‘Why? First, it actually isn’t a lot of trouble; this is such a simple machine that our carpentry workshop could make a rough approximation of it. Secondly, it is a very valuable tool, given that it would be a good few years before you would need to repeat the cipher key. That makes it very difficult indeed. If they had created a one-time pad specially for this occasion it would have to be so big that it would cover the wall over there. We can now be absolutely sure that they are not using a one-time pad because it is too impractical and would cause so many residual problems – it really could not be used successfully for real-life communications. If they are not using a one-time pad but have incorporated the cipher key into the message, there would be massive limitations. It doesn’t matter how you do it – the first two groups of numbers, the first three groups, the last two groups, the last three groups, a middle group, a middle three groups – you can’t possibly create such a big cipher key. Thirdly, Sivincy would be interested in creating a machine that generates cipher keys. You may have realized already that the reason I thought she might have done this is that Sivincy started working on this branch of mathematics at a very early stage in her career. Fourthly, I realized from her books, and indeed from her actions, that Sivincy isn’t a very profound person. She is not a black hole: in her eccentricities, cunning, changeability and slipperiness she is more like a chameleon, and that makes her very good at misleading people. Since she herself lacks depth, the ciphers that she creates can’t be that difficult or complex. Given the limitations on the level of difficulty intrinsic in her cipher, she would want to make up for that by adding to the complexity of the adjuncts, like the key to the cipher.’

‘What do you think, Deputy Director An?’ asked Comrade Chen. ‘Do you really think it is possible that they are using a machine to generate their cipher keys?’

I didn’t answer him straight away, but turned to Huang Yiyi. ‘I am currently working on the supposition that your theory is correct and that the enemy really is using a machine to create their cipher keys, so the next step is that we need to create a copy. Making a copy relies on deductions; it is easy for them to make the original, but it is going to be difficult for us because we can’t afford to make any mistakes – a centimetre’s error could create massive problems for us. Of course I understand that what we actually need to copy is the mathematical formula, so do you have the data to work it out?’

She handed me a folder. ‘The formulae and figures for the exercise are all here.’