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The Imitation Game

Does it apply to Now?

Male
Timmee  Male  Hampshire 19-Sep-2018 12:49 Message #4725647
I recently watched 'The Imitation Game' about the Bletchley code breakers for the first time. I really enjoyed it and one aspect strongly reinforced and gave a precedent for thoughts I already have quite often about the present day and the way things work.

When the team finally crack the Enigma code and realise they can prevent an imminent attack on a convoy, they have a furious discussion about whether they should alert everyone and save lots of British lives. They conclude very sadly that, if they do, the Germans will realise that Enigma has been broken and instantly change all their operating procedures - thus putting the code crackers back into the dark. Benedict (Turing) and Keira shoot off to London to see their MI5 handler Mark Strong. They conclude that almost no one - not even Charles Dance (The Senior Naval Intelligence Commander in charge of Bletchley Operations) should know they've cracked Enigma and can now read German signals. They devise a clever statistical formula so that any interventions made as a result of reading Engima signals will appear to be only chance to the Germans and NOT systematic.

Okay, so where am I going? Well I've often thought to myself - when our press tell us what our intelligence services can and cannot do, how much can we believe?

I've always liked the scepticism of the George Gershwin song:
"It ain't necessarily so
The things that you're liable
To read in the Bible
It ain't necessarily so."

One example might be the 2015/16 FBI/Apple Encryption Dispute and court case about whether Apple should be forced to unlock the encryption on an i-phone that the FBI confiscated from terrorist suspects. My thoughts were: 'Are the FBI and the resources of the U.S. government REALLY unable to unlock this i-phone?...Do the NSA know how to do it but are not telling the FBI?...Does some obscure bit of the NSA/CIA know the phone can be easily cracked they're not telling anyone else? Is Apple REALLY refusing to cooperate? It seems to me quite possible the whole court case and dispute was just a charade for concealment's sake. How many vital surveillance operations might go dark, and become useless if the FBI were to say 'Okay Good News everyone - we've unlocked the phone and now have all we need to convict the bad guys in court.'?
Male
Jeff  Male  East Sussex 19-Sep-2018 14:25 Message #4725648
I heard very recently (I can't remember where) that practically nothing in the film "The Imitation Game" was true, and that no allied people were sacrificed so as to keep secret that codes had been broken. If a code was decoded, then Intelligence tried to get another way to verify what the code said. For example, if a code was decoded to say that there was an enemy convoy in a certain place, then an aeroplane was sent to the area, which would be spotted by the convoy, and if an allied convoy subseqently went there for a fight, then the enemy convoy would assume that the aeroplane gave them away, (even if they had shot down the aeroplane), rather than assume that a code had been cracked.

As for cracking current codes, they are much more difficult than the Enigma codes, and it is very possible that, even with the best computers, it would take may trillions of years to break them. So I can believe that many codes aren't cracked, and a court order to reveal them is required.

In Quantum mechanics, systems are designed such that if a code is intercepted then the message is automatically destroyed.


Incidentally, in a recent maths class we were shown a Turing machine (type of computer) which included two semi-circles. I remarked that if they were circles, then it would be a two-ring machine!
Male
Timmee  Male  Hampshire 19-Sep-2018 15:12 Message #4725654
I accidentally rated you excellent LOL.

What I meant to say is that I'm sceptical of the 'no Brit servicemen's lives sacrificed to protect the secret' narrative.
It is no surprise at all to hear that much of the film was NOT authentic - that is only to be expected. If I gave the impression that I thought the film an accurate account, then I did not mean to. Yes, as you say, they would search for credible alternative explanations for knowing stuff they'd got from reading Enigma: but they would have to have been extraordinarily frugal when acting on the materiel they had in order to keep their secret.

There has been extraordinary secrecy and silence surrounding Bletchley Park and what was done there until pretty recently.
Male
SQL  Male  Devon 19-Sep-2018 22:59 Message #4725670
Timmee - 19-Sep-2018 12:49

When the team finally crack the Enigma code

There is a common misconception that 'Enigma' was cracked - it never was. What the team at Bletchley Park devised was a way to decode the actual rotor settings for that day ONLY. The initial settings were changed every day by the Germans to minimise the chances of decryption. So every single day Bletchley Park had to predict what the Enigma settings were to be able to read that day's messages in 'clear text'..
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

Jeff - 19-Sep-2018 14:25

As for cracking current codes, they are much more difficult than the Enigma codes,

Not true, yes they take longer but are no more difficult. If Bletchley park had had access to a modern laptop then they would have been able to crack the Enigma code - guaranteed - every day in about 8 seconds.
Any code created by a computer is entirely deterministic and thus can be cracked/decoded given enough resources and time. It all depends on the value placed on the data and how long it has any relevance.


In Quantum mechanics, systems are designed such that if a code is intercepted then the message is automatically destroyed.

I think you are talking about Quantum computers - anyway - how does a system know if any message has been intercepted and decoded?

SQL
Male
Timmee  Male  Hampshire 20-Sep-2018 12:44 Message #4725690
"There is a common misconception that 'Enigma' was cracked - it never was. What the team at Bletchley Park devised was a way to decode the actual rotor settings for that day ONLY. The initial settings were changed every day by the Germans to minimise the chances of decryption. So every single day Bletchley Park had to predict what the Enigma settings were to be able to read that day's messages in 'clear text'.."

Happy to acknowledge that SQ - my "cracked the code" was shorthand for your more comprehensive account.

Regards, T
Male
Jeff  Male  East Sussex 20-Sep-2018 12:44 Message #4725691
Jeff: "it is very possible that, even with the best computers, it would take may trillions of years to break them"
That was very badly phrased (and "many" is misspelled), and is a gross understatement, so replace it by: "Currently the best computers would take 10 to the huge power of years to crack current codes. However, in future quantum computers could crack them, perhaps within days, if the code isn't based on too many digits."


Enigma messages were decoded by Polish mathematicians (e.g. M.A.Rejewski), not just English ones (e.g. A.Turing), largely through carelessness of German operators. Their methods are in the public domain, such as in Simon Singh's "The Code Book" chapter 4.

The first Enigma machine was invented in 1918 and it and its successors used rotors to convert one letter to another. Current codes use completely different methods, such as public and private keys (e.g. the RSA system). They apply not just for one message per day but for many messages using that code. In this method there is one huge number anybody can see, for example it can be printed on a T-shirt, and a different private huge number, utilising the difficulty of factorising numbers having hundreds of digits. I suspect that they are much more difficult to crack than Enigma, and that above those there are much harder encryption and descryption methods currently secret.

Quantum computers are orders of magnitude times faster than ordinary computers, because they can be in many quantum states at the same time. In due course as they become more powerful, they may well be able to crack such codes, (e.g. our banking transactions could be at risk), but post-quantum cryptograpy is trying to address this problem.


Using conventional names, if Alice send Bob a message using a quantum mechanics technique, then if eavesdropper Eve intercepts the message, then the message is destroyed or made internally inconsistent (like a parity check), because of the delicate, indeterminable and crazy (e.g. entanglement) properties of each quantum, and that a measurement changes its state. So Bob will know that it has been intercepted. Eve cannot receive Alice's message and make a copy of it and send it to Bob, because QM has a no cloning theorem.
Male
tumbleweed  Male  Gloucestershire 20-Sep-2018 13:15 Message #4725695
I know I shouldn't joke in the forum, but the imitation game sounds to me like it could be about Brucie impersonators from one of his game shows. Also, is it possible to dislocate your jaw whilst doing a Brucie impression. I think I nearly did.

The next bit, courtesy of Philomena Cunk, who mentioned something like Turing being shrouded in mystery, which is where the Turing shroud comes from.

Anyway, sorry to go off track. Normal service will be resumed shortly.
Male
Timmee  Male  Hampshire 20-Sep-2018 19:58 Message #4725723
Big Philomena Cunk fan here.

:-)
Male
SQL  Male  Devon 21-Sep-2018 10:00 Message #4725731
Jeff - 20-Sep-2018 12:44

Using conventional names, if Alice send Bob a message using a quantum mechanics technique, then if eavesdropper Eve intercepts the message, then the message is destroyed or made internally inconsistent (like a parity check), because of the delicate, indeterminable and crazy (e.g. entanglement) properties of each quantum, and that a measurement changes its state. So Bob will know that it has been intercepted. Eve cannot receive Alice's message and make a copy of it and send it to Bob, because QM has a no cloning theorem.

I must confess that I really laughed at this - as good as some politician's election promises. Just to point out the flaw in this 'info' - data has to be transferred from on place to another. It is in this data transfer that interception is possible. Quantum effects are very local, distances of far less than those needed to transfer data from London to Bristol for example. Signals in copper wires can be detected, signals in optical fibres can be detected, in both cases without disturbing the original signal.

Enigma messages were decoded by Polish mathematicians (e.g. M.A.Rejewski), not just English ones

As the Polish expertise and equipment was shipped to Britain early in the war before the Nazis could capture it, why did we need Bletchley Park then?

SQL
Male
Timmee  Male  Hampshire 22-Sep-2018 12:07 Message #4725816
Slight shift in subject (back to unacknowledged technical capabilities)

I distrusted Bitcoin - which on the face of it would seem a possible method of hedging against continual debasement or more sudden & severe crises with the fiat currencies.

It always seemed implausible to me that the various security agencies around the world could not bring down Bitcoin with cyber techniques at ANY time they chose. It always seemed to me that they would reveal that capability except at PRECISELY the moment the Dollar, Yuan, Yen, Euro etc. were under greatest pressure and peeps were bailing out to buy the Bitcoins carefully accumulated at low prices by the hedgers..
Male
Jeff  Male  East Sussex 22-Sep-2018 13:36 Message #4725826
SQL,

"Signals in copper wires can be detected, signals in optical fibres can be detected, in both cases without disturbing the original signal."

You quoted me "if Alice send Bob a message using a quantum mechanics technique". That paragraph isn't about ordinary signals that we use every day in copper wires and optical fibres.


"It is in this data transfer that interception is possible."

But QM offers methods of destroying the message if it is intercepted.
And it prevents another meaning of "The Imitation Game" - a quantum state cannot be cloned, so the intercepter Eve cannot copy it and send on the copy.


"Quantum effects are very local"

I mentioned "crazy (e.g. entanglement) properties of each quantum". In 1935 using the EPR argument, Einstein objected to quantum "spooky action at a distance" of two quantum particles possibly millions of miles apart reacting in related ways yet by chance, contradicting his Relativity saying that information cannot travel faster than light. It is like throwing two independent dice far apart yet their scores always add up to 7 - "crazy" but it happens in QM, and Einstein was wrong. In 1964 J.Bell proved that there are no "hidden variables" to control the particles.

Although physicists don't understand the mechanism, they do calculations on it and use it. One application is teleportation, another application is sending messages.


"why did we need Bletchley Park then?"

Some thoughts that spring to mind are:-
- Even having the equipment, one couldn't decode messages without knowing how the rotors were set, or the logical/mathematical equivalent of the effects of the rotors.
- Different people have different ideas and different skills.
- Some techniques needed many attempts and guesses, needing many people.
- People were needed to make the tea, and the devices to help decoding.

https://www.bletchleypark.org.uk/our-story/bletchley-park-people/who-were-the-codebreakers says "Nearly 10,000 people worked in the wider Bletchley Park organisation", but when I searched that website for M.Rejewski, H.Zygalski & J.Rozycki and "Polish" but nothing was found, although there was close collaboration with them working abroad.
Male
SQL  Male  Devon 30-Sep-2018 11:34 Message #4726184
Jeff - 20-Sep-2018 12:44

but Jeff you stated quite clearly: "Enigma messages were decoded by Polish mathematicians (e.g. M.A.Rejewski), not just English ones" (just to be pedantic fr a change).

SQL
Male
Jeff  Male  East Sussex 30-Sep-2018 22:20 Message #4726227
SQL,

I have no objection to anybody being pedantic, as it can help to clarify the situation or show errors by me or by anybody else. Are you suggesting that there is inconsistency between my sentences?:-
(a) "Enigma messages were decoded by Polish mathematicians (e.g. M.A.Rejewski), not just English ones (e.g. A.Turing), largely through carelessness of German operators"
and
(b) "Even having the equipment, one couldn't decode messages without knowing how the rotors were set, or the logical/mathematical equivalent of the effects of the rotors."

I think that they are consistent and accurate, except that as well as rotors there was a plugboard and scramblers - I don't know the mechanical & electrical details. The mathematicians were fluent in German, as their university in Poland was Poznan which was part of Germany until 1918. They decoded some of the messages by working out (by logic & maths) the settings of the Enigma machine for the day. Before 1939 they had plenty of practice, as their boss sometimes had answers but didn't reveal them. In January 1939 the Germans increased the numer of possible keys to 159,000,000,000,000,000,000.

The carelessness of German operators included using 3 consecutive keyboard characters (e.g. QWE) or a swearword to generate a key. This greatly reduced the number of keys to be considered.



An ideal method for Alice to transmit a secret message to Bob using ordinary means for them to use the same very long key which is generated randomly. But how do Alice and Bob agree what key to use without eavesdropper Eve finding it out? That is the "key distribution problem", and again where Quantum Mechanics can be used.
An essential part of QM is randomness. (That was another aspect of QM in which Einstein was wrong.) Using QM techniques Alice can send Bob a provisional key, which they can determine whether Eve has intercepted it, and if so then Alice & Bob can abandon part or all of it. After they agree on the key, it doesn't matter if Eve reads their subsequent messages, as Eve can't decode the randomness.

To give a simplified example that I have just made up:- If A=1, B=2, C=3 etc, then for Alice to send Bob the letters "C-A-B" would be 3-1-2. But if a key of random numbers, e.g. 383 & 5296 & 11 & so on randomly were added to each digit and leading zeroes are inserted to make each number 4 digits, and Alice sends Bob message say 0386-5927-0013, then Bob can easily decode it (by subtracting 383 & 5926 & 11 from each set of 4 digits). If Eve didn't know the key, then even if Eve intercepts 0386-5927-0013, there is no way in which Eve can work out that it is 3-1-2 or C-A-B.


I hope that you have found that your previous laughter was inappropriate - a kind of converse to your thread title "Just for fun Many a true word spoken in jest ??"!
Male
Jeff  Male  East Sussex 1-Oct-2018 09:36 Message #4726233
Correction: Replace "But if a key of random numbers, e.g. 383 & 5296 & 11 & so on randomly were added to each digit" by "But if a key of random numbers up to say 9500, e.g. 383 & 5926 & 11 & so on randomly, were added to each number representing a letter."


SQL: Current codes "take longer but are no more difficult ... Any code created by a computer is entirely deterministic and thus can be cracked/decoded given enough resources and time."

But random numbers generated by QM are not deterministic.

I'm not an expert in this subject, but I think that even the simple method that I outlined gives an unbreakable code, i.e. eavesdropper Eve cannot crack it.
If you think that a person or machine can decode "0386-5927-0013", (with more random numbers determining further letters), to produce "CAB", without knowing the randomly generated 383 & 5926 & 11 key, then please indicate how a person or machine might go about decoding it.

Like in the Enigma machine, a message having several occurrences of the same letter would give that letter a different number each time. Whereas the Enigma machine deterministically changed it, a QM method would change it based on a random number.

If you think that say spaces between words can indicate word length, the code A=1 B=2 C=3 etc can be extended to numbers and punctuation (e.g. space=40), and in my example spaces get converted to sets of 4-digit codes by addition of a random number and inserting leading zeroes.

If you think that the message length can indicate the message, (e.g. "Attack from the south" as distinct from "Flee"), then Alice can add to a short message letters such as a load of Z's somewhere (e.g. "ZZZ..." at the end) so that all messages have the same length, and after decryption Bob ignores those Z's, but Eve sees those Z's as 4-digit codes like any other letters/numbers/punctuation in the important part of the message, and doesn't know where the "ZZZ..." starts.

If you think that, on adding a random number up to say 9500, Z=26 would generate on average higher numbers than A=1, which might help Eve, the original message could include some Z's in random places.

Male
Timmee  Male  Hampshire 1-Oct-2018 18:39 Message #4726254
Hope you MSE'ers out there got all that?
Male
tumbleweed  Male  Gloucestershire 1-Oct-2018 18:41 Message #4726255
I think we should all adopt that code when we are posting on here. Just to be safe.
Male
TheSarcasticOne  Male  Essex 1-Oct-2018 22:07 Message #4726270
The difference today is the you can combine many codes, encrypt and re-encrypt many times using a digital device.

You can take 10 simple codes like the A=1 B=2 C=3 . . . . Z=26 then a second code similar to A=N B=O C=P . . . . Z=M

Repeat in any order 1,000's of times in a split second all based on a password entered by the user.

The number of times this can be is basically limitless but you get the picture, the more you encrypt the longer it takes to decrypt or break.
Male
Jeff  Male  East Sussex 2-Oct-2018 11:26 Message #4726304
SQL: "Quantum effects are very local, distances of far less than those needed to transfer data from London to Bristol for example."

In 2017 Pan Jianwei in China used quantum mechanics entanglement over more than 1,000 km. This can be used for distributing random keys. (He has also worked on quantum teleportation.)


Timmee,

I guess you're being sarcastic. Alice encrypts a message using a "key", sends it to Bob, perhaps overheard by Eve, Bob decrypts it using a reverse process to the key, hoping that Eve doesn't also know the key.
One method is for the key to convert each character (letter/number/punctuation) to something else (such as another character or say a 4-digits number) in a fixed way. See my answer to TheSarcasticOne.
An improvement, used by the Enigma machines, is to make the same character produce a different result each time it is used, for example the 1st "E" encountered is changed to a "T", the 2nd "E" is changed to a "K", the 3rd "E" to a "U", etc.) So even if "E" is the most common letter in the original message, the coded message's most common letter doesn't decode to "E". But even that method was cracked.

A message whose key is based on random numbers cannot be cracked, like in my 0386-5927-0013 example above. Yet it is extremely easy to encrypt (just add agreed random numbers to A=1, B=2, C=3) and to decrypt (just subtract those agreed random numbers then 1=A, 2=B, 3=C).

How can Alice and Bob agree on a key without Eve finding out what it is?
They could meet somewhere and have a physical handover, but that has risks, and do they would have to meet every time they want to change the key.
A better method, also using randomness, uses quantum mechanics. Anybody who wants more details can read about quantum key distribution, and watch YouTube videos on the BB84 protocol.
Male
Jeff  Male  East Sussex 2-Oct-2018 11:31 Message #4726305
TheSarcasticOne,

Your shuffling certainly has a lot of possibilities, especially if not so ordered as your example. For example, restricting it to capital letters, "A" could transform to "R", "B" could transform to "G" and so on.
So "A" could transform to any of 26 letters, and for each of those transformations "B" could transform to any of 25 letters, and so on, giving a number of possible "keys" as 26 x 25 x 24 x ... x 2 x 1 (which is called 26 factorial) = approx. 403,291,461,100,000,000,000,000,000 possible codes.
But after the initial shuffling of letters, further shufflings don't make it any more difficult, just as already well-shuffled cards doesn't shuffle them more. (They could even become more ordered, but we won't go into that.)
For example, "A" transforms to "R" which transforms to "C" which ... (more transforms) ... which transforms to "L", so the end result is that "A" transforms to "L", which isn't more complicated than the initial "A" transforms to "R". When Alice sends Bob a message, Bob (or his computer) only needs to use a key of the end result for each letter, (e.g. end result "A" transforms to "L").

If a key has letter "A" always eventually transforming to say "L", similarly "B" always transforming to say "P", etc, then a message might be partially decoded by techniques such as assuming that the most commonly used letters used in English are E then T then A then O then N etc, and looking for the most commonly used letters in the coded message. Partial decoding can greatly decrease the number of possible codes, and reduce computer time.

Another method is to refer to a book (page/line/character numbers) or poem, but that has flaws.
(Incidentally, one of my favourite poems "The Love That I Have" was written by S.O.E. codes officer as a poem code for agent V.Szabo.)

An uncrackable method is to base the key on an agreed set of random numbers. Then the question is how Alice and Bob can agree on that set without Eve finding out. That question can be answered by quantum key distribution.
Male
TheSarcasticOne  Male  Essex 2-Oct-2018 19:20 Message #4726315
Jeff, the beauty of digital encryption is that you are not really limited by the size of a piece of paper.

One of the best methods is to use obfuscation. Turn a 100 letter message into a 100,000 letter message before encryption takes place.

Computers also have the advantage they to do not see letters the same way we do, they see a value, A=65, a=97, B=66 and b=98.

As you can imagine the permutations expand and are almost limitless.

The problem has always been passing the key, so what is needed is a keyless system which is possible but not practical for public use. It is possible to create a code that is linked directly to the machine decoding it. You still need to keep both machines secure, but the message can be passed in public.


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