[syhprum (OP)]

The decrypting of enigma traffic with electromechanical computers only just worked due to sloppy operating procedures and lots of intelligent  guess work.

How easy would it have been if modern computers had been available?

[homebrewer]

Many thousand lives, both civilians and military would have been saved, if faster computers with powerful software would have been available earlier.

What takes  always time, is the analysis of the system used, and the Enigma created initially some considerable problems for the data scientists.

[evan_au]

Cracking the Enigma code was assisted by having the plans of an Enigma. Machine available for study. And a group of highly skilled mathematicians to analyse it.
But today's computers would have been much faster than the electromechanical devices used to crack Enigma.

An even more interesting story is about Colossus, which was used to crack the more sophisticated German Lorenz code. The technology in this device led to the flowering of vacuum-tube computers after WW2.  This was kept secret until the 1970s, so is less known than cracking Enigma.

[Bored chemist]

Enigma was cracked by the very clever people at one end and the very human people at the other.
The second group had been told it was "uncrackable"- so they got sloppy.

If they had strictly followed good cryptographic practice then I don't think even today's supercomputers could "brute force" enigma.
https://en.wikipedia.org/wiki/Enigma_machine#Mathematical_analysis

[homebrewer]

The Blechtley people used very rudimentary relay logic on the hardware side and for the first time statistical analysis techniques to appraise each and every message received.

Forgotten seem to be the efforts of the many forgotten girls in the wire room, which painstakingly assisted in this intelligence effort.

Here i shall express my personal gratitude.

[wolfekeeper]

If the Allies had had access to modern computing, a back-of-the-envelope calculation suggests that a single one of today's smart phones should have easily outperformed all of the Allies' bombes-several hundred Bombes- and by a huge margin, and completed ALL of their daily runs in a tiny fraction of a second!

[syhprum (OP)]

Several emulation program are available so that you can have your own Enigma machine on the screen, unfortunately they are 16 bit and need minor modifications to the normal 64 bit system to run

https://www.groovypost.com/howto/enable-16-bit-application-support-windows-10/

[Bored chemist]

If the Allies had had access to modern computing, a back-of-the-envelope calculation suggests that a single one of today's smart phones should have easily outperformed all of the Allies' bombes-several hundred Bombes- and by a huge margin, and completed ALL of their daily runs in a tiny fraction of a second!

The bombes only worked because the Germans made mistakes like using predictable keys like HITLER and sometimes sending the same message twice.

[wolfekeeper]

Yes. If only they hadn't made mistakes. Someone should have given them a stern talking to, and told them not to make any more mistakes.

But modern computing can't change human nature. We f up a lot, particularly when doing cryptography. Cryptography is hard.

[syhprum (OP)]

Would the Lorenz code ever have been cracked but for the fortuitous capture of a code book from a submarine.
Was it known that code books were in use and navel people instructed to hunt for them .
Did every lorenz machine have its own unique code book ?

[syhprum (OP)]

Even with modern equiptment  it is not easy to record teleprinter transmission from the HF band so how did German submariners do it with enemy vessels and air craft hunting them.

I understand that during a recent competition to decode Lorenz type transmissions Bletchly park came second because they were unable to receive the transmissions although during the war no doubt they had better facilities.

[evan_au]

Was it known that code books were in use and naval people instructed to hunt for them .

Yes, ever since the use of cryptography, experts have known that the easiest way to crack a secret code is to have a copy of the codebook. Then its not so secret any more. (...provided the ones you are monitoring don't know that you have a copy of the codebook!)

So collecting the codebooks is the first priority of intelligence agencies - and destroying them is the first priority of the communications staff when it looks like they will be captured.

Secret codes are changed regularly - but if you have recorded many messages, you may be able to go forward in time, and monitor future communications for a while, and go back in time and decode some messages that were previously gibberish.

how did German submariners do it with enemy vessels and air craft hunting them.

Morse Code (well, the German-language equivalent).

It works very well with low signal strength and a poor signal-to-noise ratio. And the submarine doesn't need to transmit (hence giving away its position) to successfully receive messages.

See: https://en.wikipedia.org/wiki/Morse_code

[wolfekeeper]

Would the Lorenz code ever have been cracked but for the fortuitous capture of a code book from a submarine.
Was it known that code books were in use and navel people instructed to hunt for them .
Did every lorenz machine have its own unique code book ?

You seem to be confusing two things, Naval Enigma and Lorenz.

Lorenz was completely cracked without any code books at all (something that is considered one of the greatest intellectual achievements of the war) based on a 'depth' where two similar messages had been encrypted with the same key.

For Naval Enigma, the submarine gave them the code books.

https://en.wikipedia.org/wiki/German_submarine_U-559

Whether they'd be able to crack it without this is unknown- quite possibly not. They'd been stuck for several months prior to that; but they'd been stuck before.

[evan_au]

How easy would (decryption) have been if modern computers had been available?

If modern computers had been available, the encryption method could have been much more sophisticated than in the Enigma machine.
- The Enigma machine used mechanical rotors which each had a unique electrical path. The rotors clicked forward one step after each key was pressed, producing a unique encryption for each letter, not affected by the letters around it. Even the tougher naval version of Enigma had "only" 151 trillion settings, which today we would describe as 50 bits of secret key to be determined in decryption.
- If we take a fairly modern encryption standard like AES 256 (the algorithm is publicly defined), the secret key is 256 bits long, and each extra bit in the key means it is twice as hard to decode. The data is encrypted in blocks of 128 bits, so the encryption of every character depends on 16 nearby characters; in some modes, the encryption of every character depends on every prior character in the message. To make it tougher, the encryption process is repeated 14 times (14 "rounds") for AES 256.
- With today's Public Key Encryption algorithms, key lengths are even longer - over 1000 bits. These algorithms are so processor intensive that they are rarely used to encrypt a whole message, but instead are used to transfer the encryption key for an encryption algorithm which is less computationally demanding.

The availability of increased computer power just steps up the battle between the encryptors and the decryptors to another level. National security agencies (who often play both roles) have divided loyalties in defining public encryption - they want the public to use methods that are hard for the public to decrypt (for now), but which are still feasible for them to decrypt.

This contradiction is visible in the GSM mobile phone standard, where encryption was intentionally weakened to make interception possible - and now any laptop can quickly decrypt GSM transmissions.

See: https://en.wikipedia.org/wiki/Cryptanalysis_of_the_Enigma#Security_properties
https://en.wikipedia.org/wiki/Advanced_Encryption_Standard#Security
https://en.wikipedia.org/wiki/Public-key_cryptography#Computational_cost

[Bored chemist]

It depends what you mean by a trillion.
From WIKI
"Combining three rotors from a set of five, the rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 (nearly 159 quintillion) different settings.[17]"

That's a whole different ball game from 151 trillion settings.
If your computer could test  a billion possibilities each second (and that's unrealistic) then it would take 158 billion seconds to try all the possibilities.
That's 5000 years. They would still be trying to decode the instructions for stonehenge.
Even having multiple machines doesn't help much.

[syhprum (OP)]

I understand some navel communications have only recently been decoded 75 years after they were sent but as you say a brute force technique is impossible so I do not know how it was done

[Bored chemist]

I understand some navel communications have only recently been decoded 75 years after they were sent but as you say a brute force technique is impossible so I do not know how it was done

The easy way might be to ask the Germans.

[wolfekeeper]

It depends what you mean by a trillion.
From WIKI
"Combining three rotors from a set of five, the rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 (nearly 159 quintillion) different settings.[17]"

That's a whole different ball game from 151 trillion settings.
If your computer could test  a billion possibilities each second (and that's unrealistic) then it would take 158 billion seconds to try all the possibilities.
That's 5000 years. They would still be trying to decode the instructions for stonehenge.
Even having multiple machines doesn't help much.

Yeah, it does. 5000 machines isn't all that many. And don't forget modern machines are superscalar.

That's not an intractable number anymore, it's a 'how bad do you want it?' number. 5000 machines cost ~£5 million plus electricity and warehousing.

[Bored chemist]

It depends what you mean by a trillion.
From WIKI
"Combining three rotors from a set of five, the rotor settings with 26 positions, and the plugboard with ten pairs of letters connected, the military Enigma has 158,962,555,217,826,360,000 (nearly 159 quintillion) different settings.[17]"

That's a whole different ball game from 151 trillion settings.
If your computer could test  a billion possibilities each second (and that's unrealistic) then it would take 158 billion seconds to try all the possibilities.
That's 5000 years. They would still be trying to decode the instructions for stonehenge.
Even having multiple machines doesn't help much.

Yeah, it does. 5000 machines isn't all that many. And don't forget modern machines are superscalar.

That's not an intractable number anymore, it's a 'how bad do you want it?' number. 5000 machines cost ~£5 million plus electricity and warehousing.

You need something of the order of 1000 cycles to check a particular combination of settings, so I was assuming you were running something like 1000 machines in parallel to get a billion checks per second.

You think a wartime message that you translate a year later is still useful enough to stack up (and fuel) 5,000,000 machines?

How do you decide which of the thousands of messages sent and received is the one you need to put all that effort into?
It's clearly impossible.
So you need roughly 5 million machines grinding away for a year for each message decrypted.
There were (I guess) hundreds of Enigma machines, each of which was  used for many messages each day- perhaps hundreds a day.
So you need a hundred sets of a hundred sets of 5 million computers.
That's about 5 computers for everyone on the planet
Good luck asking Mr Churchill for resources for that during a war.


Next time  I tell you that something doesn't help much, you might want to look carefully at the numbers before assuming I'm wrong.

[wolfekeeper]

Nah. You don't need anything like 1000 clock cycles to prove that a particular guess is wrong. Most of them will fail in six memory lookups at the first hurdle.