...and Never Cackled
The work carried out at
Bletchley
Park was of immense importance
to the war effort and, as such, was extremely top-secret. It
seems that none of those involved squealed about the important
breakthroughs, and the Germans remained unaware that every
message they transmitted via the Enigma was being deciphered and
read by the British. Towards the end of the war, a common joke
among top-level intelligence staff was that if Hitler wanted any
information about the movements of his admiralty, he need only
ask the British, who knew more about German naval movements than
the Germans themselves!
Winston Churchill famously referred to the workers at
Bletchley
Park as “my geese that laid the golden egg and never cackled”.
The work at Bletchley Park was so secretive that details of the
important codebreaking carried out there were not made public
until the 1970s. And important it was: the intelligence produced
at BP was so crucial to the Allied war effort it has been said
that without this, the war may have been up to two years longer
(some believe it may have been up to 4 years longer).
Enigma
We saw
these Enigma machines in the Science Museum in London.
It was
an exhibit on Alan Turing, one of the brains at BP.
In the early 1920s, a German engineer was having much success
with his machine that could code and transmit secure
information, the Enigma machine. Enigma used electrical
connections to encrypt messages, and so the process was much
quicker than it had been when an operator had needed to perform
encryption by hand, using a table of codes. Most importantly,
the resulting encrypted messages were considered impossible to
crack. For this reason, by 1933, all of the German armed forces
were using their own variants of the Enigma.
An Enigma machine looks like a typewriter, but with some extra
features. The operator types in their message, then the machine uses
three to five rotors (depending on the version of the machine) to
scramble the text and produce different letters of the alphabet.
This is known as a substitution cypher, as one letter is substituted
for another. The receiver of the message needs to know the exact
settings of the rotors in order to reconstitute the text. Over the
years the basic machine became more complicated as more rotors were
added and as German code experts added plugs with electronic
circuits.
One key point of difference with the Enigma is that when an
operator inputs a letter, that letter will never be enciphered
as itself. That is the weakness that eventually enabled the
machine’s codes to be ‘cracked’. There were certain words that
would generally appear in a message, for example ‘to’ at the
start, and yet the letters from those words never appeared in
the encrypted messages.
By 1932, the Polish had managed to decipher Enigma messages. At
that stage, the cypher was only altered every few months, but as
the 1930s rolled on and German military operations began to
increase in frequency, so did the number of messages being
transmitted. It wasn’t long before the cypher was being changed
at least once per day. This gave 159 million million million
possible settings to choose from! It is no wonder the Germans
considered the machine to be unbreakable.
As the encryption became more complicated, the Poles were
unable to continue deciphering the messages. In 1939, they
handed their data to the British, and Bletchley Park became the
new centre for efforts to decrypt the Enigma.
The first break into Enigma came in January 1940, when a team
worked out the key used by the German Army. Soon after, they
also unravelled the key used by Luftwaffe officers who
coordinated air support for army units. BP staff based in a
neighbouring hut turned the deciphered messages – known as
Ultra - into intelligence reports. As the cracking of Enigma was
extremely top-secret, the resulting reports were made to look
like they had been produced by an MI6 spy, codenamed Boniface,
with a network of imaginary agents inside Germany.
At this stage, there were some amazing minds working at BP.
Dilly Knox, Alan Turing, Gordon Welchman, and Max Newman knew
that deciphering Enigma messages by hand was taking too much
time. By the time the messages were unravelled, the intelligence
was of little operational use. Alan Turing, with the support of
the others, created a device that would run through all possible
Enigma wheel configurations, in order to reduce the possible
number of settings that could have been used to encrypt the
message. This reduced the amount of codebreaking work that had
to be done by hand. The machines were known as Bombes, and were
generally operated by Wrens, members of the Women’s Royal Naval
Service.
(Unfortunately we couldn't get any pictures of a Bombe, as that
part of BP was closed for renovations. You can find a picture of
it here: http://www.theregister.co.uk/2009/03/23/bletchley_bombe/)
The resulting intelligence – Ultra – was extremely valuable to
the Allies. Throughout the First Battle of the Atlantic, Ultra
gave the navy vital information about the positions of German
submarine packs (‘wolf packs’) and the Admiralty was able to
fight off the U-Boats which attacked merchant ships bringing
supplies to Britain from North America. Ultra also enabled the
Allies to discover if the Germans had swallowed deception plans
they had planted, such as those for the invasion of Sicily in
July 1943. Before the operation, secret agents planted false
intelligence suggesting that plans to attack Sicily were only a
ruse, and that real landings would take place elsewhere. Ultra
revealed that the Germans had fallen for the false intelligence
and believed an Allied operation in Sicily would only be a ruse
for real attacks elsewhere. The resulting invasion of Sicily was
a success, and was one of the main turning points in the war.
Ultra also played a key role in the success of the
D Day
landings in June 1944. Ultra intercepts showed that the Germans
had believed the deception campaigns, and were convinced a
landing was to be made in the Pas de Calais. This meant that
when the eventual landings took place in Normandy, and over
150,000 Allied troops arrived by air and sea, German resistance
was low and the Allies were able to finally re-gain a foothold
in Europe. Right to the end of the war, the Germans did not
believe that the Enigma had been broken and they continued to
send sensitive information which was promptly deciphered by a
select few at BP.
Lorenz
Another triumph of Bletchley
Park was the deciphering of messages sent using a Lorenz cypher.
Before the war, the High Command of the Germany Army had
requested the construction of a teleprinter cypher machine that
would enable them to send secret messages via radio. The Lorenz
Company designed a machine that featured up to twelve wheels all
with a different number of cams, or pins, in them. From here, it
all gets a bit complicated for me, but I understand that this
means the possible encoding options are huge. (Wikipedia
it or use Tony
Sale’s amazing website if you want to know more: )
The Lorenz machine used a combination of dots and crosses and
Boolean 0s and 1s to print a message. It then used the Vernam
system of adding a random set of obscuring characters before
transmitting the message. At the receiving end, the random set
of obscuring characters would be added back on to the message,
they would cancel themselves out, and the original message
characters could then be printed. This cypher system, which uses
one-time purely random obscuring characters, is unbreakable.
Until you factor in human error.
On August 30, 1941, the Germans made a terrible mistake. An
operator had a long message of nearly 4,000 characters to be
sent from one part of the German Army High command to another.
He set up his Lorenz machine, sent a twelve letter indicator to
the receiving operator – this would tell the receiver which
settings to put onto his Lorenz machine - and keyed in his long
message. The receiving operator then signalled that he had not
received the message and to send it again. Both operators then
put their Lorenz machines in the same start position they had
used for the original message – even though this was
forbidden. The second time around, the sending operator made
some abbreviations and mistakes. The interceptors at Knockholt
realised that the same message was coming through, as it was
using the same one-time obscuring sequence. However, the message
was slightly different and this set off alarm bells. The
incoming text was quickly sent to Bletchley Park, where one of
the top codebreakers, John Tiltman began to study it.
Eventually Tiltman was able to work out a chunk of the
obscuring character sequence that the cipher machine generated.
After three months, his team had failed to make any further
headway, and 24 year old mathematician Bill Tutte was brought
in. In two months, Tutte worked out the complete logical
structure of the cypher machine. Without ever seeing a Lorenz
machine (in fact, the British would not come face-to-face with
one until 1945), Tutte managed to reverse engineer the cypher
machine. This was a huge breakthrough, possibly one of the
greatest intellectual feats of the War.
Soon, the team had constructed a machine, known as the Tunny,
using Tutte’s calculations. Further developments produced a
family of machines known as the Robinsons, though these were
still too slow to be of much use to the war effort. It was time
to call in the big(ger) guns.
Above, Tunny and Heath Robinson machines
Max Newman, a mathematician, and his engineer sidekick Tommy
Flowers soon designed and constructed THE COLOSSUS. (*Cue
dramatic music*) The Germans enciphered a message with the
Lorenz, transmitted it by radio, when it was intercepted and
recorded on to paper tape at BP. The tape was joined into a loop
with special punched holes at the beginning and end of the text.
Colossus was able to read the tape at 5,000 characters per
second.
(For computer geeks, “At 5,000
cps the interval between sprocket holes is 200 microseconds. In this
time Colossus will do up to 100 Boolean calculations simultaneously
on each of the five tape channels and across a five character
matrix. The gate delay time is 1.2 microseconds. Colossus is so fast
and parallel that a modern PC programmed to do the same
code-breaking task takes as long as Colossus to achieve a result.”
According to Tony Sale, the former curator at BP.)
By Christmas 1943, a Mark 1
Colossus was assembled at Bletchley. The machine could
break Lorenz messages in hours, which was a huge advance. It was
just in time to decipher messages related to D-Day, and the
resulting deciphered messages revealed that Hitler had fallen
for the deception campaigns (such as the phantom army in the
south of England, phantom convoys moving across the Channel –
look it up, it’s very exciting stuff!) and was convinced that an
attack would be launched on the Calais area of northern France,
rather than at the correct location of Normandy. This was
extremely valuable knowledge to possess, and it was all thanks
to the hardworking teams at Bletchley Park.
By the end of the war, nine
more Colossuses (Colossi?) had been built, and 63 million
characters of German messages had been decrypted.
Knockholt
While we were in the Computing Museum, we were excited to come
across some information about Knockholt.
Knockholt is our
neighbouring village, and in it sits a large farm house called
Ivy Farm. This house was recently for sale at £1.25 million, and
it hides an exciting past.
During WW2, Ivy Farm was requisitioned by
GC&CS and was used as
a wireless intercept station. There was a wireless room at BP,
but concerns around German detection of the site soon dictated
that other stations should be created in numerous locations
throughout the United Kingdom. One of the most important of
these was at Ivy Farm in Knockholt. The Farm served as a Radio
Intercept Station for messages transmitted by means other than
Morse Code, e.g. such as those that had been enciphered using
the Lorenz.
Isn't that exciting?! Living just minutes from one of Britain's
most important intelligence locations of WW2?
Well that concludes the story of our trip to Bletchley Park - a
place I've wanted to visit for many years. It was wonderful to
walk on the ground where such exciting history unfolded, and to
picture the many Wrens and genius codebreaking minds engaged in
their valuable work. Sometimes I feel like I was born in the
wrong era, as the excitement and mystery of the 1930s and 1940s
appeals to something deep inside of me. Being at Bletchley Park
for the 1940s festival with so many remnants of the war, and so
many people dressed in costume was an amazing experience.
Of course, we know how truly lucky we are not to have to
experience the fear, death, and dishonour that was the reality
of life in war-torn Europe. As we stood on that ground, rich
with history, we also said thanks to the men and women who
served their country with their valuable intelligence work and
helped secure a better future for all of us.
(For the information about Enigma and Lorenz machines, I have relied heavily on the website of Tony Sale, who was the original curator at the Bletchley Park Museum. Thank you to Mr. Sale for his interesting website and the informative reports on codebreaking at Bletchley Park. He describes the mechanisms of Enigma and Lorenz in depth on the website, so if you want to know more, click on this link and be directed to Mr. Sale's website.)
Remembering Bill Tutte Another Brilliant Codebreaker From World War II
QUOTE
One of the greatest mathematicians and codebreakers of the 20th
century, William (Bill)
Tutte, was born a century ago this Sunday, May
14 [ 2017 ].
His wartime work enabled the British to break into the communications of the highest levels of the Nazi regime, motivated the development of a special-purpose electronic codebreaking computer, shortened World War II and saved countless lives.
Tutte, who died aged 84 in Canada in 2002, went on to do far-reaching work in mathematics but few people have heard of him and his contributions.
First breakthrough
Tutte’s origins were humble. He was born in Newmarket, a market town
in England north of London, the son of a gardener and a housekeeper.
He excelled at school and entered Trinity College, Cambridge, in 1935, where he majored in chemistry.
While still an undergraduate he became close friends with three mathematics students: Leonard Brooks, Cedric Smith and Arthur Stone. Together, these four threw themselves into mathematical problem-solving and research.
They were attracted to a simple recreational puzzle, on whether it is possible to divide a square up into smaller squares, all of different sizes, known as Squaring the Square.
The prevailing belief was that it could not be done. But they managed to do it, partly by discovering an unexpected link with the mathematics of electrical circuits.
The theoretical framework they developed has had a lasting influence. A German mathematician, Roland Sprague, working independently, just pipped them to a solution to the puzzle, but not the theory behind it.
The work of Tutte and his friends was published in an academic journal in 1940. It got Tutte noticed at Cambridge, and from there he joined Britain’s wartime codebreaking operation at Bletchley Park in 1941.
The codebreakers
Other Cambridge mathematicians were there before Tutte. Among them
was
Alan Turing, who had worked out how to break the version of the
Enigma code used by the German navy.
The Enigma code was already so difficult that even there, at Bletchley Park – the best codebreaking operation of the War – it had sat in the too-hard basket until Turing’s arrival. It was a very tough problem, even for him.
Tutte worked on different cypher machine, known as the Lorenz cypher. This was the one used by the Nazi High Command, including Hitler himself.
It was much more complex than Enigma, and on top of that, the British knew very little about how it worked, whereas with Enigma they knew everything.
So it was a harder problem with less information, and yet Tutte solved it. It was a staggering achievement.
Tutte’s breakthrough was based on careful analysis of intercepted encrypted traffic to identify some periodic behaviour that indicated the size of a “wheel” component in the machine.
Tutte’s attack on Lorenz needed to be automated. This led to the design and construction of the Colossus machines, led by Tommy Flowers.
These are sometimes regarded as the world’s first computers, having most of the fundamental characteristics that the term “computer” is taken to embrace today.
They were so successful at breaking into the encoded messages of the Nazi regime’s high command that they were often able to decode the messages at the same time as the intended German recipients were reading them.
This gave an incalculable advantage to the Allies in the later years of the war, including their preparations for invading Normandy.
Tutte’s work on Lorenz has been described as the greatest intellectual achievement of the second world war. As a result, he was given a fellowship at Cambridge and went on to do his PhD there.
From codes to networks
Another big effect of the Squaring the Square puzzle was to turn
Tutte’s attention more to mathematics, while he was majoring in
chemistry, and in particular to the theory of graphs.
These are not the simple graphs you would use to chart things such as daily temperatures over time. Rather, they are abstract networks, consisting of objects (called vertices or nodes), and interactions between them (called edges or links).
Think of the network of train stations, together with the rail lines between them. Or we might have web pages, with hyperlinks between them, making the graph we know as the World Wide Web. We might have people, with friendships between them. And so on.
One of Tutte’s major contributions was to determine the exact place of graphs among some other mathematical objects for which more theory was known.
In mathematics, the simplest objects to deal with are those that are straight and flat – for example, lines and planes. We call such things linear.
Much of mathematics is about taking things that are non-linear – meaning that they are curved or bent rather than straight or flat – and trying to make them linear, or nearly linear, or to replace them with something linear.
For example, mathematicians can study curves by zooming in so that they look straight, or close to it.
Now, graphs – or networks – are much more complex objects than simple straight lines or planes. Nevertheless, it turns out that there are linear ways of looking at them.
Extra dimensions
But these come at a price. You have to work in many many dimensions,
not just the three dimensions of space that we are used to. It’s hard
for us to imagine these extra dimensions, as they represent directions
that are so weird, so outside our universe, that we can’t even point in
them.
In these vast multidimensional worlds, it’s not so easy to tell graphs apart from other linear objects you find. This is what Tutte showed us how to do. He pinpointed exactly what was special about graphs.
This theory brought a new depth to the subject, and related this new field to older and more developed parts of mathematics.
So it was that a purely recreational problem, a source of mathematical fun for undergraduates, sowed seeds that grew into a major contribution to overthrowing the Nazi regime, and raised up a new branch of mathematics that is now used to understand the complex networks that permeate the modern world.
More than a decade after Tutte’s death a memorial was erected in his former home town of Newmarket.
This article is based on a
talk
by the author at The LaboraStory. For information on any Tutte
Centenary events, including an event at Bletchley Park on Sunday May 14,
see the Bill Tutte
Memorial Fund.
UNQUOTE
The author knows what he is talking about. Bill was a better man than
Turing but he did not get the publicity because he was not
Homosexual. The Wiki agrees in re his
achievement, saying:-
QUOTE
Diagnosing the functioning of the Tunny machine in this way was a truly
remarkable cryptanalytical achievement which, in the citation for Tutte's
induction as an Officer of the
Order of Canada, was described as "one of the greatest intellectual feats of
World War II".
UNQUOTE
Being lucky helps but making your luck matters big time.