Alan Turing - and the Enigma

First, a Turing Machine, just for fun:

Nearby Rich says:

Just to start with an aside, for me, Alan Turing is a huge figure in several fields: mathematics, computer science, programming, computer systems engineering, artificial intelligence… but also probability and cryptanalysis. He managed to get a lot done even in his short life. I thoroughly recommend Andrew Hodge’s biography Alan Turing: The Enigma.

But here Rich challenges us with two or three related questions: the role of Turing in cracking Enigma; the roles of the Polish mathematicians; and the public perception of those respective roles. I would never be surprised to find Hollywood presenting a story which is written to sell and to entertain rather more than it is written to inform. To the extent that Hollywood steers the public perception, we shouldn’t be surprised to find misattribution and distortion in the public mind.

The fundamental flaw in Enigma, as I understand it, is that a letter will never be mapped to itself. That feels like a tiny flaw indeed. And yes, I think the Poles saw a way in, and the technique was smuggled out and found its way to Bletchley Park. But, I believe, it was also necessary for the Axis powers to make design errors in their procedures and operational mistakes in their usage. Enigma as deployed over the course of the war became ever more difficult to crack, and it was a race between the cryptographers and the cryptanalysts. Had Enigma been used from the start as it was at the end, it might well never have been cracked.

(Among the great innovations brought to bear in decryption was the diagonal board - if you’re so inclined, it’s well worth trying to understand that. It enormously reduced the search space that the Bombes explored.)

Anyway, enough of my vague statements - here are some links. First, GCHQ on Turing:

He met Polish counterparts in Paris in January 1940, a meeting at which they gave him the insights he needed to build on their foundations by designing the Bombe. This was the first special-purpose cryptanalytic machine, and made major contributions to the exploitation of German Naval Enigma, before moving on to work on secure speech systems.

Here’s Tony Sale’s take: Alan Turing, the Enigma and the Bombe.

Graham Ellsbury’s site is very technical: The Enigma and the Bombe

Andrew Hodges again: The Military Use of Alan Turing which is part of his extensive website on Turing, a companion to his biography mentioned above.

This article will review Alan Turing’s mathematical work in the Second World War, discuss how this relates to the history and philosophy of computing, and then raise the wider question of his place in mathematics and war.

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“If I have seen further than others, it is by standing on the shoulders of giants.” – Isaac Newton.
No scientific breakthrough has been done by a single person. Einstein’s theories of relativity turned physics on its head, but it was built on the work of others. In hindsight it is easy for us to say “well, this guy contributed this part and that guy contributed that, so we really shouldn’t give him all the credit.” But Newton, Maxwell, Einstein, and Turing took all the bits and pieces and a lot of hard work and put the pieces into a single framework that answered the previously unanswered questions.
In our (over) simplified world, where we often read about, or discuss at the watercooler, or see in a Hollywood movie, things we don’t fully understand, we get bored by details and say Einstein discovered relativity or Turing cracked Enigma. Although those statements are true they leave out the context of how those discoveries were made and the other people who contributed. That is true in any big breakthrough. That’s how it is. It’s just our nature.

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The Poles just didn’t happen to discover that a letter won’t encrypt to itself, they did massive amounts of theoretical work, and were reading Enigma traffic as early as 1936. The Polish gov’t feared German invasion very early, and put huge resources into crypto. The fact that the Poles don’t get ALL of the credit is the real shocker here. When I see the way things are presented at Bletchley Park, it looks like a coordinated effort to remove the Poles from history. The Quintessential book on the Poles contribution to Enigma is this:

This book was so eye opening when I was doing my research it blew my mind.

Sure, the allies had massive resources and could build cool machines once the Poles turned over their work, but that’e because they had massive resources.

Oh indeed, it’s quite a step from knowing that a letter can’t self-map to having any kind of way in. But my understanding is that the Enigma which the Poles were able to crack was very soon no longer the Enigma in operational use [citation needed]. Their contribution was necessary, but not sufficient. Thanks for the book recommendation!

Well, so what are you saying? Are you talking about the differences between Wehrmacht (Army) Enigma and Naval Enigma? Or are you talking about the Germans adding additional rotors?

The Enigmas in operational use did not change during the war, except that instead of being able to choose and re-order 3 rotors, they eventually added two, so you had 5 rotors to choose from for key selection.

Of course the Naval Enigma had a 4th rotor actually in the machine (Wehrmacht only allowed 3 in the machine) and a different Reflector, so this complicated things significantly for the Poles.

From my readings of the history of Enigma, the Poles did all of the theoretical work necessary to understand Enigma, and constructed their own Enigma machines. Everything after that was about finding the keys to be able to decrypt the messages. The Poles had built their own electro-mechanical devices to help with that, but the addition of the two new rotors simply exceeded their ability to calculate keys with their “Bomby” (what their mechanical computers were called) in a reasonable amount of time. They needed more resources which they simply did not have.

The very first paragraph on the Wiki page for Enigma in the “Breaking Enigma” section seems to get the history right.

As I understand it, Alan Turing saw their Bomby, and made some improvements, and then the allies with their massive resources just built a ton of computing power to find keys. But all necessary theoretical work had been done by the Poles years earlier.

AIUI, it was procedural changes which made the Polish methods obsolete - but those methods had allowed the Brits to get to a position where they could “hang on by their eyebrows” as the procedures changed.

I’m having a quick read of
Welchman, G. (1986). From Polish Bomba to british Bombe: The birth of ultra. Intelligence and National Security, 1(1), 71–110. doi:10.1080/02684528608431842
which, although a telling from the UK side, does speak to this question. I’m working on the basis that histories are interesting, even if not all in exact agreement. I’m more interested in being interested than in having a complete and correct understanding, which is something very hard to come by. Each account differs.

Edit: here’s a quick snippet from Welchman:

I did not become involved in the breaking until May 1940, when the sheets suddenly became useless. As will become apparent when I discuss Rejewski’s work in part V, all the pre-war achievements of the Poles depended on the double encipherment of the wheel setting used to encipher and decipher the text of a message. Soon after they invaded France, the Germans abandoned this double encipherment. Hut 6 was on its own from then on.

The Germans were sloppy with key selection and key management in general. This is all about the keys. The Poles and/or the allies having an actual 100% accurate working replica of the machines did nothing for them unless they were able to determine keys. That’s what the “computers” were for.

The Poles methods were not obsoleted in any sense of the word. The addition of the new rotors simply meant they couldn’t calculate quickly enough the keys in time to be useful in wartime.

Intelligence information has an expiration date. If the Enigma message was about a battle tomorrow, then decrypting it the day after does no good.

The allies just brought more resources to the effort, which allowed them to calculate keys faster. A vacuum tube computer was simply faster than the Poles’ electromechanical Bomby. The Poles couldn’t have built one of those.

As I understand it after a decade of research, without the Poles we might all (well, you anyway in the UK) might have been speaking German. When the Poles gave their work to the allies, IIRC correctly, the allies were completely blown away that they had working Enigma replicas.

Would the allies have been able to do ll of this without any of the Poles’ help? Who knows. They were smart guys with resources, but it would have taken more time. Who knows how it would have played out. From where I sit, we owe a MASSIVE amount of debt and gratitude the the three Poles. Yet they don’t get a movie, and this makes me angry. My Aspergers gives me a sense of justice and fairness, and I see no justice in how the history of this has played out.

This of course has led to massive misreading of history in many places. Like the film Patton. He is portrayed as some sort of military savant who could crush all of his enemies, when the reality was he was only able to stay 1 step ahead of Rommel because we were reading Rommel’s Enigma traffic. This hadn’t been declassified yet at the time the film was made, but even if it had, I doubt the film would have changed much. Americans seem to need to have their toxic male superiority myths.

One of the basic tenets of cryptography is to assume that your adversary has your method/machine. They key IS the hard part.

from pg 14:

A fundamental premise in cryptography is that the sets M, C, K, {Ee : e ∈ K}, {Dd : d ∈
K} are public knowledge. When two parties wish to communicate securely using an encryption scheme, the only thing that they keep secret is the particular key pair (e, d) which
they are using, and which they must select. One can gain additional security by keeping the
class of encryption and decryption transformations secret but one should not base the security of the entire scheme on this approach. History has shown that maintaining the secrecy
of the transformations is very difficult indeed.

While this is true today, it wasn’t as obvious when WWII opened. In particular, the Germans tried very hard to keep their Enigma machines a secret, destroying them (by sinking them, crushing them, etc.) when overrun.

I should say, it was true then, but it wasn’t universally understood and acknowledged. :slight_smile:

(It’s often worth keeping your methods secret while you can, even if they are not the basis of your security. It’s defence in depth.)

You are absolutely right. But it was true, even if they didn’t realize it. The point was that deciphering how the machine worked, while certainly not easy, was considerably easier than breaking the keys themselves.

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Right, which is why I said “assume” they have it, not give it to them :slight_smile:

BTW, it turns out that Welchman’s 1986 paper forms a large part of the later edition of his The Hut Six Story which corrects some errors and assumptions, and also addresses the position taken by Kozaczuk’s book. As it turns out, I don’t have either the earlier or later edition of that book. (Although, as with much else, it can be found online.)

First, I consent with the Polish work not having been recognized as deserved. Even the word “bombe” is derived from the Polish “bomba”. As I do understand it, Turing’s work was decisive for deciphering the front connectors, which introduced a massive problem of their own. In a nutshell, it’s about a mathematical proof that you may discard all members (interim assumptions made on some properties) of a logical search path, if the particular path results in a contradiction, which transformed this to manageable problem. The Numberphile YouTube channel had once an episode on this: Flaw in the Enigma Code - Numberphile - YouTube

Edit: I think, there is (or, at least, was) a general tendency towards hero building in computer history. For years, many books were about “our man, who invented everything” – and many important contributions have been ignored in favor of this. E.g., the British work and even practical demonstrations on/of the fundamentals of packet-switched networks and its influence on ARPANET comes to mind. In the case of Turing and Enigma, I guess, much is owed to partial information becoming public around 1980. When I became interested in the subject, it was quite an established fact that Turing had somewhat single-handedly cracked Enigma (with some obscure, preliminary Polish work involved) and that this would lead to the building of Colossus (which is obviously not the case). On the other hand, the entire Enigma-story and its importance had been unknown previously, so the role of cypher in WWII was the bigger message at the time. (By this, again, overshadowing other important contributions, like the Western Approaches command of the Royal Navy, which’s role may have been comparable to the Dowding system in the Battle of Britain.)

I have an idea!
Hey, it happens once in a while :astonished:
Since this post originated from Ricardus being concerned about the three Polish gentlemen being slighted, perhaps he (or someone else) could write an informational post about them and their contribution. To me, that would be time better spent than arguing about whether they deserve it or not.
Just my half cent’s worth.

The plugboard (Stecker) adds complexity to the number of combinations, but it’s really a simple input/output patch bay (very much like we use in recording studios, or like telephone operators used 80 years go) and was well understood by Rajewski. I drew a schematic for the whole unit when I was doing my research back in the day (I mentioned this in my “Introduction” post.)

My understanding of Turing’s contribution, was that he took the Bomba that the Poles had already built, and he found ways to improve them, and then he built a proper electronic computer to find keys.

I don’t think it’s any exaggeration to say the Poles did all of the theoretical work to understand the cipher and the machine, and to first start decrypting German Enigma traffic. Again, they were reading it in 1936.

The book I mentioned somewhere up there ^^ has extensive interviews with Rajewski talking about exactly what he did, and when, and it was nothing short of unimaginable.

Say nothing of the fact that at one point the three crypto guys had to escape Poland, and did much of their work being hidden in occupied France, by the French resistance, before they were smuggled across the channel to England.

I’m not arguing. Just trying to correct the record.

And haven’t I been writing about their contributions? Their contributions have been in all of my posts.

But I have no interetest in re-writing the Władysław Kozaczuk book, or transcribing its contents here. Please, go read it. Not only is it an amazing record of the history, it’s an adventure book/thriller since it goes into detail about what I mentioned in my last post, about how they had to leave Poland and go to France.

I’m not arguing either - and I hope my starting this thread is not seen as any kind of challenge. It was merely a way to take an interesting point made in the Introduce Yourself thread and give it some air - and to keep that thread from drifting.

It seems the Polish Government put together a traveling exhibition in about 2016 (Edit: 2011?) to tell the story - I see several mentions of this exhibition online but no very detailed description. Here are some links I’ve found which relate to the Polish contributions:

https://www.cryptomuseum.com/events/2011/maczek/index.htm

(OK, let’s please not argue about not arguing.)