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“That, at least, is what she pretended. But obviously she had her own agenda. I know that Kajsa was impressed by the way she built alliances with people and got herself political protection. She probably would have been loyal to Camilla for ever if she hadn’t become scared.”

“What was she scared of?”

“Kajsa got to know a former elite soldier — a major, I believe — and just lost her bearings. According to confidential information that Camilla had access to via her lover, the man had carried out a few shady operations for the Russian government. Among other things he had killed a well-known journalist, I presume you’ve heard of her, Irina Azarova. She’d taken a line against the government in various reports and books.”

“Oh yes, truly a heroine. A horrible story.”

“Absolutely. Something went wrong in the planning. Azarova was supposed to meet a critic of the regime in an apartment on a backstreet in a suburb south-east of Moscow, and according to the plan the major was supposed to shoot her as she came out. But no-one knew that the journalist’s sister had developed pneumonia, and Irina had to look after two nieces aged eight and ten. As she and the girls walked out of the front entrance the major shot all three of them in the face. After that he fell into disgrace — not that anybody was particularly bothered about the children, but public opinion was getting out of hand and there was a risk that the whole operation would be uncovered and turned against the government. I think the major was afraid he’d be made a scapegoat. He was also dealing with a load of personal problems at the same time. His wife took off, he was left alone with a teenage daughter and I believe there was even a possibility of his being evicted from his apartment. From Camilla’s perspective that was a perfect set-up: a ruthless person whom she could use, and who found himself in a vulnerable situation.”

“So she got him on board.”

“Yes, they met. Kajsa was there too, and the strange thing was that she immediately took a liking to this man. He wasn’t at all what she’d been expecting, nothing like the people she knew at Svavelsjö M.C., who were also killers. The man was very fit, very strong, and had a brutal look about him, but he was also cultivated and polite, she said, somehow vulnerable and sensitive. Kajsa could tell that he felt really terrible about shooting those children. He was a murderer, a man whose speciality had been torture during the war in Chechnya, but he still had his moral boundaries, she said, and that’s why she was so upset when Camilla got her claws into him — almost literally. She dragged her nails across his chest and hissed like a cat, ‘I want you to kill for me.’ Her words were charged with sexual tension, and with the skill of the devil she awakened the man’s sadism. The more gruesome his descriptions of his murders, the more excited she became. I’m not sure I understood it all, but it scared Kajsa to death. Not the murderer himself, but Camilla. Her beauty and allure managed to bring out the predator in him.”

“You never reported this to the police?”

“I asked Kajsa over and over. I told her she needed protection. She said she already had it and she forbade me to talk to the police. I was stupid enough to listen to her. After her death I told the investigators what I’d heard, but I doubt they believed me — presumably not. It was nothing but hearsay about a man without a name in another country. Camilla was nowhere to be found in any records, and I never discovered anything about her new identity. And certainly poor Kajsa’s murder is still unsolved.”

“I do understand how painful this must still be,” Blomkvist said.

“You do?”

“I think so,” he said, and was about to rest a sympathetic hand on her arm.

He was brought up short by his mobile buzzing in his pocket. He hoped it was Zander. But it was Stefan Molde. It took Blomkvist a few seconds to identify him as the person at the N.D.R.E. who had been in touch with Linus Brandell.

“What’s this about?” he said.

“A meeting with a senior civil servant who’s on his way to Sweden. He wants to see you as early as possible tomorrow morning at the Grand Hôtel.”

Blomkvist made an apologetic gesture in Fru Dahlgren’s direction.

“I have a tight schedule,” he said, “So if I’m to meet anybody, at the very least I want a name and an explanation.”

“The man’s name is Edwin Needham, and it’s about someone using the handle Wasp, who is suspected of serious crimes.”

Blomkvist felt a wave of panic. “O.K.,” he said. “What time?”

“Five o’clock tomorrow morning would work.”

“You’ve got to be joking!”

“Regrettably there’s nothing to joke about in all this. I suggest that you’re punctual. Mr Needham will see you in his room. You’ll have to leave your mobile at reception, and you’ll be searched.”

Blomkvist got to his feet and took his leave of Margareta Dahlgren.

Part III

Asymmetric problems

24. xi — 3.xii

Sometimes it is easier to put together than to put asunder.

Nowadays computers can easily multiply prime numbers with millions of digits. Yet it is extremely complicated to reverse the process. Numbers with only a few hundred digits present huge problems.

Encryption algorithms like R.S.A. take advantage of the difficulties involved in prime-number factorization. Prime numbers have become secrecy’s best friends.

Chapter 25

24. xi, Early Morning

It had not taken long for Salander to identify the Roger whom August had been drawing. She had seen a younger version of the man on a website showing former actors from Revolutionsteatern in Vasastan. He was called Roger Winter. He had had a couple of major film roles at the beginning of his career, but lately had fetched up in a backwater, and was now less well known than his wheelchair-bound brother Tobias, an outspoken professor of biology who was said these days to have distanced himself altogether from Roger.

Salander wrote down Roger Winter’s address and then hacked into the supercomputer N.S.F. M.R.I. She also opened the program with which she was trying to construct a dynamic system for finding the elliptic curves which were most likely to do the job, and with as few iterations as possible. But whatever she tried, she was unable to get any closer to a solution. The N.S.A. file remained impenetrable. In the end she went and looked in on August. She swore. The boy was awake, sitting up in bed writing something on a piece of paper, and as she came closer she could see that he was doing more prime-number factorizations.

“It’s no good. It’s not getting us anywhere,” she muttered, and when August began to rock to and fro hysterically once again she told him to pull himself together and go back to sleep.

It was late and she decided that she too should rest for a while. She took the bed next to his, but it was impossible to sleep. August tossed and turned and whimpered, and in the end Salander decided to say something, to try to settle him. The best she could think of was, “Do you know about elliptic curves?”

Of course she got no answer. That did not deter her from giving as simple and clear an explanation as she could.

“Do you get it?” she said.

August did not reply.

“O.K., then,” she went on. “Take the number 3,034,267, for example. I know you can easily find its prime-number factors. But it can also be done using elliptic curves. Let’s for example take curve y = x3 — x + 4 and point P = (1.2) on that curve.”

She wrote the equation on a piece of paper on the bedside table. But August did not seem to be following at all. She thought about those autistic twins she had read up on. They had some mysterious way of identifying large prime numbers, yet could not solve the simplest equations. Perhaps August was like that too. Perhaps he was more of a calculating machine than a genuine mathematical talent, and in any case it didn’t matter right now. Her bullet wound was aching again and she needed some sleep. She needed to drive out all her old childhood demons which had come to life again because of the boy.