PopCo (39 page)

‘Which one is Aaron?’ I say.

‘The one with blond hair.’

‘Oh.’ He is in my class for history, I think.

‘Well? Do you like him?’

This is a potential minefield. If I say yes, and she sends the message back to the boys, there is every chance they will just jeer at us and shout out things like ‘No chance’, or just make gross noises meaning ‘You’re ugly/yucky’. This is the kind of thing that happens at school. However, things are different in town.

‘Why?’ I say, in the end.

‘He’s asked you out,’ she says.

Bloody hell. A boy has asked me out. Is this a joke?

‘Don’t take all day,’ one of the other boys shouts from their bench. I glance over and see Aaron punch him on his arm.

‘Tell him yes,’ I say quickly, to Emma.

She nods in the direction of the boys, and three of them cheer, while Aaron blushes. I avoid catching his eye. It’s almost time for me to go and get my bus. It is arranged, via Emma and Michael, that my new boyfriend will walk me there. All the way to the bus stop, and with the others walking behind saying things like ‘Oooh’, and ‘Kissy kissy’, I ask Aaron things about whether he likes school, and other things that pop into my head. I have this idea that if you are going out with someone, you should get to know them. Aaron doesn’t say very much but, when we reach the bus stop, he checks to see that his friends aren’t looking and then kisses me on the cheek. He blushes, says, ‘See you at school’, and then runs away.

As soon as the bus has pulled off, and my friends are no longer in sight, my stomach clenches like something in a vice in woodwork. I am the only person on the top deck and it is too quiet up here. I close my eyes and see a mess of images: animals in cages, rows of cosmetics, children jeering, beef burgers. I see Aaron’s face leaning in to kiss mine. He wanted to kiss my lips but I turned away. I have a bag of contraband school uniform, that I stole dinner money to get, and a lip-gloss in my pocket that I stole from a shop. I am a liar and a thief.

Walking home from the village bus stop, I look at Rachel’s house
and wish she was home. I will write her a letter tonight, I think. What have I become? Still, I am in too deep to go back now. I will not show my grandparents that I am upset. I will conceal the lip-gloss and new school clothes from them. I will only cry on my own, when no one is looking. I think of Aaron’s kiss, and I wish it had been Alex. I wish I went to chess club.

There is a car in the driveway that I haven’t seen before. Is it the police? With my heart beating wildly, I walk around to the back of the house and let myself in. I feel sick crossing the threshold to my own home, as if the Alice that should live here is dead because I killed her. That makes me an impostor. I don’t want to be found out. I want to hide for a million years.

‘Ah, the wanderer returns,’ says my grandfather when I walk through the back door. He sounds happy, so maybe the visitor isn’t the police. She doesn’t look like the police, actually. She is sitting in the kitchen with my grandfather, drinking a glass of wine.

‘Hello,’ she says to me. ‘You must be Alice.’

She is about my grandparents’ age but more glamorous. She is wearing a black kaftan and a crimson silk scarf. Her lips are the same shade of red as her scarf and glisten like a cut beetroot.

‘Hello,’ I say shyly. Then I remember that I am an impostor and cannot say too much in case I am discovered. In fact – I must look like an impostor in Emma’s clothes. Just as I have this thought, my grandfather glances at me again and does a double-take.

‘Is it the wine or is there something different about you?’ he asks me.

‘I borrowed Emma’s clothes,’ I mumble as I walk through the kitchen and go upstairs to my room. From up here I can hear the sounds of laughter downstairs. I place the carrier bag (which hasn’t been noted, thank God) on my bed and take out my lip-gloss. I apply some of it to my lips but it feels wrong so I wipe it off with the back of my hand. I slip it in my school pencil case instead and think about doing some homework. I half-heartedly take out a couple of books and my folders but my life feels like an open wound at the moment and I can’t focus on homework. Instead, for the next hour or so I lie on my bed with the radio on, trying to convince myself that I like Aaron. Then there is a knock at my bedroom door. It’s the police! No, in fact it is my grandmother.

‘I think dinner is almost ready,’ she says to me. ‘Did you have a nice time with your friend?’ I climb into my grandmother’s head and imagine her ideas about the kinds of things two friends would do on a Saturday. I see two girls playing Ludo, helping with each other’s homework, talking about life, families, dreams and ambitions. My grandmother would never understand what I have done today.

‘Yes, thanks,’ I say.

‘Jasmine is here for dinner. Did you meet her? She’s an old friend of ours. Very interesting woman.’

‘Yes,’ I say. ‘I did meet her.’

‘Alice?’ says my grandmother. ‘Are you all right?’

I immediately bristle. ‘Yeah, of course. Why?’

‘No reason. Well, see you downstairs in a minute, then.’

‘OK.’

Jasmine reminds me of a very grown-up version of Roxy. She has been travelling, it transpires, which is why my grandparents haven’t seen her for so long. She has been to India, Africa and even China! No one knows anything much about what goes on in China so for ages she tells my grandparents things she has seen there. After we have finished our main course, she lights a long, black cigarette and leans back in her chair like she has no problems in the world. Why can’t I feel like this? Then my grandfather serves his famous homemade Black Forest gateau, and something about this scene is so comfortable and homely that I want to cry. I want to cry and tell them all that I never want to go to school again.

‘So how’s the world of cryptography, Peter?’ Jasmine asks.

‘You mean cryptanalysis, of course.’ He laughs.

She laughs too. ‘I was never too great with all that terminology. Code-breaking, then, that’s an easier term. How’s it going?’

‘It’s going well. I – well, Alice and I – are working on a fascinating project at the moment. I’ll show you after dinner. It’s called the Voynich Manuscript …’ His voice fades out slightly. In my head, every synapse I have is singing, ‘Alice and I, Alice and I …’ My grandfather has described it as our project! I am so proud, I want to burst. When my grandfather’s voice fades up again, he is about to talk about something else.

‘Since you asked about cryptography, though,’ he is saying to
Jasmine, with laughter still dancing in his eyes, ‘I feel compelled to tell you the latest developments.’

‘So this is what …? Code making rather than breaking?’ She smiles. ‘
Graphy
from
Graphein. To write
.’

‘That’s right. Have you heard about Public Key Cryptography or RSA?’

Jasmine laughs again. ‘Peter, have I ever heard about something scientific before you or Beth have told me? Come on, just tell me. It sounds bloody complicated.’

My grandfather starts by way of a kind of introduction, explaining problems in cryptography, telling her that, historically, even supposedly unbreakable ciphers have always eventually succumbed to cryptanalysis. He talks about Charles Babbage breaking the Vigenère Cipher a hundred years ago and the operatives at Bletchley Park breaking Enigma. This leads the three of them to make various comments about the war, and my grandmother says something about Turing and BP while we finish our cake.

‘So,’ my grandfather says, getting up to put coffee on the stove. ‘The challenge has been for the cryptographers to come up with something truly unbreakable. Since Enigma tumbled, the ball has been truly in their court. Now, Alice, tell Jasmine what the biggest problem with cryptography is.’

Me? I gulp. What is the biggest problem of cryptography? I force my mind into reverse and try to remember all the conversations we have had on this subject.

‘The distribution of the key?’ I say uncertainly.

‘See, I told you she’s a genius,’ my grandfather says. ‘Exactly. The distribution of the key. Most ciphers are enciphered and deciphered using the same key, often a jumble of letters or numbers or a word. I could decide to communicate with you using the Vigenère Cipher, or even a mono-alphabetic cipher. We would both know that the key was, say, the word “lapsang”. No problem. I use the key word to encipher the message, and you use the same word to decipher it.’

‘How do you encipher a message using the word “lapsang”?’ Jasmine says.

My grandmother smiles. ‘Don’t ask him that. We’ll be here all night.’

We all laugh. This is true.

Still, to help this make sense for Jasmine, he quickly explains
how you could start a ciphertext alphabet with the word ‘lapsang’ (but without the second ‘a’, of course) and then follow it with all the other letters of the alphabet backwards. He writes it on a scrap of paper like this:

If both sender and receiver knew that the key word was
lapsang
, any message sent would be easy to unscramble (he doesn’t explain that any message sent using this cipher would unscramble easily anyway due to frequency analysis, though).

‘Now, say our key had fallen into enemy hands,’ he says. ‘We would need to change it. But how do I, the sender, get the new key to you, the receiver? What if, to avoid compromising the key, we decided to change it every day? We would still have to exchange it. I could phone you and say, “The key word is now ‘Darjeeling’”, but our telephone may well be bugged. In fact, if we knew our telephone not to be bugged, we could exchange secret information over the phone without any need for a cipher at all.’

‘I see,’ says Jasmine. ‘So in order to send a secret message using a key, you first have to send an un-secret message telling the other person what key you are using.’

‘Quite,’ says my grandfather. ‘And that is the weak point – the point at which the enemy can intercept the information.’

‘What if, every day, you sent a message and then, in the same code, sent the new key word for the following day?’

My grandfather brings the coffee pot to the table and fetches the best cups from the dresser. ‘People have used methods like that,’ he explains. ‘But you can see that in that situation, if one message was deciphered by the enemy they would be in the loop for all time. They would only have to crack one message to be able to crack all the others for ever.’

‘Ah,’ says Jasmine. ‘So, how do you do it, then? I know you want to tell me …’

‘Well, there are a couple of ways. The first way, known as the Diffie–Hellman–Merkle key-exchange system – named after the people who invented it – is based on one-way functions and modular arithmetic, which Beth knows more about than me.’

My grandmother smiles. ‘Believe me, Jasmine, you don’t want to know. It’s basically a complex mathematical trick where two people think of a number, run it through a function – much more complicated than “think of a number, double it and add five” but similar – and then swap the results. The exciting thing about this method is that even if the two results are overheard, the enemy can’t crack the code, because you need to know one of the original numbers to break the code – not the results. It’s very complicated to explain but it is a very clever trick indeed. It didn’t catch on because it turned out to be impractical. The sender has to communicate with the receiver beforehand every time they want to send an encrypted message. But mathematically, at least, this system is very exciting. Imagine being able to swap a key in public, rather than in secret, knowing that even if the enemy hears what you say, it doesn’t matter. It’s brilliant.’

My grandfather sips his coffee. ‘What people really needed was an asymmetric key, rather than a symmetric one. In other words, a system where the thing you use to lock a message is different from the thing you use to unlock it. If you had a system like this, you could send the
lock
to someone who wanted to communicate with you, not the
key
. The best analogy is an actual padlock. Say I had a secret box to send to you. I could buy a padlock and key, then lock the box with the padlock and try to work out how to get the key to you without it being intercepted. Or, alternatively, I could tell you I had a secret box to send to you, at which point, you could purchase a padlock and key and just send me the padlock. It wouldn’t matter who intercepted the padlock – they wouldn’t be able to do anything with it. When I receive the padlock, I just snap it on the package and send it to you. Once it’s locked, even I can’t open it, because only you have the key.’

‘That’s so clever,’ Jasmine says. ‘I like that.’

‘Couldn’t someone pick the lock?’ I say. ‘If you intercept the padlock, you could then make the key, surely?’

‘Well, this is the clever bit. The padlock and key is simply an analogy for – sorry – more maths. In fact, people came up with the concept of an asymmetric cipher several years before they worked out how to do it, mathematically. For a while, no one could think of a function that would have this effect. But, then, three chaps at MIT did it. What if I told you, Alice, that the key in this story was actually two very large prime numbers. What is the lock?’

I think for a moment. ‘I don’t know,’ I say.

‘Well, what do you get if you multiply two large prime numbers together?’ he says.

‘A very large composite number,’ I say. ‘With two very large prime factors … Oh! I see.’

Of course. If you choose two large enough primes, keep them a secret and multiply them together, someone who wanted to prime factorise the big number would have to start from 2, 3, 5, 7, like anybody else doing a prime factorisation. They wouldn’t know where the prime factors would be found, and I know as well as anyone that prime factorisation has to be approached methodically. My grandmother proved to me once that with a big enough value of
N
(with
N
being the composite number that is a product of two large primes,
p
and
q
) it could take thousands of years to find the answer, even if you could try one prime a second. Of course this is a great method of encryption. You send the large composite number to the person who wants to send you a message, they use it to encrypt this message in such a way that you need the prime factors to decrypt the message and then, bingo! Only you can read it. You could tell everybody in the world what
N
is but only you would know
p
and
q
.