BREAKING THE UNBREAKABLE

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BREAKING THE UNBREAKABLE..

                                                                Aastha Thapaliya.

 

“If there is a God, he will have to beg my forgiveness.”

These were the words carved in one camp cell by one prisoner and there were 42,400 camps and ghettos ran by Nazis alone and 6 million such prisoners. It was the horror that humanity had never faced on such a large scale. It was the World War II.

“Germany will either be s world power or will not be at all. “ Bold statement made by Adolf Hitler, one of the main reasons that started the World War II. Humanity was still standing in its trembling feet, the souls of the dead were not even at rest yet, dark clouds of smoke and the large bangs of the bombs were still a nightmare, the wounds were still bleeding fresh from the World War I, when in 1939 A.D, even bigger detestation started. That detestation was World War II (WW II). “It is not the truth that matters but victory.” Hitler was determined to win and 61 other countries were involved to prove him wrong.

WW II was not just any war. It militarized 100 million people. WW II at the end claimed 50 million lives. The horror lasted for 2,175 days. 30,000 people on average were killed every day. 15,000,000 soldiers died at the battle field and 25,000,000 were wounded. 45,000,000 civilians died. USSER alone lost 16,825,000 people. China lost 20 billion people, Germany lost 15 to 20 million lives, 6 million out of which were Jewish. Mothers lost their sons, wives lost their husbands, children lost their fathers, sisters lost their brothers and the whole world lost its neutrality. Children died buried under their own houses, they died in prisons, and they died in their mother’s frozen arms. 1.5 million Children were murdered during the Holocaust. Millions of people killed themselves because death was easier chocking on your own breath with a barbed wire around your neck than to fear the bombs that might befall and this was not just “a fear” because 3.4 million tons of bombs were dropped by the Allies alone.

The war lasted six solid years and Germany started it out with a very loud roar. Every secret attacks, every small details would be known to the Germans bit no countries knew Germany’s next move. No countries could decipher the encrypted text that Germans used to communicate their secret messages. How? They had Enigma and Enigma was unbreakable.

Enigma was a machine that looked like a type-writer. It was invented by a German Engineer Aurthur Scherbius at the end of World War I. Enigma was used by Nazis to send a secret coded messages.

Enigma consists of keyboard, roter and plug board. There were three roters in the Enigma and criss-crossed wiring. Wires are fitted inside the roter and battery is used to power the bulbs that would glow for each alphabet. (If you typed ’N’, ‘Y’ would light up).  So every time you type a message, wire turns and the battery connects to a different bulb for same letters. In order to decode the message the Nazis had special arrangement. There were three windows in the Enigma. It represents the numbers for three roters. These numbers and cryptic message would be written in a paper and would be transmitted to Nazis soldier from the original place to the submarines using a radio transmission. Soldiers inside the sub-marine would set his enigma to the same number and type the cryptic message and it would decrypt to show the real message.

Now why was Enigma unbreakable?

Suppose “NEXT ATTACK AT NINE.”  was the secret message that was to be crypted. So, if you typed this message in the Enigma, let us consider it would give result as:

NEXT             ATTACK         AT      NINE

YTHM             YIURAD         FG      WKCT

If you notice, the alphabet ‘N’ and ‘A’ are crypted to ‘Y’ for both the alphabets and ‘T’ in ‘attack’ has two different alphabets ‘I’ and ‘U’ for the same alphabet. And this is not it. It would give different results every time you type the same message. Polish, British and Americans smuggled those enigmas and tried to break the code and just having the machine was not sufficient and there were millions of possible settings for one message.

There are 26 alphabets. So each roter had 26 starting places and to make the situation worse, each alphabet would swap. So, if you had to select three roters from the set of five, there would be 543=60 possible ways and each roter would turn for 26 alphabets. So, three rotes lead to 262626=17576 possible ways. Navy Enigma also had plug boards with 10 extra plugs which were used to connect two letters in pair. If Q was connected to E, Q and E would swap over. So, the total possibility for plug board alone was

= 150, 738, 274, 937, 250 possible ways.

Where,

26! = ways to arrange 26 alphabets

10! = pairs of 10 alphabets

6! = (26-102)! = 6! = left over pairs

= Two pairs for 10 pairs (AB = BA)

So, the total possible ways to set an Enigma machine would be:

Roter:             543=60

Starting level:  262626=17576

Plug board:  = 150, 738, 274, 937, and 250

Total: 158, 962, 555, 217, 826, 360, 000 possible ways

This concludes that there are 158, 962, 555, 217, 826, 360, 000 possible ways to set an Enigma machine to decode one message. So, even if there were 10 men checking 1 setting per minute for 24 hours, for 7 days, for 12 months, it would take approximately 20 million years to figure out one setting for one message and the Nazis would change their setting at mid night. Nazis soldier also had code book which informed them about how the machine was to be set for that day. It was a monthly code chart which was written in soluble ink. So, even if anyone tried to smuggle it out of sub marine, the ink would dissolve in the water and it would be destroyed forever. It was said that Britain required a miracle to break Enigma. Britain had that miracle and his name was Alan Turing.

Alan Mathison Turing was a computer scientist, mathematician, logician, cryptanalyst and theoretical biologist born on 23 June, 1912 in Maida Vale, London. As a young boy, he was different. He did not understand normal ways of life. He had difficulty working as a team. For him trying to understand people talk was like deciphering some complex code. He was bullied at his school. His hobby was solving cross word puzzles. He used to take rest by running. Running helped him think. He showed remarkable abilities in studies he loved by solving advanced problem at age 14 without even having studied even elementary calculus. He was openly homosexual and never thought of it as a stain that needed to be removed. He had strong bond with his friend Christopher Marcom with whom he exchanged messages written in cord word because mathematics class was too easy for them. Christopher died that a very young age and Alan Turing coped with his grief by working that much harder on the topics of the science and mathematics that he shared with Marcom.

ALAN Turing was a very humble human being. He was a speck of light on the dark night. He was the silver lining to the dark clouds. He was the miracle who broke the unbreakable.

During WW II, Britain was at disadvantage because German military implemented the use of U-boats. At this time Britain was dependent on the imports of food from the other Allied countries. Unarmed Martian ships delivered 13 million tons of food every year. German U-boats destroyed two thousand seven hundred and 80 Allies ships. Churchill was terrified and Hitler believed that U-boats would win him the war. The German sub-marines would receive their encoded messages through Enigma. Engineers and mathematicians were considered unimportant in Britain British thought deciphering would be done by linguists. They hired historians, masters in Latin and Greek, astrologists and scholars in medieval German. They hired handful of mathematician and Alan Turing was selected from Cambridge. Within the first few weeks of the war, Turing designed what would be referred to as “The Bombe.” This was a high speed electro-mechanical device for testing the every possible setting of Enigma. But not even a machine could sort the millions of possibilities of the Enigma. Alan Turing used statistics to narrow down the possible settings so he and his team could decipher the message before the Germans reset the Enigma. Turing realized that he could not compare the possibilities without having the unit of measurement. He created what he called “the band.” The band is the smallest change in weight of evidence that is directly perceptible to human intuition. One band is equal to the odds of 10 to 1 in favor of a guess. However, Turing often dealt with smaller quantities like Nessa bands and cinta bands. Turing used bands to discriminate between sequential hypothesis and the bands allowed Turing to identify how much information he needed to solve a particular problem. They were actually dub bands because Turing and his partners had to match up message using strips of paper that were printed in the nearby town of Banbury. Each band made the hypothesis 10 times more likely. He also applied Bayes’ rule. The rule in its simplest form reads:

Using this rule, you can interpret the degree of belief using a Bayesian inference and update the possibility of the hypothesis based on the new evidence you gather. The faster Turing could update the possibility, the more lives he was saving. He collected his evidence of probability of a given hypothesis by matching up the letter combinations which all had to be done by hand. They found the most common letter combinations in the German language which allowed them to narrow down the correct setting. Also learning common words and phrases increased their pace. Every 6:00 AM message contained three words “weather”, “hail” and “Hitler” which allowed them to find the matches more quickly.

Nobody had imagined that Alan Turing’s machine would actually work but Turing always believed that “sometimes it is the people no one imagines anything of who do the things that no one imagines.” After two years of hard work Alan Turing finally broke the Enigma.

“When the heart breaks

When the darkness falls

When the world takes

But you’ve given your all

When you just can’t be

The real person you are or want to be

Could you crack the code?

For the beating heart?”

Alan Turing committed suicide on 8 June, 1954. In 1952, homosexuality was still illegal in the UK. Alan Turing was given a choice, either hormonal treatment or would be executed for cross indecency under British law. His hormonal treatment was designed to reduce libido. He accepted the option of treatment via injections of DES or diethylstilbestrol, a synthetic oestrogen. The treatment rendered Turing impotent and caused gynacomastia. After a year of Government mandated hormonal treatment, Turing breathed his last. He was 41 years old. Post mortem report said that he died of cyanide poisoning. An apple lay half bitten beside his bed.

Alan Turing’s machine was the Government held secret for more than 50 years. He was not recognized for his genius achievement for more than 5 decades. “We can only see a short distance ahead, but we can see a lot that needs to be done.” Historians estimate that breaking Enigma shortened the war by two years saving over 14 million lives. Alan Turing never wore a uniform, never held a gun, never went to the battle field and yet he saved 14 million people who did not have the slightest idea of who Alan Turing was.

It took a bit of time but what goes around always comes back around. Today, he is recognized as one of the greatest geniuses that the world has ever seen. Since 1996, The Turing Award has been given annually by The Association for Computing Machinery. It is widely considered to be the computing world’s highest honor, equivalent to the Nobel prize.

In 2009, British prime minister, Gordon Brown made an official public apology on the behalf of the British Government for the appalling way Turing was treated. Queen Elizabeth II granted him a posthumous pardon in 2013, honoring his unprecedented achievements. And have you ever wondered why there is half bitten apple in Steve Job’s company?

The following was carved in one of the camp cells,” I believe in the sun even when it is not shining. And I believe in love, even when I am alone. And I believe in God even when he is silent. I believe through any trial, there is always a way.”

Alan Turing was that sun. He was that love. He was that God. None of our words will justify the unfair way he was treated nor bring him back. But he left the world far, far  more better than he had found and in the end, that is what matters. Turing’s work has inspired generations of research into what today scientist call The Universal Turing Machine and we call them computers. His name will be remembered and his achievement will be honored till the end of time.

 Medical terms:

  • Diethylstilbestrol: a synthetic chemical that reduces hormones for sexual desires
  • Oestrogen: hormones that regulate the activities of reproductive organs
  • Gynacomastia: disorder of the endocrine system that cause mammary gland to increase in males.

References:

Aastha Thapaliya

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