Cracking Enigma in 2021 - Computerphile 

exactly, this is so overlooked

If you go to Bletchley Park, you'll see their contribution is well-recognized. Gays FTW!

The 2 Zlote coin has an enigma wheel on one face

@@DunderKlomp I've been at Bletchley Park Computing Museum 3 years ago and found ZERO (literally) mention about any Polish contribution.

* Turing

Indeed. But also to Arthur Scherbius, the inventor of the enigma machine itself: it’s not even trivial 80 years later.

No joke. I’m a computer science student. After watching “the imitation game” I searched up “how does Enigma work” and I thought “ah it must be so easy to understand and decode now!”. Nope.

It's an achievement of many people, including Marian Rejewski, who broke the simpler version of Enigma in 1930. His work was then used by Turing & Park as a foundation for newer Enigma in 1941.

Not to mention, Mike could code this up on his laptop, pre-built and bought at a store, in a high-level coding language. Turning *built* his computer. Imagine not simply having to write the code, but having to also physically construct a machine solely to run it. No using pre-built chips, no machine code, no assembly code, no standardization, no reference for building such a machine or any help from other learned people, as at the time, no such machine had ever really been built and there were no people who knew how to build it. He was a once in a generation genius.

@@projecttitanomega The "bomb" computers were a Polish design, not something Turing came up with.

I mean this is why I'm watching this whole video and am not even slightly bored.

Haha, I did the same, and it was fun indeed. But I wasn't able the write code to crack Enigma yet. As mentioned in the video, a brute force attack will take too long, even with modern computers.

@@alainbesseleer6516 An average laptop has like what, 4-6 cores? Try this with a basic workstation that has something like 64 cores slugging through the computations at 4ghz. Just based on the amount of alu available and their sheer size given nowadays they can operate with 64 bit values, you can do quite a bit more than you'd assume and it's relatively affordable (for cracking the enigma at least... forget anything short of a chunk from the national budget to crack a decent modern encryption).

@@Hr1s7i Even better use compute shaders and a stack of GPU's and you will be looking at thousands of cores to do the work of decryption. Also don't use a sequential brute force.

implemented*

you just to steal the machine

@@gezzuzzful Well, that's not what he said. Of course knowing how enigma works (i.e. stealing an enigma machine) is the fundament to break the code. The point here is, how do you know if the encrypted message is actually an enigma cypher? Imagine I give you some encrypted message right now. How do you know if this was encrypted with enigma or maybe RSA or AES. Maybe just a simple Caesar cipher or a simple pre-shared-key xor cypher. All your attempts to crack it as if its an enigma cypher would not really help you.

Also how difficult to decipher it would be if you didn't know what language was encrypted. If you decide Swahili or Martian successfully, it's still useless to you if you can't recognise it.

@@Bunny99s It would be abundantly clear that it wasn't a Caeser-shift cypher, if it's a known English (or American) message which fails the ETOAN frequency test. After that, I suspect that it would be a bit of a guessing-game as to what encryption system was used and I doubt that the 5-letter cluster WW2 vintage formatting would be used, as it would most likely be sent as a solid block of characters instead. A modern, digital spin on Enigma could use different sized "virtual rotors" and rather than merely 26 positions (just the English letters in one case), could have upper-case, lower-case, numbers 0-9, space and all the commonly used punctuation marks, making rotors with about 70 positions each. Then there's the possibility of eliminating the "tell" of no symbol being encyphered as itself, but whether that's considered to matter when there's now about 24million possible rotor setting combinations from one arrangement of just 4 rotors, compared to the original 4-rotor Naval Enigma with about 0.5million possible rotor setting combination from one arrangement of 26-position rotors. This is also ignoring the "reflector", which doubles the exponent (70^8 or 26^8 instead of "merely" 70^4 or 26^4) by running the circuit back through the rotors. I would also hazard a cautious guess that some loon could even construct a physical version of a 70-position rotor machine, just for the heck of it.

Lol!

How many times has he said that throughout the video? I thought I was going crazy.

Hmm, I think he should have made that more clear honestly, kinda vague.

@@pies765 Basically he said that if you get one of them correctly, the IoC will tend to get slightly better

@@AlePazzaglia WHAT?

Well, yes. That is the most important vulnerability of the Enigma scheme, and the biggest difference to modern schemes.

Lol

I was about to say!

Now I finally know

Lol

Haha yess!

He addresses that at 20:30, mentioning how with a 128-bit or 256-bit encryption, even if you get the first bit correct you'll still have random noise. The fact that Enigma *did* show marked improvement with correctly guessed settings meant that it was inherently insecure to a degree.

Not so obvious if you connect 10 stecker plugs, the IOC will hardly change if you guess 1 plug correctly. Without any stecker plugs connected you can crack 100 character text in a few minutes on a laptop.

@@martinwragg8246 fyi Stecker means plug.

@@Execuor thanks, I did know, just what I call them. 😉

Is there a cryptographic term for this property?

at my school we had a sort of computer club wher we could play call of duty (the original back IN 04, 05) to gain entry you had to get a password that was encrypted with an enigma machine. the clue was HELP (this was the start postion leters of the wheels) and the plug board was pre defined was kinda fun trying to figure it out

Programmers have a different definition for "laziness": expend 8 hours automating a solution to a job that would take 1 hour to do by hand, just in case you have to do it again in the future. The reasoning: I am lazy... 🤷‍♂️

@@costa_marco And that's why programmers are so much more efficient than most others when it comes to doing stuff on computers. Your regular guy would manually update a spreadsheet by printing out a list of things that needs to be updated on a piece of paper, tediously going over every entry. A programmer would spend 2 hours making an interpreter of the other document to automate that process. Instant 20,000% efficiency for the foreseeable future. And you'd be amazed at how many there are out there sitting at computer keyboards day in and day out doing it manually.

@@RealCadde Except xkcd 1319 ;)

Yeah pretty much the first question any programmer asks "Can I get some machine to do this process for me?"

The laziness he's referring to is not the time spent programming the decoder, but the time he'd have to spend waiting for it to produce a response. 3 rotors takes a few seconds. 5 rotors would take hours or days.

Pound's strategy of repeating "if you get one of them correct, it'll be slightly better." over and over might work for you, but the high energy of Professor Moriarty makes for a more engaging Computerphile for me.

Agreed, it also helps that he talks about more interesting topics imo

And he saved middle earth!

Which one is Professor Moriarty? I'm a big fan of Mike and Dave-but I think they are all great

most suspicious too

I 2 try to decipher Twitter messages with enigma for the real message

Also because having to reliably type and transcribe for transmission a several hundred character message was a serious chore. There were rules about not re-sending the same message, due to errors, however because on occasion this was not adhered to the security was compromised. The smarts of all the people working on decrypting these messages was staggering.

@DeHerg *14:31

A great deal of the solution is also from laziness on the part of the germans. Instead of using new codes, they used variations of the same codes. Once the english knew this, they could play with variations and find the key fairly easily.

I think the Kriegsmarine did change the codes once and it took the Allies months to decipher again (or was it adding another rotor). Though they never really change the codes afterwards. One of the flaws with the German's was they believed the Allies could not decipher enigma. If they believed the Allies could, the Germans would most likely have changed the codes (assuming they could to begin with). Instead, Germany focused too much on just espionage.

@@matthewmayton1845 The Enigma codes were changed every day at midnight. The Germans also had a way to do it every hour, but they rarely did that. What you're referring to was when the Navy added a 4th rotor, but by then the codebreaking was so advanced it didn't add much of a problem.

I like your pfp

He is great! One of my favourites is the one where he cracks passwords. Super interesting!

I second that. There are some really good speakers here, but he just combines incredible energy, understanding, humour. Love his videos.

Rob Miles tho

d

Lol, pound for pound

Yes! I'm taking second year ICT, and we were just watching The Imititation Game today (A movie about Turing breaking the Enigma cipher)

@@iHack-ms5nr I loved that movie so much. Granted, there was a lot of movie dramatization and some factual liberties taken, but it's a terrific film that does a great job of piquing viewers' interest about cryptography and WWII.

actually, there were much better rotary machines, but nobody talks about them, because they are just not as famous as Enigma.

Enigma is talked about so much because its breaking was so importance in the war. There were other, better machines, such as the American SIGABA or the British TYPEX, that are not talked about, because they don't have such a compelling story, and because their details are still secret (or they were the last time I checked).

The Enigma was simple enough to (almost) explain and the breaking of it was declassified a long time ago. The Tunny break was only declassified recently (and it was much more complicated). There was no public information until recently about the British codes (and how easily most of them were broken by the Germans). And the Enigma has Turing, of course.

Yep, it also resembles evolution: a big change by itself it's really unlikely, but small accumulative changes make you progress little by little in the right direction

@@alpardal Lies! Miles don't exist! Everything is inches!

This is the Lockpicking Lawyer and what I have for you today is this Enigma...

@@khleta4334 cracking enigma: A click on three... Ok, nothing on four...

@@barutaji two is binding...

The local library had a book about ciphers in the 1970s. Enigma machines and their post-war sale was also discussed. At the back he had written a message which had been through a virtual Enigma machine. He told the readers how to write the program which would decrypt it.

Do people without any accomplishments deserve to be treated worse?

@@tonytungsten4278 than people with accomplishments? yes, otherwise we'd give everyone a nobel prize

@@tonytungsten4278 he wasn't treated any beter than anyother homosexual male of the time. the dude was chemically castrated and arrested. eventually (potentially) killing himself via cyanide poisoning.

​@@tonytungsten4278Are you a fan of participation trophies?

Is that possible to decrypte or not?

Very true. The Polish contribution was important. Rajewski and his colleagues did some great work.

I would say was crucial as they provided decrypting algorithm. What Turing did (and it was amazing by itself) was building and electromechanical automaton, which was able to crack codes quick enough to use intercepted intelligence. The third or fourth iteration of enigma's encrypting algorithm become too hard to crack manually. In fact some of the first messages cracked by Poles directly predicted war and even Marshall Piłsudski tried to convince Charles de Gaulle to perform attack on Germany, before it will be too late. That may be one of the reasons, why this truth is not spoken widely.

Face the truth, Jerzy Rozycki, Henryk Zygalski and Marian Rejewski broke the code, wrote algorithms, then tried to come up with some engineering tools to speed braking code up. All having no knowledge about secret military cutting edge technology at that time, called computers. All what Turing made was to build a machine where the numerical methods and algorithms invented by Poles could be efficiently executed. That how the Allies won the war, then as a "thank you" they sold us out to Stalin. Humiliated Poles not inviting us to the victory parade!!! We like the Chinese do not forget this

They also made the first bombe

@@telawiw329 moron. Turing is the father of modern computer science. He's far beyond just an engineer who built a machine. That was Tommy Flowers. Turing didn't use the Polish algorithms.

Came here to say that! After reading extensively about Lorenz, the process of cracking it and the people involved, I - and excuse me - shat myself upon realization of how incredibly brilliant Bill Tutte (and a lot of others) was.

One challenge is that a lot of the messages from ww2 had loads of abbreviations and shorthand, so that'd serve to make it more difficult

@@thatcherfreeman To an extent; yes; however much of that can be figured out and added to the dictionary.... for example, dropping vowels.

another thing used was plaintext attacking a very famous line at the bottom of most messages, which i wont put here because i dont want youtube flagging this comment

@@sircalvin Yeah... something about hailing the guy in charge... 😉

Many of the american encrypts were translated into Navajo and Lacota beforehand. The Axis never cracked those messages.

I know that the polish cracked the code, but i don't know more about it, but while the british mathematicians around Mr. Turing were impressive, they still had the advantage of captured enigmas and captured documents of which rotors to use when. (Not at the start, but it helped them immensely) Still i think it was impressive that while here in the video he knew how an enigma machine works and could use his own language, it still took longer than i expected. Now imagine, not knowing how it works (the rotors and plugs and the turning) as well as having to decipher a foreign language. (And then using the Navy version with 6 rotors)

That's another thing that's better about modern ciphers. They're still hard to crack even if the enemy has full knowledge of the algorithm. The only thing that needs to be kept secret is the key.

Well, not quite. Commercial version was simplified, had less rotors and few minor differences. Enigma was cracked in 1933 by Polish mathematicians (French declared it impossible to break, British gave up independent work on breaking encryption and relayed on work of Polish Cipher Bearau). It wasn't decoded in real time, but with few hours/days delay - using Zygalski sheets, by hand. When Germany added more rotors, there was a case, when they sent by regular post device to embassy in Warsaw. Thanks to postal service workers (who delayed delivery from Friday to Monday), Poles got like 24h to study new design. What is worth mentioning: knowledge how Enigma is operating is not much of a help to break encryption. The most critical part to break encryption was set of rotors, ring settings. Without those it is far more difficult to predict result of encryption.

@@kilijanek that's why I said "dumbed down" version

@@kuhluhOG I apologize for my reaction, but I hear far too many times that Turing or US Marines were cause Enigma was broken at all (yeah, too many talks with egocentric Americans T_T )... and that is not true. In his genius, Alan Turing automated and improved process of decryption of Enigma - which is a great achievement itself. Breaking Enigma predates work done by Turing almost for a decade. Aaaaand ofc, US did almost nothing besides using decrypted messages :D

@@kilijanek well, the US also built more of the decryption machines, but yeah, the US didn't do anything more

Fun fact, stitch patterns in sewing machines used punch card programming before computers existed

@@Nekuzir Damn, I didn't know that, thanks for the fact!

Gram gram been spending too much time making sweaters

Dfn

Why?

@@AceDeclan Because he seem to be nice and smart so you wouldn't know he is villain until end of movie.

@@crusaderanimation6967 because he has a snake pet and the only people who has snake pet are animal lovers or serial killer

Indeed, and it was all done with mechanical wheels, yet it was and still is pretty effective if done properly.

Yeah, a couple of years ago I created a small program in C++ that was based on the 'logic' behind Enigma. It took me about a couple of weeks to get it working as intended. In my code, in essence, a string variable would be run through a series of functions (the digital equivalent to the Rotors) that used integers to increment/decrement each character in the string (using the integer as a shift) before passing the variable to the next function, which would repeat the process with a different 'shift', for however many times the user would want to encrypt the string, so that - ultimately - the encrypted text that was put out would be protected by the fact that, A: you could have as many 'Rotors' as required, thereby increasing the number of potential true characters that each letter could decrypt to, and B: were you to successfully decrypt the text once or twice, it would only therefore decrypt to the previously encrypted version of the string and not the true, original plaintext. Back then, I created a Decryptor that was configured as a mirror opposite to the Encryptor, with the assumption being that you could only decrypt the text correctly if you had the Decryptor. I didn't know nearly as much as I do nowadays about coding and cryptography (and I STILL wouldn't trust my skills in that department, I'm still barely an amateur). However, knowing more about Hacking nowadays, I realise that all you would need to do in order to crack the above-mentioned encryption method would be to analyse the code of the Encryptor and simply create an altered version of it in order to decrypt the text. It's a fun thing to try with coding though and I'd highly recommend it to anyone for purely educational purposes in order to practise playing around with integers and variables. Definitely leave hardcore Cryptography to the guys and gals who know their stuff in this field, it's so dangerous if you don't know what you're doing with it.

Hahaha :) Yeah, halfway through all his implementations I started to wonder where he got all the time and motivation.

Colussus was used against Tunny, not Enigma. Enigma cracking was implemented by Turing's Bombe.

@@paulwomack5866 where Tunny = the intercepted code from a Lorentz cipher machine. Highly recommend anyone go to the Bletchley museum of they are in the area. Sadly I went when the computing museum was closed, but the working Colossus machine was whirring about. Superbly knowledgeable your guides, but now I see some of the attacks that can be used, the actual working their behind it makes so much sense.

If I remember right what Bombe was doing was plaintext decryption rather than statistical. "Okay, we have a large number of possible combinations, but which ones can deliver the plaintext we think it starts with and not throw any errors down the line?" Then that much smaller subset of combinations would be tested with other analysis and against other messages (remember that they wouldn't change the code for each message so if you cracked one you cracked them all until the code cycled). I don't know if they used the computer for that or went back to doing it by hand once they had a workable subset.

@@paulwomack5866 as much as I admire Turing, he did not invent the bombe, the Polish did.

@@MrGoatflakes The Polish invented the bomba, the device used at Blethchley was a more advanced development by Turing and Welch, using the bomba as a basis

I'm sure "an awful lot" back then could be completed in a few days on a single thread of JS running on a semi-smart-phone's toy web browser

@@codegeek98 The project (enigma@home) managed to decrypt 4 messages using brute force decryption method. it took over 360,000 years of compute power (based on an AMD Athlon Xp 3500+ single thread processor) to decrypt all 4 message.

@@ragnarsdad6065 were they all done? Os it still going? Have many 6, 8, 16 core cpus spare atm.

@@tomstech4390 Just beware the power bill. I used to run Seti@Home, then Boinc aggressively in my business. It was fun. Then I came to appreciate the effect on the power bill.

@@tomstech4390 afaik enigma@home is still running? Even if not there are many math projects on the BOINC network - or other stuff. Like nedicine research. You can even get paid in cryptocoins if you use Gridcoin (for most of those projects).

Arthur Scherbius was his name. Machine was patented 1928 and was commercial system. Of course that was its first version.

@@vksasdgaming9472 I don't know too much about this. But I assume that you could just take the basic idea and make it arbitrarily more complicated by adding more rotors, plugs etc. that it easily could have been made unsolvable.

@@kreiseltower New plugs and rotors were method to make encryption more complex. In practice fact that military communications follows protocol made it easier. If every message begins with or includes known expression it is easier to break. Informally worded messages might have been unsolvable as there simply was no way to guess what there was being said.

And some actor has to shout out, "It has 3 symbols.", "It has 4 symbols. Two more and we're doomed!", etc. with ever greater urgency

That actually didn't happen in War Games. It wasn't cracking one key, it was finding ten different keys, one at a time. It didn't really explain how it was doing that, if I remember correctly.

Ikr? I’m always like… That’s not how encryption works! But apparently it did a long time ago 😅

​@@kentix417worryingly the nuclear codes at one point actually was "0000 0000" (because they wanted it to be memorable in an emergency 😂) so the computer would have probably got it on its first try...

My understanding is that it was an electro-mechanical dedicated computer which tried to "brute force" the encryption key by looking for a recognised sequence of characters in its output. It was made out of dozens of chained telephone-exchange style "uniselectors" which each had 26 positions.

More like one millisecond.

@@DesertCookie hopefully 🤗 I'd already be impressed with solving 150,000,000,000,000 combinations in 30 sec, which means 5 trillion combinations per sec... but maybe a 3000 qubits trapped ion quantum computer with no errors could do much better 🤷🏻‍♂️ tbh I have no idea.

@@YAZlakhdar How weird is it that "with no errors" was the first part of that sentence that didn't register as somehow possible one day?

@@draygoes actually very low error rates are already achieved in some Trapped ion QCs with up to 32 fully connected qubits... and we're only in 2021! Imagine what will be achieved in 10-20 years, not to mention further down the line... Think about all the things that people in the 1950's would have deemed impossible, which are now possible or even plain boring for us. I'm sure they'll figure it out ;)

@@DesertCookie actually after looking up the processing power of current state-of-the-art supercomputer, and given the nature of quantum computers, I agree with you that it should be much faster than 30 sec... potentially even a millisecond. Crazy

And only really tweets before the character count was doubled

Twitter is pretty much pointless now without President Trump's tweets.

@@yosefmacgruber1920 ???

@@gayMath Twitter and FB should be banned for their evil censorship. Or seized and turned into a utility. Did you not know about Twitter censoring truth-tellers, President Trump, and tampering with elections? Twitter has already been banned in a few countries due to that.

@@yosefmacgruber1920 wtf are you smoking i want some

This is true, but to be fair the identicle feat was later replicated by Bill Tutte at Bletchley Park with the Lorenz teleprinter device

haha, it's his energy, he can't wait to stop talking and start writing / coding.

Britains most shameful hour for sure.

@@jag1963 i don't know owning slaves and the genocide of the indigenous peoples of the Americas is pretty up there

@@evilcanuck Those things were done by people who live in the Americas, not Britain.

@@tomx641 who came from Britain

@@evilcanuck Are you self-hating, or do you come from people without sin?

I wonder which ones of our moral panics will seem unjust to viewers 70 years hence.

@@Snagabott - Factory farming

@@Snagabott Assange case

Too many to name...

@@Snagabott Social justice, probably

The number was a colossal, so yes

@@merrymonarch Before the introduction of the plug board, there were only 1,054,560 combinations on the original machines. Hardly colossal. It was the addition of the plug board on the military machines that ran it up to 1.5*10^14 combinations.

@@stargazer7644 fair point. Collosal is subjective. You're right about the plug board too. I think I read somewhere that if they'd added an extra rota it would have been too much for the computers they had at Bletchley

That is the total number of combinations, yes - but we can "break" one wheel at a time, so we don't need to try all of the combinations. The number of tests required is just 26 per wheel, so 23×3, not 23^3.

This has nothing to do with grammar. The Index of coincidence is obviously all about how the words are written, i.e. the syntax.

He doesn‘t go into details such as how to calculate the IoC, the number of possibilities etc., and how he came to know of the rotor properties (which input generates which output letter) and the notches. Statistical language analysis seems to be the key to solve crypto.

You usually don’t have to throw out all your settings.

He's said in other videos that they do indeed use high end graphics cards for this, in fact they have tons of them all working at the same time, together, in a big server. Dunno how you do that, get graphics cards to link with each other like that. But yeah he's said that's what they do, at that university. And so different classes and groups and academics have to book a time slot when they can use the dozens of graphics cards in parallel to brute force something or to use a more sophisticated method to crack a code or to model a complex system like the weather, or anything like that that academics do. The physicists use them a lot too, to model systems like perhaps individual atoms and things like that. Which makes a lot of sense, considering they computer science was originally a branch of physics, and remained there way for decades until the 70s and 80s where computer science began being seen as a separate subject altogether. But yeah, it's still linked heavily with physics.

@@duffman18 "Dunno how you do that, get graphics cards to link with each other like that. " They not have to be linked if brute force is used. Each graphic card can work on a distinct subrange of the possible settings without the need to communicate with other graphic cards

There was nothing preventing them from manually scrambling their messages on top of the Enigma encoding. All it would take is a manual alphabet switching system that changes based on the number of messages that have been sent. Turing could never have accounted for it.

Part of the problem with U-boat Enigma messages is that they weren't merely enciphered, they were also encoded. That is, the original message won't necessarily contain _any_ plaintext, so there's no way to know when you've deciphered it.

Hi I’m curious, what are those algorithms you’ve mentioned?

​@@gschadalavada8980 Usually you start with a bunch of algorithms which are just guessing. However, some will guess better than others. Keep the better ones, mutate their guesses (automatically) a little and repeat, until you have one you're happy with. Just youtube them, there's lots of really cool videos on them :)

In effect, he is doing precisely that by hand. Notice that he mentioned fitness functions specifically. Whereas the GA would be evaluating the entire solution space starting from a random draw and fiddling with the details, the presenter has chosen to stage the work such that he can evaluate one entire domain comprehensively before moving on to the next one. You could do that with a GA as well, and in my experience, it would converge to the proper solution faster than if you did the whole solution in one pass.

The allies?

@@FlyBoyGrounded That'd be TypeX - which _could_ have encrypted a letter to itself, but they decided to use the second contact on each rotor face for redundancy and reliability instead for some odd reason, rather than having the reflector circuit feed the outer signal back over the inner circuit. That is, the machine was capable, but the implementation wasn't. (If I were to guess at why, it would be because it would have needed an encrypt mode and a decrypt mode the operator would have had to select, rather than a single mode for both encryption and decryption. I'd think it wouldn't be too very hard to have your terminal equipment operators trained to throw a single switch, but what do I know?)