I've been watching Art of the Problem's videos for years and find that they are an incredible resource, not only for learning about computer science, computer engineering, mathematics, logic, communication, encryption-decryption, etc., but for discovering the common threads linking all of these fields together. As an added bonus, the films are so thoughtfully scripted, painstakingly shot, and carefully mixed--in other words, so exquisitely produced--that they provide an inadvertent crash course on film making.
I had a bit of fun making a similar encryption engine in BASIC a long while back. But PGP (or its open-source equivalent, GPG) is still more convenient for electronic information transfers. Enigma is a symmetric encryption scheme which means you have to find a secure method of transferring the keys before you can transfer secure messages. PGP and GPG use asymmetric keys, so you can send the public key through insecure means without compromising security.
It took me some time to sort out the following things: • The _rotor setting:_ which rotors were used for a particular day and the order in which they were assembled in the Enigma machine: I - II - III, II - III - I or any combination. • The _ring setting,_ which was where the letter of the alphabet on the ring on each rotor was rotated and locked in relation to the wires in each rotor. • The _plugboard setting:_ which pairs of letters of the alphabet were swapped by plugging in 10 cables to swap pairs of letters; CI, MV, etc. The above is the _key setting._ There was a different key setting for each day of the month. Every operator had a key sheet for the current month. • The _ground setting_ was the position of the letters visible in the window of the Enigma machine. When one Enigma operator sent a message to another he chose a three letter ground setting at random and sent it to the other operator in plaintext. Both operators set their machines to that three letter ground setting. The first operator would then send another set of three letters in ciphertext, scrambled by the ground setting of that first set of three letters. The second operator would type in the scrambled letters, his Enigma machine would descramble it and give him the new three lettet ground setting in plaintext. Both operators set their machines to this new ground setting. It would scramble the plaintext message into ciphertext from the sending operator on his machine and unscramble it for the receiving operator on _his_ machine. Even if the enemy had an Enigma machine he would still need a key sheet with the key settings for that particular day. Hearing the first three letter combination in plaintext wouldn’t help him because he wouldn’t know which rotors were in which order with which ring settings with which plugboard settings he needed to set up his Enigma machine. It was unbreakable. Unless the enemy cheated.
Could you once explain in which of these steps, the mistake was done by the operators mentioned at 7:30 i.e. regarding some initial position of rotors or something?
@@puneetkumarsingh1484 The mistake mentioned in the video was just changing the settings by one or two clicks: say the ground setting for the last message was FSJ and the operator just scrolled the rotors over a few clicks to something like HUL. The code breakers learned to look for goofs like that. Operators would also send out something like HIT as the plaintext setting, then send LER in ciphertext; it would be scrambled into something like XDP. But the code breakers could easily guess it was HIT and LER: Hitler. Same thing for BER LIN, LON DON, MAD RID, etc. Six letter cuss words were also popular and also easy to figure out. Some operators used their initials and their girlfriend’s initials and the code breakers figured that out. It wasn’t just that the operators were tired/lazy/indifferent, they were told over and over again the Enigma was unbreakable, so why worry?
WELL, if the operator made a random setting of the rotors how did the other operator know how to set his machine so that they matched. Unless he sent the settings to the other operator on the old settings. Then how were all the other machines set to the same settings.
@@ArtOfTheProblem That's not quite right. The sender would configure his device according to the initial settings for the day. The sender would choose and type 3 random letters (eg: "CAT") into the device TWICE, recording 6 enciphered letters. The sender would then spin the rotors until "CAT" was displayed in the windows, and then type the plaintext message, recording the enciphered message on a notepad. Then, the 6 enciphered letters and the enciphered message would be broadcast 'wireless' (all in Morse code). Anyone(!) receiving the transmission could record the letters of that Morse code broadcast. If one KNEW the correct settings (ie. other Germans), one could set one's device according to the day's configuration. One could then enter the first 6 letters received... out would come "CATCAT" One could then spin the rotors to display "CAT" and type the rest of the enciphered message, recording the plaintext. Every message was to be processed this way, including choosing different trios of random letters for each message. The difficulty for anyone trying to decipher is to determine which one of the 159x10^18 possible initial device configurations is in effect for today... At one 'try' per second, well... Consider this: The age of the universe is 13.7 billion years multiplied by about 365 * 24 * 60 * 60 which is about 0.4x10^18 seconds... Roughly speaking, a crude brute force attack would require 'trying' roughly 400 settings per second for every second since the Big Bang... On average, one might find the correct setting in only half the time since the birth of the universe. And, start from the very beginning again only 24 hours from now. If you're curious, the question is how fast would brute force have to be to be useful if the enemy's messages concerned an event to occur the following day. A day is 24*60*60 (86400) seconds, but we want to decrypt within, say, 6 hours of receiving a message at 6AM (the start of the Enigma configuration day). 159x10^18 divided by 21600 seconds is 7361 trillion tests each and every second... That's over 7 million billion tests each second. Apples' new M1 chip isn't quite up to that capability...
The Brits were trying to decipher the engima, why do you have to deal with trying to decipher the roters and all the alphanumeric conversions. The plugboard pins are a 1 to 1 conversion, if you just look at the plugboard conversation which is at the end of the chain, would it not solve the whole problem of trying to deciphering the enigma?
Didn't you say that the initial configration is called a key setting, which is something the germen operators shoudl agree on and setup the machine accroding to. But later in the video you said that the operators set their machine to some random state first, which is kinda confusing
what does a key setting look like, should it be 3 numbers ( one for each column) or should it be one number? You made it sound like the key setting is 3 numbers but in the key space table you show, you only highlighted one in the end( which I assume is the sum of the three numbers?).
How about the decoding the plug board as it increases the key space significantly even more than the rotors . In fact one can think of the plugboard as a variable wiring rotor .
Exactly right, except that this "variable wiring rotor" doesn't rotate at all... 🙂 Just like the Beatles sang about "Her Majesty", the plugboard "changes from day-to-day."
@@josebonilla8774 also, i realised after commenting he worked for khan acadrmy, and the video was very good, but at the time, I thought he stole the video, so I was mad, but he created the video
The allies got the design info of the device and rotors from a disgruntled brother of military type. They already 'knew' the electro-mechanical design (from the Poles). What helped, rarely, was capturing a useful monthly sheet listing daily configuration settings without revealing the fact the configuration was known. At month's end, the allies were effectively 'blind' again...
Rather predictable American version of history which suggests deciphering enigma was an Anglo-American achievement. Bombe and Collosus were both British.
You need to find out about the Polish mathematicians who figured out 3 rotor Enigma in 1920... They did it purely with reason initially, not "getting to peek into the machine" as the British and French did just 2 weeks before Poland was invaded...
It had basic flaws from the beginning and was useless. The Windtalkers were billion times much better. However, the Sigsaly was very good and became the current CDMA handphone. Mechanics is always behind electronics. Even nowadays Germany does not have related effective technology. Korea has SEED and KNOX 2.0 and one from korea solved the heartbleed problem of OpenSSL.
I've been watching Art of the Problem's videos for years and find that they are an incredible resource, not only for learning about computer science, computer engineering, mathematics, logic, communication, encryption-decryption, etc., but for discovering the common threads linking all of these fields together. As an added bonus, the films are so thoughtfully scripted, painstakingly shot, and carefully mixed--in other words, so exquisitely produced--that they provide an inadvertent crash course on film making.
wow never thought of it this way. I'm heartened to read this comment. I'm sad that at this moment I do not have the time to produce these videos :(
Easiest subscription decision I've ever made. Fascinating video.
Alan, what a genius, we couldn't have been more lucky.
I had a bit of fun making a similar encryption engine in BASIC a long while back. But PGP (or its open-source equivalent, GPG) is still more convenient for electronic information transfers.
Enigma is a symmetric encryption scheme which means you have to find a secure method of transferring the keys before you can transfer secure messages. PGP and GPG use asymmetric keys, so you can send the public key through insecure means without compromising security.
It took me some time to sort out the following things:
• The _rotor setting:_ which rotors were used for a particular day and the order in which they were assembled in the Enigma machine: I - II - III, II - III - I or any combination.
• The _ring setting,_ which was where the letter of the alphabet on the ring on each rotor was rotated and locked in relation to the wires in each rotor.
• The _plugboard setting:_ which pairs of letters of the alphabet were swapped by plugging in 10 cables to swap pairs of letters; CI, MV, etc.
The above is the _key setting._ There was a different key setting for each day of the month. Every operator had a key sheet for the current month.
• The _ground setting_ was the position of the letters visible in the window of the Enigma machine.
When one Enigma operator sent a message to another he chose a three letter ground setting at random and sent it to the other operator in plaintext. Both operators set their machines to that three letter ground setting. The first operator would then send another set of three letters in ciphertext, scrambled by the ground setting of that first set of three letters. The second operator would type in the scrambled letters, his Enigma machine would descramble it and give him the new three lettet ground setting in plaintext. Both operators set their machines to this new ground setting. It would scramble the plaintext message into ciphertext from the sending operator on his machine and unscramble it for the receiving operator on _his_ machine.
Even if the enemy had an Enigma machine he would still need a key sheet with the key settings for that particular day. Hearing the first three letter combination in plaintext wouldn’t help him because he wouldn’t know which rotors were in which order with which ring settings with which plugboard settings he needed to set up his Enigma machine. It was unbreakable.
Unless the enemy cheated.
Could you once explain in which of these steps, the mistake was done by the operators mentioned at 7:30 i.e. regarding some initial position of rotors or something?
@@puneetkumarsingh1484 The mistake mentioned in the video was just changing the settings by one or two clicks: say the ground setting for the last message was FSJ and the operator just scrolled the rotors over a few clicks to something like HUL. The code breakers learned to look for goofs like that. Operators would also send out something like HIT as the plaintext setting, then send LER in ciphertext; it would be scrambled into something like XDP. But the code breakers could easily guess it was HIT and LER: Hitler. Same thing for BER LIN, LON DON, MAD RID, etc. Six letter cuss words were also popular and also easy to figure out. Some operators used their initials and their girlfriend’s initials and the code breakers figured that out. It wasn’t just that the operators were tired/lazy/indifferent, they were told over and over again the Enigma was unbreakable, so why worry?
WELL, if the operator made a random setting of the rotors how did the other operator know how to set his machine so that they matched. Unless he sent the settings to the other operator on the old settings. Then how were all the other machines set to the same settings.
yes they would share those in advance
@@ArtOfTheProblem That's not quite right.
The sender would configure his device according to the initial settings for the day.
The sender would choose and type 3 random letters (eg: "CAT") into the device TWICE, recording 6 enciphered letters.
The sender would then spin the rotors until "CAT" was displayed in the windows, and then type the plaintext message, recording the enciphered message on a notepad.
Then, the 6 enciphered letters and the enciphered message would be broadcast 'wireless' (all in Morse code).
Anyone(!) receiving the transmission could record the letters of that Morse code broadcast.
If one KNEW the correct settings (ie. other Germans), one could set one's device according to the day's configuration.
One could then enter the first 6 letters received... out would come "CATCAT"
One could then spin the rotors to display "CAT" and type the rest of the enciphered message, recording the plaintext.
Every message was to be processed this way, including choosing different trios of random letters for each message.
The difficulty for anyone trying to decipher is to determine which one of the 159x10^18 possible initial device configurations is in effect for today... At one 'try' per second, well... Consider this: The age of the universe is
13.7 billion years multiplied by about 365 * 24 * 60 * 60 which is about 0.4x10^18 seconds...
Roughly speaking, a crude brute force attack would require 'trying' roughly 400 settings per second for every second since the Big Bang... On average, one might find the correct setting in only half the time since the birth of the universe. And, start from the very beginning again only 24 hours from now.
If you're curious, the question is how fast would brute force have to be to be useful if the enemy's messages concerned an event to occur the following day. A day is 24*60*60 (86400) seconds, but we want to decrypt within, say, 6 hours of receiving a message at 6AM (the start of the Enigma configuration day). 159x10^18 divided by 21600 seconds is 7361 trillion tests each and every second... That's over 7 million billion tests each second. Apples' new M1 chip isn't quite up to that capability...
The Brits were trying to decipher the engima, why do you have to deal with trying to decipher the roters and all the alphanumeric conversions. The plugboard pins
are a 1 to 1 conversion, if you just look at the plugboard conversation which is at the end of the chain, would it not solve the whole problem of trying to deciphering the enigma?
Didn't you say that the initial configration is called a key setting, which is something the germen operators shoudl agree on and setup the machine accroding to. But later in the video you said that the operators set their machine to some random state first, which is kinda confusing
what does a key setting look like, should it be 3 numbers ( one for each column) or should it be one number? You made it sound like the key setting is 3 numbers but in the key space table you show, you only highlighted one in the end( which I assume is the sum of the three numbers?).
I love this channel.
How about the decoding the plug board as it increases the key space significantly even more than the rotors . In fact one can think of the plugboard as a variable wiring rotor .
Exactly right, except that this "variable wiring rotor" doesn't rotate at all... 🙂
Just like the Beatles sang about "Her Majesty", the plugboard "changes from day-to-day."
This is the best video on enigma machine...
thanks i worked really hard on this video
@@ArtOfTheProblem really hard. More like stole video from Khan Academy's website
@@josebonilla8774 u replied 5 months later
@@josebonilla8774 also, i realised after commenting he worked for khan acadrmy, and the video was very good, but at the time, I thought he stole the video, so I was mad, but he created the video
Alan turing was a brilliant man who got treated despicably by those whom he saved
creepy music, but very informative!
0:51 I grant you that the EU is pretty much a continuation of Hitler's plan, but that map right there is a bit ahead of its time.
perfect explanation
so an initial key configration would determine the whole shiifting sequence right?
imitation game :)
very good ending line :-)
wrr
there were 5 rotors to choose from and they only took 3 so its 5 * 4 * 3
good
You're great man!
@ArtOfTheProblem So, next video will be uploaded by tomorrow evening then, Yes?
Amazing!
Roter encryption is fucking brilliant
I wonder how long it'd take my computer to decrypt an old Enigma code (without the keys that the allies discovered)..
Depends on what enigma. From minutes to millions of years.
Didn't they find the machine in a uboat?
I believe so yes, a crashed one
The allies got the design info of the device and rotors from a disgruntled brother of military type.
They already 'knew' the electro-mechanical design (from the Poles).
What helped, rarely, was capturing a useful monthly sheet listing daily configuration settings without revealing the fact the configuration was known. At month's end, the allies were effectively 'blind' again...
lucky the allies were given an enigma machine to reverse engineer hey...
IF YOU PLAY IT 1.5 SPEED HE WILL TALK AT A NORMAL PACE.
Rather predictable American version of history which suggests deciphering enigma was an Anglo-American achievement. Bombe and Collosus were both British.
You need to find out about the Polish mathematicians who figured out 3 rotor Enigma in 1920... They did it purely with reason initially, not "getting to peek into the machine" as the British and French did just 2 weeks before Poland was invaded...
It had basic flaws from the beginning and was useless. The Windtalkers were billion times much better. However, the Sigsaly was very good and became the current CDMA handphone. Mechanics is always behind electronics. Even nowadays Germany does not have related effective technology. Korea has SEED and KNOX 2.0 and one from korea solved the heartbleed problem of OpenSSL.