]  The first pair would be at rotor position MOK.
[15:19.240 --> 15:19.680]  Like here.
[15:20.060 --> 15:22.380]  And the second position would be...
[15:22.380 --> 15:25.540]  The second rotor stack would be at MOK plus three.
[15:25.700 --> 15:26.060]  Or MON.
[15:26.060 --> 15:26.740]  And...
[15:26.740 --> 15:28.420]  Uh... and like that.
[15:28.700 --> 15:29.320]  Every single...
[15:29.320 --> 15:30.700]  Uh... rotor...
[15:30.700 --> 15:32.440]  Uh... stack was at the correct position.
[15:32.780 --> 15:34.000]  That created that letter.
[15:36.600 --> 15:37.120]  So...
[15:37.900 --> 15:38.420]  Um...
[15:38.420 --> 15:40.240]  Once it was in that position.
[15:40.580 --> 15:41.500]  The rotors...
[15:41.500 --> 15:43.000]  Uh... they would check.
[15:43.240 --> 15:45.340]  They would input I into all those rotors.
[15:45.820 --> 15:47.180]  Until they had the same...
[15:47.180 --> 15:48.740]  Until each pair had the same output.
[15:49.580 --> 15:50.040]  Uh... had...
[15:50.040 --> 15:51.340]  It doesn't matter what the output was.
[15:51.480 --> 15:52.360]  Because the...
[15:52.360 --> 15:53.540]  Plugboard would change it.
[15:53.700 --> 15:54.220]  Either way.
[15:54.220 --> 15:55.220]  But...
[15:55.220 --> 15:56.380]  As long as they had the same output.
[15:56.800 --> 15:58.580]  They could deduce the ring setting.
[15:58.840 --> 15:59.380]  And the rotor...
[15:59.780 --> 16:00.360]  Uh... order.
[16:00.760 --> 16:01.360]  From that.
[16:01.500 --> 16:02.760]  And that is because...
[16:02.760 --> 16:04.820]  They knew what rotor position.
[16:05.200 --> 16:06.760]  Created those same two outputs.
[16:07.380 --> 16:08.220]  And they know...
[16:08.900 --> 16:09.420]  Um...
[16:09.420 --> 16:11.120]  They know that the offset should be three.
[16:11.320 --> 16:12.200]  Between each...
[16:12.200 --> 16:12.800]  Uh... pairing.
[16:13.160 --> 16:14.600]  So if the offset wasn't three.
[16:14.780 --> 16:16.500]  They could simply change the ring setting.
[16:16.720 --> 16:18.800]  So that the offset was indeed three.
[16:19.340 --> 16:21.960]  And so that gave them the rotor order and the ring setting.
[16:23.080 --> 16:23.560]  Now...
[16:23.560 --> 16:23.940]  Uh...
[16:23.940 --> 16:23.980]  No.
[16:24.080 --> 16:24.640]  The rotor...
[16:24.640 --> 16:26.040]  Rotation and the ring setting.
[16:26.640 --> 16:27.380]  Now we...
[16:27.380 --> 16:28.320]  We have two unknowns still.
[16:28.420 --> 16:29.080]  We have the plug board.
[16:29.240 --> 16:30.900]  And we have the rotor order.
[16:31.620 --> 16:32.100]  So...
[16:32.100 --> 16:33.220]  To solve the rotor order.
[16:33.360 --> 16:33.920]  You just...
[16:33.920 --> 16:35.120]  Had six Bombi's.
[16:35.540 --> 16:36.700]  That's the plural of Bomba.
[16:36.920 --> 16:38.040]  You had six Bombi's.
[16:39.120 --> 16:39.680]  And...
[16:39.680 --> 16:40.420]  Uh...
[16:40.420 --> 16:43.180]  You would just have each one at the different rotor orders.
[16:44.320 --> 16:45.440]  And again...
[16:45.440 --> 16:45.920]  This worked.
[16:46.640 --> 16:47.160]  Um...
[16:47.160 --> 16:47.980]  Until...
[16:47.980 --> 16:48.400]  The Nazi...
[16:48.400 --> 16:49.660]  And so using this method.
[16:49.980 --> 16:54.360]  They were actually able to decrypt about 75% of messages sent.
[16:54.720 --> 16:55.040]  Uh...
[16:55.040 --> 16:55.580]  By Enigma.
[16:56.740 --> 16:58.640]  But then in December of that year.
[16:59.020 --> 17:02.160]  The Nazis added two more rotors that could be used.
[17:02.360 --> 17:04.760]  So there were still only three rotors in every Enigma machine.
[17:04.760 --> 17:08.220]  But you could choose which ones you could use.
[17:08.760 --> 17:09.060]  So...
[17:09.360 --> 17:10.460]  That is...
[17:10.460 --> 17:10.840]  Uh...
[17:10.840 --> 17:12.160]  60 different rotor orders now.
[17:12.300 --> 17:15.000]  You would need 60 Bombi's to effectively...
[17:15.000 --> 17:15.400]  Uh...
[17:15.400 --> 17:16.420]  Solve all those messages.
[17:17.040 --> 17:20.060]  But Polish resources were already very strained by that point.
[17:20.360 --> 17:20.660]  Uh...
[17:20.660 --> 17:23.560]  Preparing for what they knew was going to be an invasion soon.
[17:24.520 --> 17:25.120]  Um...
[17:25.120 --> 17:26.440]  And that was in December of 1938.
[17:27.080 --> 17:28.120]  And then...
[17:28.120 --> 17:29.760]  One month after that...
[17:29.760 --> 17:30.440]  Um...
[17:30.440 --> 17:30.860]  The...
[17:30.860 --> 17:34.200]  Nazis actually upped the number of cables from three to five.
[17:34.900 --> 17:38.360]  From 3.5 million different plug word combinations to five billion.
[17:39.700 --> 17:40.220]  Um...
[17:40.220 --> 17:41.140]  Before...
[17:41.140 --> 17:43.540]  When they had three knowns and one unknown.
[17:43.800 --> 17:44.860]  That unknown being the plug word.
[17:45.200 --> 17:48.180]  Through manual methods, they could solve the plug word combinations.
[17:48.360 --> 17:49.620]  But not anymore with five cables.
[17:49.820 --> 17:52.840]  There's too many possible to be able to manually deduce.
[17:54.020 --> 17:54.540]  So...
[17:54.540 --> 17:57.640]  With all this happening, not being able to decrypt Enigma messages anymore.
[17:57.640 --> 18:02.420]  On July 25th, 1939, in the Quebeci woods near the town of Pyre.
[18:03.080 --> 18:03.680]  Uh...
[18:03.680 --> 18:07.640]  The Polish met up with the United Kingdom and uh...
[18:08.160 --> 18:08.780]  French intelligence.
[18:09.180 --> 18:11.420]  To actually hand over all their bombing machines.
[18:11.540 --> 18:11.900]  The cyclometers.
[18:13.060 --> 18:13.420]  And...
[18:13.420 --> 18:14.640]  Their replica Enigmas.
[18:14.940 --> 18:17.060]  And all the intel they had on Enigma.
[18:17.720 --> 18:18.320]  Uh...
[18:18.320 --> 18:18.700]  To them.
[18:19.300 --> 18:21.360]  And that was five weeks before the invasion.
[18:22.380 --> 18:23.840]  So we move on to Alan Turing.
[18:24.580 --> 18:27.480]  Alan Turing was a logician and a mathematician at Cambridge.
[18:27.480 --> 18:28.560]  Before working on Enigma.
[18:29.100 --> 18:30.320]  He was born in 1912.
[18:30.560 --> 18:33.720]  And he was already very distinguished in 1936.
[18:34.020 --> 18:35.920]  For his concept of the Turing machine.
[18:36.580 --> 18:37.120]  Uh...
[18:37.120 --> 18:38.140]  Which uh...
[18:38.140 --> 18:40.820]  Cemented him as the father of modern computer science.
[18:42.080 --> 18:45.140]  In 1939, after living in the United States.
[18:46.400 --> 18:46.960]  Um...
[18:46.960 --> 18:48.040]  Where he got his PhD.
[18:48.780 --> 18:49.200]  Uh...
[18:49.200 --> 18:49.660]  At Princeton.
[18:49.660 --> 18:51.080]  He decided to return to Britain.
[18:51.460 --> 18:52.640]  As tensions rose in Europe.
[18:53.580 --> 18:54.060]  Uh...
[18:54.060 --> 18:55.220]  Where he was recruited to the government.
[18:56.160 --> 18:56.640]  Uh...
[18:56.640 --> 18:56.960]  Uh...
[18:56.960 --> 18:58.400]  For the code and cipher squad at Bletchley Park.
[18:59.500 --> 18:59.980]  Um...
[18:59.980 --> 19:00.540]  One day.
[19:00.740 --> 19:02.440]  After the UK declared war on Europe.
[19:02.660 --> 19:03.820]  On September...
[19:03.820 --> 19:04.460]  Uh...
[19:04.460 --> 19:05.080]  4th, 1939.
[19:06.300 --> 19:07.260]  He decided...
[19:07.260 --> 19:07.900]  He...
[19:07.900 --> 19:08.260]  He...
[19:08.260 --> 19:09.820]  Reported for duty at Bletchley Park.
[19:10.220 --> 19:12.580]  And he was later assigned as the leader.
[19:13.140 --> 19:13.380]  Uh...
[19:13.380 --> 19:14.620]  As the head of HUT8.
[19:14.960 --> 19:16.920]  Which was focusing on...
[19:16.920 --> 19:18.780]  Decrypting the naval enigma messages.
[19:18.780 --> 19:20.640]  Which the Polish actually never decrypted.
[19:24.780 --> 19:25.380]  So...
[19:25.380 --> 19:26.620]  In May 1937.
[19:26.780 --> 19:27.360]  The Kriegsmarine.
[19:27.960 --> 19:28.560]  Um...
[19:28.560 --> 19:29.260]  Or the German Navy.
[19:30.020 --> 19:31.600]  Introduced the enigma M3.
[19:32.140 --> 19:34.920]  The M3 was identical to the enigma M1.
[19:35.580 --> 19:36.060]  Um...
[19:36.060 --> 19:38.500]  Except to the fact that it had eight rotors.
[19:38.700 --> 19:39.380]  To choose from.
[19:39.560 --> 19:40.420]  Not five.
[19:40.920 --> 19:42.700]  Making 336 rotor orders.
[19:43.740 --> 19:44.780]  It also...
[19:44.780 --> 19:46.880]  The operations for creating the...
[19:46.880 --> 19:48.460]  Message indicator were...
[19:48.460 --> 19:49.640]  Much more sophisticated.
[19:50.240 --> 19:51.560]  Than for the army and air force.
[19:53.260 --> 19:53.780]  Um...
[19:53.780 --> 19:54.200]  So...
[19:54.200 --> 19:56.540]  There had been basically no done work...
[19:56.540 --> 19:57.380]  No work done.
[19:57.900 --> 19:59.680]  Solving the message indicators to that point.
[20:00.980 --> 20:01.500]  Um...
[20:01.500 --> 20:01.760]  Except...
[20:02.300 --> 20:02.540]  Uh...
[20:02.540 --> 20:04.420]  The Polish worked a little bit on it.
[20:04.740 --> 20:07.540]  They knew that there was something called a bigram substitution.
[20:08.320 --> 20:08.800]  Uh...
[20:08.800 --> 20:09.620]  That was what they suspected.
[20:10.040 --> 20:10.920]  And that was true actually.
[20:11.420 --> 20:13.000]  I'll explain what that means in a little bit.
[20:13.420 --> 20:13.880]  Um...
[20:13.880 --> 20:15.800]  They knew there was some type of bigram substitution.
[20:16.400 --> 20:16.880]  But...
[20:16.880 --> 20:17.960]  There was nothing else known.
[20:19.840 --> 20:20.320]  Um...
[20:21.140 --> 20:21.620]  So...
[20:22.780 --> 20:24.240]  Turing and his team...
[20:24.240 --> 20:25.340]  Found out over a few months.
[20:25.760 --> 20:26.820]  All of the following.
[20:27.180 --> 20:28.720]  From not only looking at the...
[20:29.060 --> 20:29.480]  Messages.
[20:29.760 --> 20:30.360]  But also...
[20:30.360 --> 20:33.340]  Looking at some of the decrypted enigma messages.
[20:33.720 --> 20:34.520]  From manual methods.
[20:35.440 --> 20:35.920]  Throughout...
[20:35.920 --> 20:37.100]  Throughout all of this.
[20:37.100 --> 20:38.260]  Even though there were many machines.
[20:38.680 --> 20:38.920]  You...
[20:38.920 --> 20:39.040]  Made.
[20:39.460 --> 20:40.220]  Even from the Polish.
[20:40.400 --> 20:41.340]  And of course Alan Turing later.
[20:42.080 --> 20:43.200]  There are many machines made.
[20:43.460 --> 20:44.020]  To decrypt enigma.
[20:44.400 --> 20:45.720]  But there were always manual methods.
[20:45.920 --> 20:46.940]  That worked a...
[20:46.940 --> 20:48.860]  Very small portion of the time.
[20:49.700 --> 20:50.180]  Um...
[20:50.180 --> 20:50.840]  And so...
[20:50.840 --> 20:52.640]  I'm not going to explain how those worked.
[20:53.280 --> 20:53.800]  But...
[20:53.800 --> 20:54.540]  Uh...
[20:54.540 --> 20:56.400]  That was a point of intelligence.
[20:56.720 --> 20:57.640]  That could have been used.
[20:57.780 --> 20:58.400]  Along the way.
[20:59.620 --> 21:00.140]  So...
[21:00.140 --> 21:02.560]  Through those very infrequent.
[21:02.900 --> 21:03.160]  Uh...
[21:03.160 --> 21:04.500]  Decrypted enigma messages.
[21:04.500 --> 21:05.600]  And through...
[21:06.120 --> 21:06.600]  Just...
[21:06.600 --> 21:06.980]  Uh...
[21:06.980 --> 21:08.060]  Examining the message indicators.
[21:09.360 --> 21:09.840]  Um...
[21:09.840 --> 21:10.760]  Alan Turing and his team.
[21:11.080 --> 21:12.280]  Deduced all the following.
[21:13.680 --> 21:14.160]  The...
[21:14.160 --> 21:15.540]  The plug board and the ground setting.
[21:15.840 --> 21:16.980]  Were changed everyday.
[21:18.280 --> 21:18.760]  Uh...
[21:18.760 --> 21:19.400]  The starting...
[21:19.400 --> 21:20.120]  Rotor setting.
[21:20.280 --> 21:20.820]  And the plug board.
[21:20.880 --> 21:21.380]  Were changed everyday.
[21:21.980 --> 21:23.120]  The rotor order.
[21:23.340 --> 21:24.140]  And the ring setting.
[21:24.200 --> 21:25.480]  Were changed on odd numbered days.
[21:27.220 --> 21:27.740]  And...
[21:27.740 --> 21:29.760]  The way that the message indicator was created.
[21:30.320 --> 21:30.840]  Was...
[21:30.840 --> 21:31.140]  Uh...
[21:31.140 --> 21:32.080]  An enigma operator.
[21:32.400 --> 21:33.460]  Would out of a book.
[21:33.620 --> 21:34.260]  A settings book.
[21:34.500 --> 21:35.680]  They would choose three...
[21:35.680 --> 21:35.880]  Uh...
[21:35.880 --> 21:36.400]  Two random.
[21:36.700 --> 21:38.020]  Three letter strings of letters.
[21:38.800 --> 21:39.220]  Um...
[21:39.220 --> 21:39.480]  So...
[21:39.480 --> 21:41.720]  Let's say they choose ABC and FGH.
[21:42.520 --> 21:44.960]  The first one would be the key indicator group.
[21:45.260 --> 21:47.700]  And the second would be the message indicator group.
[21:48.540 --> 21:50.440]  The operators would offset these.
[21:50.940 --> 21:51.400]  Uh...
[21:51.400 --> 21:52.040]  As shown here.
[21:52.040 --> 21:54.700]  And they would fill the spaces with two dummy letters.
[21:56.500 --> 21:57.020]  Then...
[21:57.020 --> 22:00.380]  They would split these into four vertical bigrams.
[22:00.480 --> 22:02.200]  That's just four vertical pairs.
[22:03.020 --> 22:03.300]  So...
[22:03.300 --> 22:04.020]  Let's say...
[22:04.020 --> 22:06.240]  XF, A, G, B, H, and C, Y.
[22:08.220 --> 22:08.740]  Um...
[22:08.740 --> 22:09.520]  Then...
[22:09.520 --> 22:10.900]  With their settings book.
[22:11.040 --> 22:12.980]  They would flip to another set of pages.
[22:13.440 --> 22:15.720]  Where there were nine different tables.
[22:15.980 --> 22:17.180]  These were called the bigram tables.
[22:17.500 --> 22:18.840]  And they had a pair.
[22:19.020 --> 22:20.320]  For every single bigram.
[22:20.500 --> 22:21.640]  To be substituted into.
[22:21.640 --> 22:24.280]  There were nine bigram tables to be used on different days.
[22:24.820 --> 22:25.320]  So...
[22:25.320 --> 22:26.040]  We can say for example.
[22:26.480 --> 22:27.580]  XF turned into HO.
[22:27.920 --> 22:28.860]  AG to DL.
[22:28.980 --> 22:30.020]  BH to WY.
[22:30.260 --> 22:31.300]  And CY to NM.
[22:32.060 --> 22:34.140]  And that would become the message indicator.
[22:35.220 --> 22:35.720]  Then...
[22:35.720 --> 22:38.020]  The decrypting operator would have to do all of this in reverse.
[22:38.560 --> 22:40.240]  And then this message indicator group.
[22:40.680 --> 22:41.800]  They would...
[22:41.800 --> 22:42.160]  Uh...
[22:42.160 --> 22:43.860]  Input that to the daily ground settings.
[22:44.100 --> 22:45.240]  Also found in their book.
[22:45.680 --> 22:47.480]  They would input that into the daily ground settings.
[22:47.480 --> 22:49.260]  And whatever output they got.
[22:49.520 --> 22:51.880]  That would be the actual settings used.
[22:52.200 --> 22:52.640]  Uh...
[22:52.640 --> 22:53.900]  The rotor settings used.
[22:54.220 --> 22:55.380]  For the rest of the...
[22:56.200 --> 22:56.680]  Um...
[22:56.680 --> 22:57.460]  For the rest of the message.
[22:59.300 --> 23:02.060]  And so Alan Turing and his team after deducing all of this.
[23:02.220 --> 23:02.860]  Which is all correct.
[23:03.440 --> 23:04.620]  After deducing all of this.
[23:04.620 --> 23:08.540]  They spent many months trying to solve...
[23:08.540 --> 23:09.040]  Uh...
[23:09.040 --> 23:09.800]  The biogram tables.
[23:09.940 --> 23:11.640]  Trying to piece it together bit by bit.
[23:11.900 --> 23:12.980]  Trying to figure out what...
[23:12.980 --> 23:13.260]  Uh...
[23:13.260 --> 23:14.760]  All the substitutions used.
[23:16.000 --> 23:17.680]  This is a very slow process.
[23:17.960 --> 23:20.680]  Again, they only had the decrypted messages to work with.
[23:21.720 --> 23:22.300]  Um...
[23:22.300 --> 23:22.850]  And so...
[23:24.140 --> 23:24.720]  Um...
[23:24.720 --> 23:25.500]  That was it.
[23:25.860 --> 23:26.440]  But...
[23:26.440 --> 23:27.380]  On...
[23:27.380 --> 23:28.840]  April 26, 1940.
[23:30.380 --> 23:31.740]  The HMS Griffin.
[23:32.980 --> 23:34.340]  Captured a German...
[23:34.340 --> 23:34.860]  Uh...
[23:35.580 --> 23:36.220]  Uh...
[23:36.220 --> 23:36.780]  Which is...
[23:36.780 --> 23:37.120]  Uh...
[23:37.120 --> 23:37.700]  A patrol boat.
[23:38.780 --> 23:39.420]  Um...
[23:39.420 --> 23:41.020]  Interestingly, this patrol boat was...
[23:41.020 --> 23:43.340]  Disguised as a Dutch trawler boat.
[23:43.700 --> 23:44.880]  Which is a type of fishing boat.
[23:45.480 --> 23:45.860]  So...
[23:45.860 --> 23:48.120]  They captured this disguised German patrol boat.
[23:48.640 --> 23:50.620]  And the patrol boat didn't have...
[23:50.620 --> 23:51.920]  The settings books in them.
[23:52.760 --> 23:53.080]  Actually...
[23:53.400 --> 23:53.860]  Um...
[23:53.860 --> 23:54.940]  Those were...
[23:54.940 --> 23:55.320]  Um...
[23:55.320 --> 23:56.200]  Made out of this...
[23:56.200 --> 23:57.100]  Pink material.
[23:57.460 --> 23:58.080]  That would...
[23:58.080 --> 23:58.820]  When...
[23:58.820 --> 23:59.320]  Put in water.
[23:59.620 --> 24:00.620]  All the ink would bleed.
[24:00.980 --> 24:02.020]  And it was unreadable.
[24:03.060 --> 24:03.580]  Um...
[24:03.580 --> 24:03.780]  So...
[24:03.780 --> 24:04.680]  Those were all destroyed.
[24:04.760 --> 24:05.820]  Including all their enigmas.
[24:06.280 --> 24:06.480]  Uh...
[24:06.480 --> 24:08.100]  That was actually the main...
[24:08.100 --> 24:08.480]  Uh...
[24:08.480 --> 24:09.100]  When...
[24:09.100 --> 24:10.200]  A boat was captured.
[24:10.520 --> 24:14.000]  One of the highest priorities was to destroy everything about enigma.
[24:14.780 --> 24:15.300]  Um...
[24:15.300 --> 24:15.680]  And so...
[24:15.680 --> 24:16.380]  There was...
[24:16.380 --> 24:17.340]  Not much...
[24:17.340 --> 24:18.480]  They could get out of it.
[24:19.220 --> 24:19.740]  But...
[24:19.740 --> 24:20.460]  Through some...
[24:20.460 --> 24:20.800]  Like...
[24:20.800 --> 24:20.980]  The...
[24:20.980 --> 24:23.540]  The intelligence for the message indicators could be confirmed.
[24:24.160 --> 24:24.680]  And...
[24:24.680 --> 24:25.680]  Through more details like that.
[24:26.200 --> 24:26.720]  The...
[24:26.720 --> 24:29.260]  Creating of the bigram tables was...
[24:29.260 --> 24:29.760]  Uh...
[24:29.760 --> 24:30.580]  Quickened by a lot.
[24:32.940 --> 24:33.460]  Uh...
[24:33.460 --> 24:34.660]  Let's move on to...
[24:34.660 --> 24:35.040]  Um...
[24:35.040 --> 24:35.560]  Ian Fleming.
[24:35.680 --> 24:36.560]  I'm sure you know who that is.
[24:36.860 --> 24:38.360]  He wrote the James Bond books.
[24:38.740 --> 24:42.160]  But he was also the commander of British Naval Intelligence at Bleschley Park.
[24:43.060 --> 24:43.580]  So...
[24:43.580 --> 24:47.860]  He actually made a plan for how to capture these bigram tables in the settings books.
[24:49.520 --> 24:50.040]  Uh...
[24:50.040 --> 24:52.500]  And you might find some parallels between some of his books.
[24:53.320 --> 24:53.920]  So...
[24:53.920 --> 24:54.700]  The plan was as follows.
[24:55.200 --> 24:56.980]  A group of five...
[24:56.980 --> 24:57.760]  Uh...
[24:57.760 --> 24:58.000]  Uh...
[24:58.000 --> 24:58.060]  Uh...
[24:58.060 --> 24:59.320]  A group of five...
[24:59.320 --> 25:01.120]  With one native German speaker...
[25:01.120 --> 25:04.160]  Would dress up in authentic German military uniforms.
[25:04.460 --> 25:06.180]  With fake blood and bandages.
[25:06.480 --> 25:07.440]  Put on their suits.
[25:08.160 --> 25:11.780]  They were to get all into one captured German Luftwaffe plane.
[25:11.940 --> 25:12.540]  Air force plane.
[25:13.100 --> 25:15.960]  And fly up to a flying bomber squadron.
[25:15.960 --> 25:17.320]  As if they were there the whole time.
[25:17.440 --> 25:18.580]  They were going to pretend they were there.
[25:19.260 --> 25:21.360]  Then they were going to fake an engine failure.
[25:21.600 --> 25:22.900]  And crash into the channel.
[25:23.620 --> 25:26.040]  And then they were going to send out SOS signals.
[25:26.500 --> 25:29.460]  For a Nazi rescue boat to come save them.
[25:29.980 --> 25:31.000]  Once on the boat.
[25:31.740 --> 25:35.880]  Continuing their disguise as actually injured Germans.
[25:36.420 --> 25:39.920]  They would then shoot all of the people on board.
[25:40.240 --> 25:40.980]  Throw them overboard.
[25:41.620 --> 25:44.340]  And then drive the ship back to the UK.
[25:44.660 --> 25:46.060]  And they would have all the settings.
[25:47.600 --> 25:48.120]  Uh...
[25:48.120 --> 25:49.380]  And they got pretty far in that plan.
[25:49.780 --> 25:50.300]  Uh...
[25:50.300 --> 25:50.540]  Actually.
[25:51.020 --> 25:51.540]  Um...
[25:51.540 --> 25:54.660]  They ended up, you know, doing everything up until crashing their plane.
[25:55.320 --> 25:56.520]  But a rescue boat never came.
[25:56.720 --> 25:57.180]  Unfortunately.
[26:00.980 --> 26:01.500]  So...
[26:02.400 --> 26:04.060]  Let's move on back to Alan Turing.
[26:04.840 --> 26:05.360]  So...
[26:05.360 --> 26:08.900]  Before Alan Turing invented his famous bomb machine.
[26:08.900 --> 26:10.100]  His very large computer.
[26:10.820 --> 26:11.300]  Um...
[26:11.300 --> 26:14.960]  He was working on helping the actual manual cryptographers.
[26:14.960 --> 26:16.860]  And he created this.
[26:17.220 --> 26:17.860]  Um...
[26:17.860 --> 26:18.800]  Method called Bamberisms.
[26:20.020 --> 26:20.660]  Uh...
[26:20.660 --> 26:21.420]  To help out these.
[26:21.660 --> 26:22.260]  Uh...
[26:22.260 --> 26:23.260]  Manual code breakers.
[26:25.200 --> 26:25.840]  Um...
[26:25.840 --> 26:26.640]  The Bamberisms.
[26:26.960 --> 26:27.640]  Is a...
[26:27.640 --> 26:28.680]  A Bamberism.
[26:28.840 --> 26:29.080]  Is a...
[26:29.080 --> 26:30.400]  Is a statistical method.
[26:30.760 --> 26:32.900]  Of reducing the number of rotor orders.
[26:33.080 --> 26:34.480]  That would need to be manually checked.
[26:34.840 --> 26:36.300]  There are 336 possible.
[26:37.000 --> 26:37.520]  Uh...
[26:37.520 --> 26:39.500]  And he was working on reducing that number.
[26:41.880 --> 26:42.200]  Um...
[26:42.520 --> 26:42.980]  To start.
[26:43.540 --> 26:44.180]  Uh...
[26:44.180 --> 26:45.240]  Enigma code breakers.
[26:45.600 --> 26:46.200]  Uh...
[26:46.200 --> 26:46.380]  Or...
[26:46.380 --> 26:48.260]  He had some information available to him.
[26:48.660 --> 26:49.780]  To start this process.
[26:51.340 --> 26:51.940]  He...
[26:51.940 --> 26:52.640]  Um...
[26:52.640 --> 26:53.220]  Had...
[26:53.220 --> 26:53.740]  He...
[26:53.740 --> 26:54.800]  From the previous.
[26:55.220 --> 26:57.600]  He could solve for the message indicator group.
[26:57.860 --> 27:00.440]  He couldn't find the actual rotor positions used.
[27:00.660 --> 27:01.880]  Because he didn't have the...
[27:01.880 --> 27:03.420]  All the rest of the settings in the settings book.
[27:03.860 --> 27:06.760]  But he could deduce this message indicator group.
[27:06.760 --> 27:08.180]  Through the bigrand tables.
[27:09.340 --> 27:09.880]  So...
[27:09.880 --> 27:10.760]  What that means.
[27:11.280 --> 27:11.740]  Is...
[27:11.740 --> 27:12.780]  If he found...
[27:12.780 --> 27:13.920]  Two message indicator groups.
[27:14.120 --> 27:14.660]  That were...
[27:14.660 --> 27:15.820]  That had the same two letters.
[27:16.680 --> 27:17.180]  Uh...
[27:17.180 --> 27:17.520]  In them.
[27:17.840 --> 27:18.700]  It was likely.
[27:19.360 --> 27:19.900]  That...
[27:19.900 --> 27:20.760]  When they were actually...
[27:21.320 --> 27:22.900]  Put through the daily starting settings.
[27:23.120 --> 27:23.600]  It was...
[27:23.600 --> 27:24.180]  Pretty likely.
[27:25.140 --> 27:25.680]  That...
[27:25.680 --> 27:26.460]  They would have...
[27:26.460 --> 27:27.380]  The same two letters again.
[27:27.660 --> 27:28.780]  The same two starting letters.
[27:30.340 --> 27:30.820]  So...
[27:30.820 --> 27:31.640]  That means.
[27:31.980 --> 27:33.560]  If you have the same two starting letters.
[27:33.780 --> 27:34.240]  And...
[27:34.240 --> 27:36.500]  It's just the distance of three apart from these two letters.
[27:37.380 --> 27:37.860]  Well...
[27:37.860 --> 27:39.000]  That means that...
[27:39.000 --> 27:40.960]  If you offset the two rest...
[27:41.600 --> 27:42.980]  The two ciphertexts of the message.
[27:43.160 --> 27:43.660]  Not the preamble.
[27:43.740 --> 27:45.060]  The actual important part with the data.
[27:45.480 --> 27:46.560]  You could offset them.
[27:46.760 --> 27:48.200]  Within 50 places.
[27:48.780 --> 27:51.180]  And you knew that they would be lined up.
[27:51.400 --> 27:52.460]  At some point there.
[27:53.340 --> 27:53.820]  And...
[27:53.820 --> 27:54.720]  When they were lined up.
[27:54.800 --> 27:55.560]  It was called in depth.
[27:56.560 --> 27:57.040]  Importantly.
[27:57.800 --> 27:58.260]  Uh...
[27:58.260 --> 27:58.640]  When the...
[27:58.640 --> 28:00.560]  When you found the correct position.
[28:01.860 --> 28:02.420]  Um...
[28:02.420 --> 28:03.420]  The number of...
[28:03.420 --> 28:05.440]  Matches between vertical letters.
[28:05.820 --> 28:08.180]  Would increase from one in 26 to one in 17.
[28:10.020 --> 28:10.580]  So...
[28:10.580 --> 28:11.620]  In our example.
[28:11.980 --> 28:13.140]  We know that there's...
[28:13.140 --> 28:14.440]  There's an offset of three letters.
[28:15.200 --> 28:16.380]  He wouldn't know that.
[28:16.980 --> 28:17.460]  Um...
[28:17.460 --> 28:18.440]  And his team wouldn't know that.
[28:18.780 --> 28:19.660]  So what they...
[28:19.660 --> 28:22.080]  The Bamberisms is a statistical method.
[28:22.580 --> 28:24.300]  To actually find out.
[28:24.500 --> 28:26.560]  At what point the two messages were in depth.
[28:28.020 --> 28:29.780]  In depth means that...
[28:30.340 --> 28:31.940]  When two messages are in depth.
[28:32.120 --> 28:34.140]  That means that the overlapping portions of the messages.
[28:34.440 --> 28:36.420]  Had the same settings used.
[28:36.620 --> 28:37.620]  To actually create them.
[28:38.240 --> 28:38.620]  So...
[28:38.620 --> 28:39.720]  We don't know what the messages say.
[28:39.900 --> 28:40.560]  It's all scrambled.
[28:41.060 --> 28:43.100]  But we do know they had the same settings used.
[28:43.120 --> 28:43.900]  When they were created.
[28:45.960 --> 28:46.520]  So...
[28:46.520 --> 28:48.840]  I'll explain how that actually...
[28:48.840 --> 28:49.180]  Uh...
[28:49.180 --> 28:51.160]  Allowed us to solve the messages later.
[28:51.420 --> 28:52.900]  But let's first determine...
[28:53.500 --> 28:53.840]  How...
[28:53.840 --> 28:54.420]  How...
[28:54.420 --> 28:56.340]  Let's first figure out if they are in depth.
[28:56.600 --> 28:57.220]  At first at all.
[28:58.560 --> 28:59.120]  So...
[28:59.120 --> 29:00.140]  If the...
[29:00.140 --> 29:01.880]  Two messages were in the wrong place.
[29:01.880 --> 29:03.940]  About every one in 26...
[29:03.940 --> 29:05.600]  About every one in 26...
[29:05.600 --> 29:06.220]  About every one in 26...
[29:06.220 --> 29:06.660]  Uh...
[29:06.660 --> 29:06.900]  Parings.
[29:07.220 --> 29:08.200]  Vertical pairings of letters.
[29:08.820 --> 29:09.620]  About one in 26...
[29:09.620 --> 29:10.500]  Every 26 would match.
[29:10.680 --> 29:11.220]  Because it's random.
[29:11.440 --> 29:11.820]  Basically.
[29:13.060 --> 29:13.620]  Uh...
[29:13.620 --> 29:14.540]  In regular German.
[29:14.760 --> 29:15.980]  In decrypted German.
[29:17.100 --> 29:17.660]  Um...
[29:17.660 --> 29:18.420]  Regular speech.
[29:18.800 --> 29:20.240]  About one in 13 would match.
[29:20.520 --> 29:22.460]  But in decrypted naval enigma messages.
[29:22.460 --> 29:25.280]  It was determined that about one in 17 would match.
[29:26.380 --> 29:29.640]  These numbers are just created through this formula here.
[29:30.620 --> 29:31.140]  Uh...
[29:31.140 --> 29:33.220]  The probability of two letters matching vertically.
[29:33.720 --> 29:36.100]  It's just the probability of one letter happening.
[29:36.580 --> 29:37.300]  At all.
[29:37.480 --> 29:37.960]  Squared.
[29:38.060 --> 29:39.500]  Plus the probability of the next letter squared.
[29:39.700 --> 29:40.160]  And so on.
[29:41.820 --> 29:42.340]  Now...
[29:42.340 --> 29:44.780]  Actually finding out how many matches happened.
[29:45.040 --> 29:46.900]  Between two overlapping portions.
[29:47.240 --> 29:49.400]  That is surprisingly difficult to find.
[29:49.980 --> 29:50.380]  Uh...
[29:50.380 --> 29:51.500]  How many matches there are.
[29:52.780 --> 29:53.800]  And so...
[29:53.800 --> 29:54.740]  They...
[29:54.740 --> 29:55.620]  They...
[29:55.620 --> 29:55.800]  Uh...
[29:55.800 --> 29:57.120]  Used these paper sheets.
[29:57.340 --> 29:57.820]  With hole punches.
[29:59.040 --> 29:59.560]  So...
[29:59.560 --> 30:01.300]  In the town of Banbury.
[30:02.020 --> 30:02.540]  Uh...
[30:02.540 --> 30:04.320]  They would print these meter long sheets.
[30:04.620 --> 30:04.960]  Or...
[30:04.960 --> 30:06.300]  Meters long sheets of paper.
[30:06.540 --> 30:08.540]  With a bunch of vertical alphabets on them.
[30:08.960 --> 30:09.440]  And...
[30:09.440 --> 30:11.480]  A code breaker could simply hole punch.
[30:11.760 --> 30:13.460]  Where there was a letter in the actual message.
[30:14.540 --> 30:15.060]  Uh...
[30:15.060 --> 30:15.700]  And so...
[30:15.700 --> 30:16.740]  If you had two of these sheets.
[30:17.000 --> 30:18.460]  With hole punches for different messages.
[30:18.800 --> 30:20.720]  You can line them up over each other.
[30:20.720 --> 30:21.880]  Over a light source.
[30:22.460 --> 30:22.920]  And where the...
[30:22.920 --> 30:24.180]  Where the light shines through.
[30:24.400 --> 30:25.140]  That's a match.
[30:25.360 --> 30:27.180]  And that's how you can count the matches easily.
[30:28.540 --> 30:29.300]  And so...
[30:29.300 --> 30:31.020]  That's why the process is called Banburyisms.
[30:31.540 --> 30:33.180]  The sheets were printed in Banbury.
[30:33.520 --> 30:35.600]  The sheets themselves were called Banbury's.
[30:36.040 --> 30:36.960]  And so the process was Banburyisms.
[30:39.960 --> 30:40.600]  That...
[30:40.600 --> 30:41.580]  I'm gonna show you some math.
[30:41.760 --> 30:42.300]  Um...
[30:42.300 --> 30:43.840]  About how the actual...
[30:43.840 --> 30:44.480]  Uh...
[30:44.480 --> 30:45.580]  Statistical process worked.
[30:45.860 --> 30:48.740]  It was based on Bayes' theorem of conditional probabilities.
[30:49.440 --> 30:50.480]  And so...
[30:50.480 --> 30:53.020]  When you divide this theorem by itself.
[30:53.320 --> 30:55.200]  You get Bayes' rule here.
[30:56.700 --> 30:57.860]  And so...
[30:57.860 --> 31:00.240]  We can start solving for what...
[31:06.300 --> 31:06.940]  Uh...
[31:06.940 --> 31:08.300]  This one would mean the messages are not in depth.
[31:08.580 --> 31:11.280]  And so that actually turns out A2 is the complement of A1.
[31:11.380 --> 31:12.020]  Or the opposite.
[31:12.760 --> 31:13.240]  So...
[31:13.240 --> 31:13.940]  If A1...
[31:13.940 --> 31:15.840]  If A2 is the opposite of A1.
[31:16.140 --> 31:18.180]  You can just swap out every A2 with...
[31:18.180 --> 31:18.580]  Uh...
[31:18.580 --> 31:19.260]  A1 complement.
[31:20.820 --> 31:21.300]  So...
[31:21.300 --> 31:21.900]  When...
[31:21.900 --> 31:23.620]  I'm gonna explain how this notation works.
[31:23.620 --> 31:27.000]  If you have P of A line B.
[31:27.260 --> 31:29.660]  That just means the probability of A given B.
[31:30.060 --> 31:31.730]  So this first theorem here says...
[31:32.340 --> 31:33.840]  The probability of A given B.
[31:33.960 --> 31:36.300]  Is equal to the probability of B given A.
[31:36.540 --> 31:37.900]  Over the probability of B.
[31:38.400 --> 31:39.580]  Times the probability of A.
[31:41.240 --> 31:41.820]  So...
[31:41.820 --> 31:42.620]  If we...
[31:43.220 --> 31:44.040]  Have...
[31:44.410 --> 31:47.240]  If we have the probability of A1 given B.
[31:47.920 --> 31:50.260]  Over the probability of A complemented given B.
[31:50.700 --> 31:52.440]  That's the same thing of saying...
[31:52.440 --> 31:54.120]  The odds of A given B.
[31:54.320 --> 31:56.660]  Keep in mind, this is not big O notation.
[31:57.080 --> 31:58.200]  That just says odds.
[31:58.740 --> 32:10.680]  So the odds of A given B is equal to the probability of B given not A times the odds of A.
[32:10.880 --> 32:17.460]  So that we can just plug in what A means and what B means.
[32:18.120 --> 32:32.240]  And so the probability of the messages being in depth given a match is equal to the probability of a match given they're in depth over the probability of a match given they're not in depth times the odds of being in depth.
[32:32.840 --> 32:37.980]  That just means the probability of a match given in depth is 1 in 17.
[32:38.940 --> 32:47.120]  There's 1 in 17 letters will match over randomness over 1 in 26 letters will match times the odds were in depth.
[32:47.120 --> 32:57.120]  So, if we are in-depth and we have a match, the probability that the two messages are in-depth are multiplied by 26 over 17.
[32:57.760 --> 33:10.960]  We can do the same process for the probability of getting a match, the probability of being in-depth given a not match, and so those get multiplied by 416 over 425.
[33:12.620 --> 33:20.560]  So, if we return to our message, there are 9 matches over... and there's 25 not matches.
[33:20.880 --> 33:31.700]  So, we just take these numbers, we do 26 over 17 to the 9th power, 416 over 425 to the 25th power, and we get this number 26.81.
[33:32.160 --> 33:38.420]  That means we're 26.81 times more likely to be in-depth than randomly.
[33:40.100 --> 33:48.460]  So, we are 1 out of 1.8 times, we are going to be in-depth, or there's a 55% chance we're in-depth.
[33:49.020 --> 33:50.500]  But that's not true, actually.
[33:51.820 --> 33:53.200]  Well, no, I shouldn't say that yet.
[33:53.640 --> 33:57.740]  Let's look at the scoring system used, and then I'll explain why that's not true.
[34:01.380 --> 34:14.320]  So, back in the 1940s, it is very taxing to do these multiplications with these annoying numbers so much, because you wouldn't have like a calculator to just use them.
[34:15.220 --> 34:22.580]  And so, if we take the log of these numbers instead, we can turn these multiplications into additive scores.
[34:22.580 --> 34:30.680]  And so, 26 over 17 is turned into 0.185 bands, that is the unit used.
[34:31.680 --> 34:38.220]  So, 0.185 bands, which is equal to 1.85 decibands, or 3.7 half decibands.
[34:38.780 --> 34:43.340]  And we can do the same for the, if we don't get a match.
[34:45.020 --> 34:51.400]  So, if it was determined that if you have a score above 34, then you are more likely to be in-depth than not.
[34:52.400 --> 35:00.860]  But our actual message has a score of 52, meaning it has 8 to 1 odds of being in-depth, or 400 times more likely than in randomness.
[35:01.260 --> 35:14.340]  The reason that its odds are so high, even though there's only 9 matches, which doesn't line up with the addition, the reason its odds are so high, is because we have 2 pairs of 2 matches in a row.
[35:15.180 --> 35:23.560]  And when we get 2 matches in a row, and 3 matches in a row, and 4 matches in a row, and so on, the odds, the scores that get added get way higher.
[35:24.320 --> 35:27.540]  And so, Turing and his team used this.
[35:28.140 --> 35:30.220]  I'm not going to go over it, because the math gets pretty hard.
[35:31.100 --> 35:32.380]  I don't think I have time for that.
[35:32.600 --> 35:36.040]  But, keep in mind, it does get way more complicated from here.
[35:36.960 --> 35:43.440]  So, once we are sufficiently satisfied, the messages are in-depth through this scoring system.
[35:44.060 --> 35:47.540]  We can look at the last two letters of the message indicator groups.
[35:47.820 --> 35:49.240]  That was A and E.
[35:49.920 --> 35:52.000]  And we see that the offset is 3.
[35:52.240 --> 35:53.940]  So, E is equal to A minus 3.
[35:54.740 --> 35:58.320]  And you can find a bunch more messages that are in-depth.
[35:58.320 --> 36:01.620]  And you can keep getting these numbers.
[36:02.220 --> 36:04.900]  And eventually, you can make a string out of that.
[36:05.320 --> 36:08.840]  So, E space space A space space F then K.
[36:10.180 --> 36:12.480]  And you can just line this up against an alphabet.
[36:13.660 --> 36:15.240]  You can line this up against an alphabet.
[36:15.880 --> 36:19.580]  And as long as the same letter isn't paired to two different other letters.
[36:20.040 --> 36:22.020]  Or, a letter isn't paired to itself.
[36:22.800 --> 36:25.960]  You can see here first, A is paired to E and A is paired to D.
[36:26.160 --> 36:28.420]  So, this can't be the right position along the alphabet.
[36:28.960 --> 36:31.380]  You can keep checking until it finally works.
[36:31.860 --> 36:33.780]  And there will be multiple positions where it works.
[36:35.780 --> 36:37.060]  And you can keep checking.
[36:37.960 --> 36:40.340]  And eventually, once you get enough of these strings.
[36:41.920 --> 36:43.400]  Once you get enough of these strings.
[36:43.780 --> 36:46.020]  Such as SGL, POV, W, X.
[36:46.360 --> 36:47.740]  And keep in mind the spaces are important.
[36:49.360 --> 36:51.220]  There will only be one spot.
[36:52.780 --> 36:56.220]  Where the rotor crossover doesn't happen in the middle of a string.
[36:58.620 --> 37:01.740]  And where that spot happens determines what rotor is there.
[37:01.740 --> 37:02.820]  Oh, shoot.
[37:04.100 --> 37:04.840]  What did I do?
[37:05.260 --> 37:05.900]  Oh, perfect.
[37:08.440 --> 37:11.600]  When the rotor crossover doesn't happen in the middle of a string.
[37:13.560 --> 37:14.360]  Oh, sorry.
[37:14.620 --> 37:15.220]  I mean to say.
[37:15.420 --> 37:19.100]  A rotor cannot cross over while in the middle of one of these strings.
[37:19.580 --> 37:23.020]  So, we can filter out all the wrong rotors until we find the right one.
[37:24.460 --> 37:24.900]  Sorry.
[37:25.440 --> 37:28.160]  The rotor one crossover is between O and P, actually.
[37:29.580 --> 37:35.060]  So, O and P is the only rotor crossover point that isn't in the middle of one of these strings.
[37:36.880 --> 37:41.140]  So, we know that rotor one has to be the rotor on the rightmost side.
[37:42.600 --> 37:45.660]  And we can repeat this process for the rotor in the middle.
[37:45.660 --> 37:48.920]  It's way harder now because we have...
[37:48.920 --> 37:50.780]  Because there's...
[37:50.780 --> 37:53.120]  The Bamburisms work much less effectively.
[37:53.380 --> 37:56.060]  But you can keep doing this and you can deduce...
[37:56.060 --> 38:00.940]  You can reduce the number of rotor possibilities to about three to 90 from 336.
[38:03.860 --> 38:08.440]  Unfortunately though, the three rotors that were added to the model M3.
[38:08.440 --> 38:10.660]  The rotors 6, 7, and 8.
[38:10.960 --> 38:13.060]  They all had the same crossover point.
[38:13.360 --> 38:16.940]  So, the Bamburisms would only tell you if it was one of those three rotors.
[38:17.080 --> 38:19.060]  It would not tell you which one it was.
[38:21.660 --> 38:23.500]  So, now that we know the...
[38:23.500 --> 38:28.440]  Now that we know the rotor order, or we know enough of them, or we could...
[38:28.880 --> 38:31.320]  Or we have reduced the number that we have to check.
[38:31.320 --> 38:34.620]  We can finally move on to what Alan Turing is most...
[38:34.620 --> 38:37.800]  Or one of the most famous things Alan Turing is known for.
[38:37.960 --> 38:38.980]  His bomb machine.
[38:42.020 --> 38:47.040]  So, famously in the movie, you have two cribs that were used.
[38:47.120 --> 38:52.280]  A crib is just a string of letters that we know is going to be in the message.
[38:52.280 --> 38:54.440]  Or we're very sure is going to be in a message.
[38:54.600 --> 38:57.400]  In the movie, they use weather report, which is written here in German.
[38:57.620 --> 38:59.120]  Or Heil Hitler as well.
[39:00.680 --> 39:05.940]  And so, if you have the actual message, you can line this up against the message.
[39:07.240 --> 39:07.940]  Like this.
[39:08.220 --> 39:10.560]  So that two letters don't overlap.
[39:10.880 --> 39:13.080]  Because again, a letter cannot encrypt as itself.
[39:14.380 --> 39:17.220]  So, let's assume we have the right position here.
[39:17.520 --> 39:20.960]  You would have to have found the right position with that one...
[39:21.880 --> 39:24.760]  You would have to have found the right position for the bomb machine to work.
[39:25.560 --> 39:31.520]  But assuming we did, we now have 13 pairs of letters in rotor position one.
[39:32.040 --> 39:35.180]  Of course, they were letters before, so it isn't the real rotor position one.
[39:35.440 --> 39:37.320]  But for our sakes, we can say it is.
[39:38.300 --> 39:41.060]  For rotor position one, J and W are paired.
[39:41.300 --> 39:42.700]  That's shown here on this map.
[39:42.700 --> 39:48.480]  T and E are paired on positions two, three and four... are paired on position two.
[39:48.960 --> 39:50.720]  And I have starred here.
[39:51.140 --> 39:52.580]  Every position T is paired.
[39:53.740 --> 39:56.680]  And so, we can make a map.
[39:56.680 --> 39:58.020]  This is called a menu.
[39:58.360 --> 40:01.320]  It's a diagram of all the... of all the pairings.
[40:01.560 --> 40:06.000]  We can make a menu of all of the pairings as shown.
[40:06.460 --> 40:09.140]  The more cycles we see between three letters, the better.
[40:09.400 --> 40:13.960]  Because a cycle makes it much faster for the Enigma machine to do its job.
[40:14.180 --> 40:15.060]  Which I'll explain in a minute.
[40:16.600 --> 40:23.820]  So, a decryptor, assuming they found the right position, they know a few... they know some things.
[40:24.660 --> 40:29.880]  They know that T goes through the plug board.
[40:30.020 --> 40:32.260]  It goes through rotor position two.
[40:32.780 --> 40:35.040]  And then it goes through the plug board again.
[40:35.180 --> 40:36.100]  And it outputs E.
[40:36.500 --> 40:44.680]  So, what the actual bomb machine did was it would take a guess at the first plug board pairing.
[40:44.680 --> 40:46.660]  It would say T and A are connected.
[40:47.960 --> 40:49.940]  Then, we know rotor position two.
[40:50.280 --> 40:55.800]  So, A would go into P. We know what it would go to because we know the rotors and the internal wiring and the setting.
[40:57.320 --> 41:00.640]  So, A would go through the rotors at position two.
[41:01.580 --> 41:04.060]  And now we know what the last pairing has to be.
[41:04.320 --> 41:07.180]  P and E must be paired if T and A are paired.
[41:07.660 --> 41:09.080]  And so, we keep going on.
[41:09.180 --> 41:11.000]  We have four different pairings T has.
[41:11.280 --> 41:13.820]  So, we assume T and A are paired.
[41:13.820 --> 41:20.420]  A goes through rotor position 3 to get K, and K and S must be paired.
[41:20.580 --> 41:23.160]  See here, rotor position 3 has T and S paired.
[41:24.620 --> 41:26.540]  So K and S must be a plugboard position.
[41:26.760 --> 41:29.700]  We do this again for T and R and T and J.
[41:30.000 --> 41:33.100]  But at T and J, there's a contradiction.
[41:33.600 --> 41:37.140]  T is paired to A, and T is also paired to J.
[41:37.700 --> 41:39.560]  That cannot happen on Enigma.
[41:39.920 --> 41:43.100]  A letter can only be paired to one other letter on the plugboard.
[41:44.800 --> 41:51.060]  So, that means T and J cannot possibly be on the plugboard in this rotor position we're checking right now.
[41:52.140 --> 41:54.580]  It cannot possibly be on the plugboard.
[41:56.660 --> 42:02.540]  So, if it can't be on the plugboard, well, this is where Alan Turing's machine is genius.
[42:04.380 --> 42:06.420]  Every setting is reversible.
[42:06.980 --> 42:09.700]  You might be checking T and J later, right?
[42:09.700 --> 42:19.520]  So, if T and J aren't on the plugboard, and that's a contradiction, in the exact same way, T and A cannot be on the plugboard either.
[42:20.180 --> 42:25.600]  And because T and A are connected to these other plugboard settings, none of these can be on the plugboard.
[42:25.600 --> 42:27.640]  They're all equally contradictory.
[42:28.620 --> 42:35.400]  So, if we check for a letter, if we check A, B, C, and those are all of our guesses.
[42:36.300 --> 42:39.380]  We wouldn't check J, because we've already shown that can't be possible.
[42:40.540 --> 42:46.380]  If we check every single one, and all of them contradict, that rotor position cannot possibly work.
[42:46.820 --> 42:49.920]  And you might wonder, well, what if it's just not connected on the plugboard?
[42:50.440 --> 42:52.900]  Well, the Enigma machine also checked T paired to T.
[42:53.380 --> 42:55.700]  If T is paired to T, that would never have it on the plugboard.
[42:56.280 --> 42:57.840]  It would just mean there's not a plug there.
[42:59.980 --> 43:04.860]  So, if all 26 pairs contradicted, you would step the rotor on the entire machine.
[43:06.700 --> 43:10.400]  If zero pairs contradicted, you might think, well, that's 26 possible solutions.
[43:11.200 --> 43:15.560]  But it turns out that that actually happens quite a lot.
[43:16.560 --> 43:23.660]  And it usually means that we got unlucky with the rotor position, and that it just paired the wrong letters to the wrong places.
[43:23.960 --> 43:27.780]  And so, this solver was really not a solver.
[43:27.960 --> 43:29.520]  It was just a candidate finder.
[43:29.620 --> 43:32.160]  It found what was the most likely candidate to work.
[43:32.780 --> 43:35.820]  So, if zero pairs contradicted, we would rule that out.
[43:35.900 --> 43:37.060]  It's probably not right.
[43:37.740 --> 43:39.720]  It could be, but it probably isn't.
[43:40.320 --> 43:44.320]  If some pairs contradict, again, we would just step the rotor, because it's probably not right.
[43:44.540 --> 43:46.620]  But it is more probable than before.
[43:46.980 --> 43:54.600]  So, on later updates of the enigma of the bomb machine, on later updates, it would actually be able to log those rotor positions.
[43:54.940 --> 44:05.720]  So, if only one pair survives, and the machine stops, and that pair is a false positive, we could go back and check those possibilities.
[44:06.400 --> 44:16.360]  Now, like I said, if only one pair survives, just like the actual concept of the turning machine, the bomb machine would stop right there.
[44:16.540 --> 44:17.660]  And that is the output.
[44:18.000 --> 44:21.940]  We would know all the plug board pairings, like I said before.
[44:22.300 --> 44:24.680]  We would know the rotor positions.
[44:25.140 --> 44:26.480]  We would know the rotor order.
[44:26.480 --> 44:29.100]  And we would know the ring setting.
[44:29.960 --> 44:32.520]  And that would be manually checked by a person.
[44:34.580 --> 44:42.020]  Now, for a pair to survive, that means that we would also have to check all the pairings between these other letters.
[44:43.700 --> 44:48.200]  So, let's say, for T, we have checked the letter F.
[44:48.400 --> 44:49.340]  And it works.
[44:49.600 --> 44:50.620]  The letter F works.
[44:50.760 --> 44:54.720]  There's no contradiction between these four statements here.
[44:56.220 --> 44:58.280]  Well, now we know the outputs.
[44:58.520 --> 44:59.900]  We already know what they should be.
[45:00.400 --> 45:01.680]  So, we know the outputs.
[45:01.920 --> 45:03.400]  Now we check each one of these.
[45:03.600 --> 45:05.340]  We check E and everything it connects to.
[45:05.480 --> 45:07.220]  We check S and everything it connects to.
[45:07.960 --> 45:12.860]  And we branch out sort of like that until we've checked every single possible pairing.
[45:14.220 --> 45:25.460]  And when we find that only one pair survives and every single other combination doesn't, every single guess we make doesn't, that means the machine stops.
[45:26.280 --> 45:27.820]  And so, that's the Enigma machine.
[45:28.300 --> 45:30.820]  That's the bomb machine.
[45:31.000 --> 45:33.020]  That's his very famous machine.
[45:38.760 --> 45:39.960]  So, yes.
[45:40.660 --> 45:41.440]  Thank you.
[45:41.600 --> 45:41.920]  That's it.
[45:42.440 --> 45:50.820]  I would like to thank the Euler Cryptography Circle for actually getting me interested in doing this.
[45:51.380 --> 45:54.480]  And the runner of that, Dr. Simon Rubenstein-Salzito.
[45:55.100 --> 46:06.000]  I would like to thank Dr. James Grime for answering my emails and writing his paper on the answering the Enigma machine, which was a very useful source.
[46:07.480 --> 46:12.280]  Similarly, I'd like to thank Dr. Klaus Schmay for helping me with some questions.
[46:12.960 --> 46:13.760]  Dr. A.
[46:13.840 --> 46:22.280]  Ray Miller and Ryan O'Reilly for contacting me and writing the cryptology mathematics of Enigma.
[46:22.280 --> 46:27.820]  Dr. David Riemann and Momath for also answering some questions.
[46:28.720 --> 46:30.060]  And Dr. Chris Christanson.
[46:30.760 --> 46:34.380]  And Dr. Tom Pereira for answering my emails.
[46:35.600 --> 46:36.680]  Are there any questions?
[46:45.680 --> 46:46.360]  Yes.
[46:47.960 --> 46:52.120]  The Polish composer, did he survive the war?
[46:52.620 --> 46:54.480]  I'm not sure about that.
[46:55.860 --> 46:56.540]  Yes.
[46:58.120 --> 46:59.000]  Great talk.
[46:59.360 --> 47:00.480]  Fascinating material.
[47:00.720 --> 47:02.380]  I'm just wondering two things.
[47:02.600 --> 47:06.640]  First of all, there's always this cat and mouse game with the Germans, right?
[47:06.800 --> 47:09.520]  And so they keep changing their ciphers.
[47:09.680 --> 47:13.380]  They keep introducing greater and greater complexity to their machines.
[47:13.580 --> 47:18.560]  To what extent has it been filled in through, you know, greater archival research and things like that?
[47:18.680 --> 47:23.120]  The extent of German knowledge of allies' advancement.
[47:23.120 --> 47:28.860]  In other words, did they just keep making it more and more complicated because they were doing that?
[47:29.020 --> 47:36.180]  Or was it more, you know, on their side, they were getting intel, you know, saying the allies are cracking this one.
[47:36.280 --> 47:37.280]  We've got to make it more and more.
[47:37.420 --> 47:38.440]  That's the first question.
[47:38.580 --> 47:41.180]  The second question is to what extent...
[47:41.180 --> 47:43.180]  Because obviously since this is a character...
[47:43.180 --> 47:45.600]  It's a character substitution stuff, right?
[47:45.760 --> 47:46.040]  Yes.
[47:46.040 --> 47:47.460]  So that...
[47:47.460 --> 47:48.980]  In other words, the...
[47:48.980 --> 47:50.100]  You're gonna...
[47:50.780 --> 47:58.180]  There's presumably gonna be, like, involvement of German linguists and people like that who recognize patterns and, oh, this is this word, this could be...
[47:58.180 --> 48:07.060]  To what extent were you able to find the ways in which the code breakers work with the linguists and back and forth?
[48:07.320 --> 48:07.620]  Yes.
[48:07.920 --> 48:08.220]  So...
[48:08.220 --> 48:10.020]  I'll answer your second question first.
[48:10.100 --> 48:10.200]  Yes, sir.
[48:11.560 --> 48:12.700]  There were actually...
[48:12.700 --> 48:13.540]  There was not...
[48:13.540 --> 48:15.440]  There were not many linguists involved.
[48:15.980 --> 48:24.180]  This was actually the first cryptological problem that had basically no linguistic use and all mathematical use.
[48:24.400 --> 48:26.300]  You can actually see in the movie The Imitation Game.
[48:27.540 --> 48:29.080]  Once Alan Turing...
[48:29.080 --> 48:30.380]  I don't think this is a real fact.
[48:30.480 --> 48:31.320]  I think this is drama.
[48:31.860 --> 48:33.180]  But in the actual...
[48:33.180 --> 48:41.820]  In the movie, Alan Turing fires two linguists and he says they're terrible, they're bad linguists and they're terrible cryptographers.
[48:43.200 --> 48:45.920]  And so, yeah, linguists were not very necessary.
[48:45.920 --> 48:51.040]  As long as somebody could speak German and, you know, choose a crib well, it was basically math from there on.
[48:51.960 --> 48:53.500]  And the first question...
[48:53.500 --> 48:58.480]  Yes, it was a cat and mouse game, but for some of it.
[48:58.680 --> 48:59.980]  And there was...
[49:00.800 --> 49:02.660]  And some of it was just the German...
[49:02.660 --> 49:05.240]  The Nazis increasing their security as they went along.
[49:05.240 --> 49:07.560]  For example, during the Polish efforts...
[49:08.700 --> 49:10.240]  During the Polish efforts...
[49:11.020 --> 49:11.540]  I think...
[49:11.540 --> 49:15.940]  I'm pretty sure that it was more of the Germans increasing their security as they went along.
[49:16.120 --> 49:23.220]  Like, as you know, there were four years where the Polish could very quickly decrypt the messages using just their cyclometer and their database.
[49:24.100 --> 49:25.600]  And so there was...
[49:25.600 --> 49:26.440]  There...
[49:26.440 --> 49:30.220]  And, you know, on November 1st, they changed the wiring of the reflector.
[49:30.500 --> 49:34.400]  If they had known the Polish were decrypting their messages, they would have done way more, of course.
[49:34.400 --> 49:35.660]  So I...
[49:35.660 --> 49:39.260]  And they would have changed the message indicator right from there instead of waiting a year.
[49:39.760 --> 49:40.680]  So there I'm...
[49:40.680 --> 49:45.600]  I'm pretty sure it was just a standard security increase.
[49:52.980 --> 49:57.140]  So I forgot to say, this was all done in 1940.
[49:57.660 --> 49:58.020]  They...
[49:58.020 --> 50:01.940]  The UK had solved it in 1940, way earlier than you might have thought.
[50:03.160 --> 50:04.200]  And so...
[50:04.880 --> 50:05.860]  And so...
[50:05.860 --> 50:14.680]  And so in 1942, the naval operators, they knew that, like, they had a suspicion something was up.
[50:14.840 --> 50:21.820]  Of course, with the intel, like, again, this is a drama point in the movie, they were very careful on what they acted on.
[50:21.820 --> 50:22.800]  And there...
[50:22.800 --> 50:27.760]  Whenever they acted, they made sure there was another way they could have gotten that intelligence.
[50:28.120 --> 50:31.280]  They made sure there was a way that they could have gotten it without Enigma.
[50:31.580 --> 50:35.240]  Because the Germans, they thought Enigma was unbreakable, rightfully so.
[50:36.520 --> 50:37.000]  And...
[50:37.480 --> 50:39.020]  And so they thought it was unbreakable.
[50:39.160 --> 50:43.060]  And so if they found out it wasn't, you know, it would be very bad for the intelligence.
[50:43.600 --> 50:46.980]  But they had some small suspicions in 1942.
[50:47.280 --> 50:48.460]  And so they...
[50:48.460 --> 50:55.460]  The naval Enigma intelligence released the Enigma Mark IV, or the Enigma M4, which actually had a fourth rotor.
[50:55.820 --> 50:57.380]  It was a weird rotor.
[50:57.600 --> 51:01.660]  I'm not sure entirely on the mechanics, but it wouldn't rotate very much.
[51:02.080 --> 51:03.580]  But it was a fourth rotor added.
[51:04.080 --> 51:04.780]  So, yes.
[51:05.840 --> 51:06.320]  I...
[51:07.040 --> 51:13.440]  I'll help with the answer to the question, because I met Peter Hilton, Dr. Peter Hilton later.
[51:13.920 --> 51:14.080]  Wow.
[51:14.080 --> 51:17.840]  In the movie, he's the guy that punches out Alan Turing.
[51:18.600 --> 51:20.560]  Which I think he would have thought was really funny.
[51:20.680 --> 51:21.580]  He's been gone for a long time.
[51:21.660 --> 51:23.500]  But he answered that question for us.
[51:23.620 --> 51:31.240]  He said that they didn't know, but they thought that Rommel knew, because Rommel kept lying on all of his reports.
[51:31.900 --> 51:37.220]  And they said, so Rommel seemed to always tell them that he's out of guns and all of that.
[51:37.300 --> 51:40.680]  And then the British would fight Rommel or the Americans later.
[51:40.940 --> 51:43.380]  And all of a sudden, Rommel was fine.
[51:43.620 --> 51:46.480]  But he said that they didn't seem to guess it.
[51:46.480 --> 52:02.180]  But the other thing that he said was that the one... the other help they had was that every time the Nazis would say, send this out on all the wires, it would go to the lesser secure sites.
[52:02.360 --> 52:08.600]  And so they would get the free... they would get a free hand from the Nazis, because here's Hitler's speech sent to everybody.
[52:08.600 --> 52:11.220]  And now they have all the settings for everything.
[52:11.940 --> 52:15.900]  And they said the worst that ever happened to them was the Italians getting out of the war.
[52:16.160 --> 52:22.940]  Because the Italian cipherers, Peter said they could... they could... you get a beer, you could finish it before you finish the beer.
[52:22.940 --> 52:23.900]  Okay.
[52:25.580 --> 52:26.260]  Very well.
[52:26.760 --> 52:27.760]  Any more questions?
[52:28.300 --> 52:28.680]  Yes.
[52:29.040 --> 52:36.760]  How often were the codebooks exchanged and how long did this duration for the English as well?
[52:37.280 --> 52:38.920]  How long did the codebooks last?
[52:39.140 --> 52:39.300]  Yeah.
[52:39.720 --> 52:44.180]  Like, say, codebook had code to daily codes for what duration of time?
[52:44.600 --> 52:45.440]  I'm not sure.
[52:45.720 --> 52:48.300]  I think it was a few months, but I'm not very sure.
[52:50.460 --> 52:51.000]  Oh, yeah.
[52:51.200 --> 52:57.520]  So like, like shown here, they were... the plugboard and ground settings, they were changed every day.
[52:57.900 --> 53:00.060]  The rotor and order and ring settings were on odd days.
[53:00.140 --> 53:02.840]  And you can, you know, you can see how dense the info is packed in here.
[53:03.000 --> 53:05.540]  I'm pretty sure it was a few months that each would last.
[53:05.660 --> 53:07.740]  And then they would change it out across the entire Navy.
[53:08.820 --> 53:09.520]  Any more questions?
[53:09.880 --> 53:10.120]  Yes.
[53:10.420 --> 53:15.060]  So you talked about the British and Polish intelligence being your own documents.
[53:15.060 --> 53:19.200]  Were there any other countries that contributed to the research?
[53:21.660 --> 53:23.040]  I'm not sure.
[53:24.700 --> 53:25.540]  Any more questions?
[53:27.840 --> 53:28.340]  Yes.
[53:28.640 --> 53:34.860]  You made a comment earlier in your talk about the wiring, about the theoretical basis behind the wiring in the rotor.
[53:35.020 --> 53:36.460]  Can you elaborate on that anymore?
[53:36.560 --> 53:38.720]  Do you know more about how the wiring was chosen?
[53:38.940 --> 53:41.720]  Or was it just... I've always assumed it was just random.
[53:43.220 --> 53:44.340]  Yeah, here.
[53:47.260 --> 54:02.520]  I'm pretty sure that the wiring was chosen at random, but across every Enigma machine, if you had a rotor labeled one physically on the rotor, that rotor would have the same internal wiring as every other rotor one across the Enigma machines.
[54:02.760 --> 54:03.140]  Sure.
[54:03.560 --> 54:03.600]  Okay.
[54:04.460 --> 54:05.680]  Within a rotor?
[54:05.680 --> 54:05.720]  Sure.
[54:06.860 --> 54:07.780]  Like the actual wiring?
[54:09.220 --> 54:09.380]  Chosen.
[54:09.480 --> 54:10.000]  You know it's just random?
[54:10.300 --> 54:11.360]  Yes, it's just random.
[54:13.580 --> 54:14.020]  Yes.
[54:14.420 --> 54:15.080]  Are you...
[54:15.980 --> 54:16.420]  Okay.
[54:17.200 --> 54:17.560]  Okay.
[54:17.680 --> 54:18.420]  Thank you everybody for coming.