In the Dark, page 18
I found this out by chance when the support for my washbasin broke and the whole thing would no longer stand up properly. I went to the carpentry shed to ask for a nail, and came across the master carpenter, Comrade Zhang, who was cutting holes in a piece of wood. Beside him there was a hand-drawn plan for something that looked a bit like an adding machine, with measurements. I thought that it looked like Huang Yiyi’s handwriting, and felt curious, so I asked the carpenter and he said that Comrade Huang had asked him to make it, but he had no idea what it was for. On my way out, I noticed a pile of things in the corner, some round, some conical, some cylindrical and some spherical, and asked the carpenter what they were for. He said he had made them for Comrade Huang some time ago, but now she didn’t need them any more and had brought them back to be broken up. My interest was even more piqued – what on earth could Huang Yiyi want such bizarre objects for? All the racket from her room, was it because she was playing with them? I couldn’t see that these toys could bear any relation to the decryption of RECOVERY. Later on when Huang Yiyi explained her idea, I was very impressed. You just had to be impressed: an ordinary person is an ordinary person and a genius is a genius – if you meet one you know about it.
That day when I left the woodworkers’ shed, I found Huang Yiyi in the nearby forest. I was expecting her to be there feeding the squirrels, but instead she was standing underneath one of the trees discussing something with the madman who spent his time running around the forest. The madman raised his head to look at the treetops, or perhaps it was the sky; maybe he was talking to her, but then on the other hand maybe he wasn’t – he could easily have been talking to himself, lost in a world of his own. He was the man Huang Yiyi had asked about the first time she went to Chen’s office, the lunatic. His name was Jiang Nan, a cryptographer who had joined us at the same time as Chen, and who was eventually driven mad by decrypting PORPHORY. He knew too many secrets to be allowed to leave Unit 701 even though he was mad. We couldn’t even let him see his family, so we let him roam through the mountains, spending his days running through the forest. He had the silent trees, he had the flowers and squirrels, he had this whole beautiful, illogical world for company. If he saw a stranger he would stop them and say, ‘I cracked PORPHORY, the most difficult of all the KMT ciphers. No one else could crack it, only me …’
The people he stopped were always very polite to him, and would say kindly, ‘Yes, of course you cracked it: you really are amazing.’
Then he would be really happy, and spreading his arms wide like the wings of a bird, he would run along the road shouting, ‘I cracked PORPHORY, I really am amazing, I really am amazing …’ Everyone who saw him felt deeply sorry for him.
That day, I didn’t say much to Jiang Nan, but I lit his cigarette for him and sent him on his way as politely as I could. Then I asked Huang Yiyi what she had been talking to him about, and she said she had asked him how he’d found the key to PORPHORY.
I said jokingly that she should have asked me – well, it wasn’t entirely a joke; I could have told her.
She answered the question I hadn’t asked. ‘I saw you leave the carpenters’ shed – you’ve been checking up on me.’
I tried to sound convincing when I denied it, and told her that it was purely by chance that I had discovered she was making some mystery machine, and I hoped she would tell me what it was for. She then explained her domino theory. It seemed very strange to me, and I wanted to ask her more about it. She said, ‘That’s enough – I’ve already given up on it, but I do have a new idea. Last night I had a dream. In the dream I was holding a fistful of hornets, and the hornets stung my hand and then flew away, leaving all these holes. My hand looked like a sieve full of holes, and Arabic numerals came tumbling through them …’
There are many people in this world who don’t believe in dreams, but for a cryptographer, dreams are a secret passage that those who fight using only their intellects use to reach the opposite bank victoriously. In the history of cryptography, there is no lack of examples of people who succeeded thanks to some sudden illumination in their dreams. Huang Yiyi told me excitedly that her dream had reminded her that the key to unlocking RECOVERY, that is the key to the cipher, might well be an original and modern cryptographic bombe! To use her imagery, it would be a sieve that created a domino effect. The sieve was separated into nine layers, and each layer would have 365 holes, so that in total the sieve would have 9 × 9 × 365 = 29,565 holes, and each day’s radio messages would correspond to one hole. That would mean the messages could only be decrypted through one hole, but if you found that hole, the entire day’s output could be read. If we compared the numbers in the radio intercepts to grains of rice, and used a sieve to sieve and re-sieve them, in principle once one grain of rice had come through the system and fallen through the final hole at the other end, then we had cracked it, and all the other grains of rice (the remaining radio intercepts picked up on the same day) would all roll through as well. That is the domino effect – the difference being that traditionally with dominoes the first action that sets everything in motion is human, whereas what she had in mind was a sieve-initiated effect. To put it another way, the dominoes weren’t set up to form a line but a circle, a single plane, but once you cut it and lined up the first set of numbers against the first set of holes, once one had found the right path, then the rest would follow suit in order. In very much the same way that if you have a bucket of water and pierce a hole in the bottom, the water will form a stream.
I was very excited and urged her to continue. Huang Yiyi said crossly, ‘I hadn’t realized you were so impatient. If you were equally excitable in emotional matters that would be wonderful.’ Since that was her attitude, it was obvious that she hadn’t given up hope in spite of all my efforts. She then made a request, saying that she would only continue talking if I sat down next to her. Really! But as it happened we had already walked into the wood and there was nobody else around, and I was tired, so there was no reason why I shouldn’t sit with her. I guessed that if I sat down that would be followed by a whole series of other requests, so I made my own demand: that after I sat down she would have to do what I said. She agreed to that, and then we both sat down and she carried on her explanation. She said that the current trend in cryptography was to make the key to the cipher highly complex, but that this process was limited by the constraints of wireless technology, particularly in cases where the communication had to be sent vast distances or to numerous places, so mostly the key was hidden in the message.
‘For example ULTRA, which was a high-level cipher – do you know what its key was?’
‘The first three sets of numbers on even-number days, the last three sets on odd-number days.’
‘Right. And it was concealed in the message text. Why did they want to make it part of the message?’
‘Because they were using a lot of different wirelesses and it was during wartime, so the sets were moving around a lot and there was a high turnover in personnel. If they hadn’t done it that way – if, for example, they had used a key from a one-time pad, if the person with the pad got killed, communications would be crippled.’
‘That’s the point. RECOVERY is the cipher that Sivincy designed for the American military, and since the end of the Second World War the US army has been involved in many theatres, with bases all over the world. With their bases so spread out, and their communications networks so numerous, we can be sure that it is impossible for RECOVERY to have its own one-time pad.’
‘Mmm. A one-time pad also wouldn’t suit the uses that the KMT are putting it to now, letting their special agents use it.’
‘Right. The KMT are using RECOVERY as the cipher through which Taiwan communicates with their special agents on the Mainland, and so we can be sure that the key is part of the message. The special agents have to split up – they need to be able to work in the widest field possible – so if the key isn’t part of the message, the whole system could easily break down.’
‘Mmm.’
‘So I believe that the key to RECOVERY must be hidden in the message. But where is it hidden? If it were just like ULTRA, and on even-number days it was this set of numbers and on odd-number days it was that set, neither Sivincy herself nor the American army that was employing her would have been happy with it. Within the limitations imposed by her cipher, she would certainly want to work out an unusual and clever new key. After I considered that for a bit, I remembered that Sivincy at an earlier stage in her career discovered a mathematical principle which is called the Shadow Principle or the Light Principle, popularly known as Honeycomb Theory. The substance of this theory is that if you take any given honeycomb structure, with the help of a moving light source, you can distinguish black and white, shadow and light. Right now I don’t have the equipment, so I can’t demonstrate it for you.’
‘I can imagine it. For example, if the roof was in fact made of some honeycombed substance, we’d see pinpricks of light.’
‘Exactly. And what’s the point of all this? It means that if you make sure you are forever moving at the same speed as the light, you can always keep yourself hidden in the shadows. This has significant implications for astrophysics.’
I felt she was wandering away from the point. ‘Let’s get back to our key.’
‘Right now I’m making my cryptographic bombe. When it’s finished we’ll give it a run-through, and then you’ll understand.’
I opened my eyes wide. ‘So all that banging about in your room, and those things like bottles and bowling balls was all preparation for a cryptographic bombe?’
‘Yes. What did you think I was doing?’
I was embarrassed. ‘Chen thought you were playing some stupid game.’
She sniffed. ‘You people really do look at everyone else in such a negative way!’
I quickly apologized for misunderstanding her, but I wasn’t expecting her to giggle and say charmingly that as long as I understood that she loved me, she didn’t care about anything else. As she spoke, she reached for my hand. Fortunately I had already made my request that she should obey me, otherwise she would have caused even more trouble on this occasion.
That day, after Huang Yiyi had left, I stayed in the forest alone and walked round and round one of the trees like the madman, Jiang Nan. I looked up at the treetops, and at the sky above the treetops, and thought about the holes that the carpenter was cutting in that piece of wood, and I seemed to see light streaming from each hexagonal hole, followed by every secret encrypted in RECOVERY. At that moment I understood why Jiang Nan spent every day walking round the trees talking to himself, and yet was clearly so happy; it was because he had experienced the strange pleasure of having cracked PORPHORY. That day, I really identified with the strange pleasures of a madman.
17
About a week later, Huang Yiyi’s cryptographic bombe was delivered from the carpenters’ workshop, and I called all the members of our special working group into the conference room in order to listen to her explanation.
The cryptographic bombe wasn’t actually particularly complicated. Both in shape and in the way it worked it was somewhat like those machines you see on street corners for measuring your height, where the scale rod moves independently. The difference was that the scale rod on the bombe was a wooden honeycombed board, about thirty centimetres high and as thick as a piece of card. At the bottom there was a square tray, and on all four sides there were troughs, in which you could place the radio intercepts.
Huang Yiyi demonstrated how it worked as she talked. ‘This is the cryptographic bombe I’ve designed. As you can see, we have an upper plate in which there are many round holes in a honeycomb pattern, and on this gauge there are thirty-one notches to represent the thirty-one days of the month. The upper plate is mounted on rollers, so that it can move up and down of its own accord; again, it can be raised or lowered by thirty-one notches. At the top of the gauge there is a light source, and right here, in the hollow underneath, is where we put the radio intercepts. We can clip them in like this. This tray can also be moved sideways along its thirty-one notches, and again one notch represents one day. Now we must imagine that in addition to the upper plate moving up and down and the tray moving from side to side, our light source is also in constant motion. If the group of numbers illuminated by our light is the cipher key that allows us to read that day’s messages, then we can calculate how big the key must be: there are three hundred and sixty-five possibilities, which means that it is one whole year before the cipher key has to be repeated. Now if we want to make it more difficult for our light source to reveal the key, for example by adding another plate, then that gives us twice as many possible combinations; and extrapolating from that, the more plates you add, the more years it is before you have to repeat your cipher key. Now my first demonstration model has nine levels of plates …’
Chen got up and cut her short. ‘Comrade Huang, let me say this: if this bombe helps us crack the cipher then that is wonderful, but to my knowledge no cryptographic unit anywhere in the world uses a machine to generate cipher keys. Have any of you ever heard of such a thing?’
‘Have you ever heard of anyone daring to steal the portrait of Chairman Mao off the gate at Tiananmen?’ asked Huang Yiyi.
I laughed. ‘Only Sivincy.’
‘Exactly. Just as I told Deputy Director An, I am now more and more convinced that Sivincy’s plagiarism of the Enigma machine isn’t a straightforward rip-off; it is because she is so intelligent and so cunning that she is always up to nasty tricks – she enjoys breaking the rules.’
Comrade Chen said, ‘But have you considered, Comrade Huang, that the key to the cipher isn’t actually part of the cipher itself, it is an adjunct. Not having it will stop the novice but not the expert, so why would Sivincy go to so much trouble to hide it?’
‘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.’
I took the folder and saw that it contained a thick stack of papers, each page covered in formulae and the data for the calculations. The formulae were all very complex and there was a mass of figures to work through – so densely packed that as I read through them my eyes widened. I said, ‘Oh hell, this is going to be a huge exercise.’
‘Of course it is big,’ she said. ‘Each stage in the separation process is a living thing: when the top plate moves, the others all change; when the left figure moves, so does the one on the right. If you have to work through a whole stack of calculations even to get to the starting point, there is a limit to how small the exercise can possibly be.’
I handed the folder over to the manager of the Calculations Office, Comrade Jiang. ‘You have a look and estimate roughly how long this is going to take you to do.’
Comrade Jiang looked at it and said, ‘If we split our people into three teams and work round the clock, it will take us about a month.’
Huang Yiyi gave a sharp exclamation. ‘That long!’
‘We don’t have the facilities or the people to do it in less.’
‘If only we had computers.’
‘What happens if you’re wrong?’ asked Comrade Chen. ‘That is one hell of a waste of time!’
