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Wednesday, May 1, 2013

mathematician solves WW2 letters

de bene esse: literally, of well-being, morally acceptable but subject to future validation or exception


For 60 years, mysterious coded letters from a British prisoner of war have refused to give up their secrets.

Relatives of imprisoned naval officer John Pryor were unable to discover the hidden messages in the dozens of letters he sent back to his family.

Finally, with the help of a top mathematician, the wartime cipher has been cracked.

See Vid Here: http://www.bbc.co.uk/news/uk-22359307
 
Decoded: Letters sent by war hero John Pryor contained messages for the Allies, and these have now been deciphered for the first time
Decoded: Letters sent by war hero John Pryor contained messages for the Allies, and these have now been deciphered for the first time

The letters sent back home by Sub-Lieutenant John Pryor from a German prison camp seemed innocent. They often began with 'My Dear Mummy & Daddy' and discussed mundane topics including gardening and a 'vegetable patch' but his British wartime letters actually contained hidden messages, only now deciphered by academics. It is the first time the captured serviceman's family have been able to understand the secret messages.

Sub Lt Pryor was captured at Dunkirk in 1940 and sent to a prisoner of war camp.
He was held for five years and as a reward for good behaviour, was allowed to send letters to his parents in Saltash, Cornwall. His letters contained secret messages for the British military - and involved a fiendishly complex alphanumeric code.
In one letter, he hid intelligence about the sinking of a British submarine by writing about the PoW camp's vegetable garden.

He wrote: 'Many seeds are left, being saved from several plants which did very well some time ago.
'Our last year's harvest was extremely good. Well worth repeating again for this year.'

It meant: 'HMS Undine attack failure. Trawler depth-charged, scuttled in 70 feet, three burnt.'

From this, experts were able to deduce a coded message about the sinking of the British submarine, the HMS Undine, which was destroyed in 1940.

Scroll down for complete breakdown of how the code was cracked
One of the letters sent by Sub Lt John Pryor to his family from a German prison camp
One of the letters sent by Sub Lt John Pryor to his family from a German prison camp. Subtle markers such as underlining his name at the bottom indicated the message contained a secret code

CRACKING THE CODE: THE FIRST PHASE

This extract from the letter above shows some of the initial markers to crack the code.The word count of the hidden message is determined by multiplying together the number of letters in the first two words of the first line of the letter after the salutation. In the above case, this is 'last week' - two groups of four letters. A grid is drawn with 16 squares in it (i.e.4 x 4). The rest of the first line is ignored. Starting with the second line of the letter, select the fifth and fourth words alternately and place them in the grid starting top left and working left to right.
My Dear Mummy & Daddy, Last week (4x4 grid) I received a short letter from Robert.
The envelope had the marks (5) of five of the (4 - start alphabet code) RAF censors. I can’t
imagine what his new number on the envelope means, maybe he has been turned
over to rather different occupations, which of course I can’t know anything
about. I am glad the information (5) I sent you, especially (4) about the Uffa
Fox and (5) other books of the (4 – start alphabet code) sailing variety, reached you. As regards
other possible books, my present desires seem mostly for interesting
literature of events in our country’s history. A subject I am unfortunately
very weak in.
Ultimately the code in the letter would read: ‘Clothing and local maps obtained require some of borders especially swiss passport information and renten marks’. See bottom of article for full analysis.


John Pryor was born in 1919 and died in 2010, aged 91. He was a naval officer and was evacuating troops from the beaches at Dunkirk in 1940 when he was captured by the Nazis. He spent the rest of the war imprisoned in the notorious Marlag und Milag Nord death camp in north-west Germany, from where he penned 20 letters home containing secret codes. After returning to Britain, he continued serving in the Navy until his retirement.
 
Mr Pryor wrote his memoirs in 1980 and attempted to include extracts of the letters but by then could not remember how the codes worked - and never told his family about them.
The secret codes were deciphered after his son Stephen Pryor, a chancellor at Plymouth University, showed the letters to a PhD student studying PoW escape plans.They were then cracked by a team of mathematicians, historians and geography experts - 70 years after they were written.

Stephen, 58, of Saltash, Cornwall, said: 'I had known for 30 years that my father had these letters but their contents lay hidden.
'His letters from the camps were always addressed to my grandfather but would have already passed through German censors.
Captured: After Dunkirk Sub-Lieutenant John Pryor was put in a PoW camp (pictured fourth row, fourth from left), but it did not stop him helping Britain's war effort
Captured: After Dunkirk, John Pryor was put in a PoW camp (pictured fourth row, fourth from left), but it did not stop him helping Britain's war effort
Stephen Pryor with some of his father John's wartime letters
Stephen Pryor with some of his father John's wartime letters

CROSSWORD AND WORDSEARCH: THE BRITISH WAY OF MAKING CODE

The codes John Pryor adopted to evade Nazi snoops were inspired by the British love of wordsearches and crosswords.
Dr Harry Bennett said German agents relied on machines and industrial technology to decipher secret messages.
The British meanwhile had a more whimsical approach inspired by classic puzzle-solving that their Nazi counterparts simply could not understand.
Dr Bennett said: 'It would take several hours in a classroom to explain exactly how the code worked but obviously if it was simple the Germans would have rumbled it.
'First off, they would signal in one of two ways that a letter contained a code. One signal was writing the date in a continental method using numbers rather than words.
'The second thing they would typically do was underline the signature. Either would confirm to MI9 that the letter contained a code.
'With John Pryor's letters, every fourth of fifth word offers you a clue. You then have to take the exact letters and reorganise them in a different way to make a sensible message.
'The German approach to cryptography was mechanical and industrial and they would typically use a machine, like the Enigma machine, to encode stuff for them.
'The British codes were a bit more like crosswords or puzzles - a form of super-Sudoko for the 1940's generation.'
'My father was among tens of thousands of young men who as PoWs lost the best years of their youth and could never hope to regain them.
'But I can now see that despite their plight, he and his peers took incredible risks and it has only made me admire their resilience and ingenuity even more.'
The research began after military intelligence expert Barbara Bond, a pro-chancellor at the Plymouth University, Devon heard about the letters from Stephen, a university governor.

Despite several efforts, they failed to decipher the codes and it took mathematics Professor David McMullan to finally crack them. Using what little information was available on  codes used by the MI9 section of British Military Intelligence, he revealed the coded words alternated between every fourth and fifth word.
However, if those words happened to be 'but' or 'the', it triggered an intricate alphabetic and numeric sequence which Sub Lt Pryor used to hide requests for items such as maps, passports and currency.

MI9 was the British Directorate of Military Intelligence Section 9 - a department of the War Office between 1939 and 1945. During the war, it was tasked with aiding resistance fighters in enemy occupied territory and recovering Allied troops who found themselves behind enemy lines. It also tried to communicate with British prisoners of war and sent them advice and equipment.
Experts say an escape committee inside the PoW camps decided what needed to be included in the messages.
Part of the alphanumeric key that was needed to decipher the PoW's messages
Part of the alphanumeric key that was needed to decipher the PoW's messages
Dr Harry Bennett, associate professor of history at Plymouth University, said: 'Coded messages played a huge part in the war effort on both sides, as they were undoubtedly the best way to get messages or instructions through.
'The MI9 code was especially important, as their chief mission was to source equipment and supplies for prisoners of war who would then attempt to orchestrate an escape.
'But from these letters we now know they were also passing on information about key German sites, such as munitions dumps.
'The letters go to emphasise just how invaluable the code writes were to the Allied war effort.'

TIME TO CONCENTRATE... HOW THE CODE WAS CRACKED

Harry Bennett provides a detailed report of David McMullan's findings...
1. How the code works
The coded letters are immediately identifiable by the form of the date: 22/3/42 rather than 22 March 1942 indicates it is coded. Underlining the signature also confirms that the letter carries a coded message.
The length of the message is determined by multiplying together the number of letters in the first two words of the first line of the letter after the salutation. Using the letter on which I had based all my attempts (22/3/42) the first 2 words are ‘lucky again’ which is 5 x 5 = 25.
A grid is drawn with 25 squares in it i.e.5 x 5. The rest of the first line is ignored. Starting with the second line of the letter, select the fifth and fourth words alternately and place them in the grid starting top left and working left to right.
However, the message is eventually read starting bottom right, reading across and then diagonally, across and diagonally, etc, as shown below, reading in sequence 1 – 25
2524221915
2321181410
20171396
1612853
11742

If the word ‘but’ occurs as the 5th or 4th letter, it signifies the end of the message. Words which are hyphenated or have an apostrophe in them are treated as one word for the purposes of counting e.g. ‘two-days’, ‘I’ve’.

2. Letter dated 22/3/42
In the 22/3/42 letter, the 5th word is ‘acknowledge’ so this goes into the top left box of the grid and is, therefore, the final word of the message.

The 4th word after this is ‘the’ which indicates that the alphabet code starts at this point. This means that, starting with the next sentence, the first letter of each consecutive word is written down in groups of three, each letter is identified on the alphabet listing shown below and then the number of the column in which it occurs.
Thus, on the 22/3/42 example, you go to the sentence which starts ‘Which brings the’ and list the first letter of every word in groups of three.
Each group of 3 letters signifies a letter in the table. When I originally did this, I used the table starting with O and it produced goobledygook. What David McMullan did was to realise that, if there were variations in the numerical code such as 5 6 and 5 4, then there could well be variations in the alphabet code.
Instead of the O table shown below, the start letter might be different. He worked systematically through the alphabet, looking for the code to produce a word that made sense.
It was not until he got to the 19th letter (S) that he got a recognisable result. The word was ‘elder’ followed by a full stop.

O 111 P 211 Q 311
R 112 S 212 T 312
U 113 V 213 W 313
X 121 Y 221 Z 321
. 122 A 222 B 322
C 123 D 223 E 323
F 131 G 231 H 331
I 132 J 232 K 332
L 133 M 233 N 333

S 111 T 211 U 311
V 112 W 212 X 312
Y 113 Z 213 . 313
A 121 B 221 C 321
D 122 E 222 F 322
G 123 H 223 I 323
J 131 K 231 L 331
M 132 N 232 O 332
P 133 Q 233 R 333

So instead of the O table, we have the S table, shown above, and using the same dated letter, we have the first recognisable word:-
WBT 222 = E
COM 331 = L
PWW 122 = D
HBW 222 = E
OUC 333 = R
ISC 313 = .

We know from John Pryor’s memoirs that his colleague in captivity was Lt.Cdr. Elder. So the 2nd word on the grid and the penultimate word of the coded message is ‘Elder’.

3. Testing the hypothesis
David then chose a letter at random and tried the same approach using the S table.

The letter he chose is dated 7/5/42 and has an underlined signature, both aspects indicating that the letter contained a coded message. The first 2 words of the letter are ‘Last week’ which indicates a grid of 4 x 4 and a coded message of 16 words.
Using the 5 4 S approach, starting with the second sentence, the 5th word is ‘marks’ which becomes the first word in the grid and the last word of the message.
The 4th word is ‘the’ which indicates that the alphabet code starts. Starting with the next sentence, the first letter of each word is listed in groups of 3, converted into numbers on the S table and then into alphabet letters.

ICI 333 R
WHN 222 E
NOT 232 N
EMM 211 T
HHB 222 E
TOT 232 N
RDO 313 .

The word spells ‘renten’ and becomes the second word on the grid. (Don’t worry, he too did not initially recognise this as a ‘real’ word until he googled it and discovered that the currency of Germany from WWI through to 1948 was the renten mark).

At the point where the full stop occurs, you need to revert to the 5 4 sequence at the start of the next sentence in the letter but maintaining the correct rhythm.
Having finished on the 4th word at the previous stage, you start this time again with the 5th word. This gives the word ‘information’ which becomes the 3rd word on the grid.
The following 4th word is ‘especially’ which becomes the 4th word on the grid. The 5th word is ‘and’ which becomes the 5th word on the grid. The 4th word is ‘the’ signalling that the alphabet code starts again at the beginning of the next sentence. This produces the following:-

ARO 133 P
PBM 121 A
PDS 111 S
MFI 133 P
LOE 332 O
IOC 333 R
HAS 211 T
IAU 313 .

It contains a spelling error but is nonetheless recognisable as the word ‘passport’ which becomes the 6th word on the grid.

Reverting to the start of the next complete sentence in the letter and picking up the 5 4 rhythm, the 5th word is ‘borders’ which becomes the 7th word on the grid. The following 4th word is ‘require’ which becomes the 8th word on the grid. The following 5th word in the letter is ‘the’ which indicates that the alphabet code starts again, as follows:-

PAM 111 S
TMN 212 W
ITL 323 I
SMP 111 S
GAA 111 S
FSO 313 .

The 9th word on the grid is ‘swiss’.

Reverting to the start of the next complete sentence in the letter and keeping the 5 4 rhythm, the 4th word is ‘of’ which becomes the 10th word on the grid. The following 5th word is ‘obtained’ which becomes the 11th word on the grid. The following 4th word is ‘local’ which becomes the 12th word on the grid. The following 5th word is ‘some’ which becomes the 13th word on the grid. The following 4th word is ‘the’ which indicates that the alphabet code starts again at the beginning of the next sentence. This produces the following:-

AFW 132 M
AWA 121 A
ARU 133 P
SSM 111 S
CGL 313 .

The 14th word on the grid is ‘maps’.

Reverting to the start of the next complete sentence in the letter and keeping the 5 4 rhythm,
the 5th word is ‘and’ which becomes the 15th word on the grid. The following 4th word is
‘clothing’ which becomes the 16th and final word on the grill. To re-enforce the point, the
5th word after this point is ‘but’ which confirms the end of the coded message. The grid
reads as follows:-

marks renten information especially
and pasport borders require
swiss of obtained local
some maps and clothing

4. Conclusion
Starting in the bottom right corner and reading across and diagonally in sequence, the message reads ‘clothing and local maps obtained require some of borders especially swiss passport information and renten marks’.
It is a clear request for maps of the Swiss border, German currency and information which would allow them to produce passports. It also carries an indication that they have already been able to obtain local maps and clothing.

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