Page 14 of The Dark of the Moon
Finn
I asked Philly what the difference was between a code and a cipher.
‘A code replaces words with other words. A cipher replaces each letter of a word to make it unintelligible.’
So when Mum and Dad were talking about me changing schools, but instead of saying the word ‘school’ they said ‘shirt’, they were using a code. It wasn’t a very good one, though. I broke it straight away. They should have used a cipher. I hated my old school, it was too bright and too loud, and it smelled of chips and a brand of floor polish that made me feel sick, but the new one I went to next was even worse. It was bad enough in the classroom, which was full of all sorts of smells, but when it was lunchtime we had to go to the dining hall, which was incredibly noisy and smelled even worse. I managed to queue up and get a plate of macaroni cheese. I said to the dinner lady, ‘No carrots, thank you.’
‘You have to have a few. They’ll make your hair curl,’ she said.
I didn’t want my hair to curl. It’s hard enough to brush it already and the tugs hurt so much they make me want to yell.
‘Here you go,’ she said, dumping a spoonful on to the plate. ‘See, I’ve only given you five, my dear.’ Those 5 pieces of carrot were probably what tipped me over the edge. I felt the sick coming up into my mouth, but I swallowed it back down because I knew I was supposed to try and Fit In.
I carried my tray to one of the tables where there was nobody sitting but then some other kids came and sat down on both sides of me and that made me feel even more panicky. I picked up my fork and ate one piece of macaroni. And then I threw up all over my plate and the plate of the girl next to me and a bit went on her hand too which made her scream and then I screamed even louder.
Once things had calmed down a bit, the teacher told me to go to the toilets and clean myself up. I went into the girls’ toilet by mistake. After that – which was only my first day at that school – I got bullied a lot for being weird and a Mentalist, which is what the other kids called me. They called me a lot of other things too, but Mum and Dad said we don’t say those words. We don’t, but those kids did.
In the end, I stopped talking completely in case I said something else that made everyone laugh at me and call me those names. That’s why I’m home-schooled now, and Dad is my teacher. He says it’s not as if he has anything better to do. I think that might be sarcasm, but I don’t know because it’s hard to tell when people are being sarcastic. People should just say what they mean. There’s a special school I can go to in a couple of years’ time. I don’t know if that will be better, but at least I’ll be with other Mentalists and so they won’t be able to pick on me for being weird.
Thinking about school made me feel a bit anxious so I thought I would do some maths to calm my brain down. I decided to go through the workings for the number of possible combinations for the Enigma cipher machine.
First you have to work out the number of rotor configurations:
The most basic model had slots for 3 rotors, with a choice of 5 available.
So the first slot would have a choice of 5 rotors, the second slot a choice of 4 and the third slot a choice of 3. So that means there are 5 x 4 x 3 = 60 ways to configure the 5 rotors.
Next you have to work out the number of possible starting settings:
Each rotor has 26 letters of the alphabet on it. So with 3 rotors and 26 possible starting positions for each rotor there are 26 x 26 x 26 = 17,576 choices for the starting settings.
The Germans added a plugboard to scramble up the letters even more. So next you have to work out the number of possible combinations yielded by the plugboard:
Since there are 26 letters of the alphabet, there are (26 x 25 x 24 ... all the way down to 1) ways to arrange the letters. That’s called 26 Factorial, which is written as 26! The plugboard could only make 10 pairs of letters, so it meant they could only scramble 10 + 10 = 20 letters of the alphabet, with 6! left over that must be divided out.
Furthermore, there are 10 pairs of letters, and it does not matter what order the pairs are in, so also divide by 10! Since the order of the letters in the pair does not matter, also divide by 210.
So now we can work out the number of combinations yielded by the plugboard:
26! / (6!×10!×210) = 150,738,274,937,250
Finally, we need to put together the three components – the rotor configurations, the starting settings and the plugboard combinations:
Hence the number of ways to set up a military-grade German Enigma machine is 60 x 17,576 x 150,738,274,937,250 = 158,962,555,217,826,360,000
That’s 1.5896255521782636 x 1020.
No wonder they needed Philly’s crib sheets.
I laminated my workings and showed them to her, and she nodded. Then she told me the Germans had increased the number of possible rotor combinations on their Enigma machines even more and at that point the British had to invent another evenbigger machine to try to decode the ciphers. It was called Colossus and it was the world’s first supercomputer, even if there’s more computing power in her old iPad nowadays. It was Top Secret so no one knew about it either, until recently. The Americans claimed they’d made the first one in the 1960s. But it was really Colossus and the British who got there first. It was destroyed after the war, to keep the secret.
Philly told me some other cool things about Bletchley Park and the Enigma code. One was that the code had a major flaw, which the cryptologists in her hut discovered. This was that a letter could never be encoded as itself, which gave the codebreakers a piece of information they could use to help decrypt the messages by a process of elimination. It was a Major Breakthrough.
She also told me the food was really terrible at Bletchley Park. Marmite sandwiches would have been welcome. Because she had to sign the Official Secrets Act, she can only talk about these things now.
They’re showing a film calledThe Imitation Gameat an open-air cinema in Sainte-Marie. We’re going to go tomorrow night. Usually, I don’t like going out to watch movies because there are too many people talking and I don’t like sitting next to Strangers whose elbows take up too much of the armrest and who eat noisy things like crisps, and sweets with rustly wrappings. But I want to go and seeThe Imitation Gamewith Philly because it’s about the work she did at Bletchley Park. I can sit in between her and Mum.
Philly
