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“How do you mean?”

“There’s a reason why they leaked this to me. I could tell right away that there was something odd about it. Why did Needham insist on coming to talk to me here in Stockholm, and at 5.00 in the morning?”

“So you think that what he’s doing is sanctioned higher up?”

“I suspected it, but at first I didn’t get what he was doing. I just felt that something was wrong. Then I talked to Salander.”

“And that clarified things?”

“I realized that Needham knew exactly what she’d dug up during her hacker attack, and he had every reason to fear that I would learn all about it. He wanted to limit the damage.”

“Even so, he hardly presented you with a rosy picture.”

“He knew I wouldn’t be satisfied with anything too pretty. I suspect he gave me just enough to keep me happy and let me have my scoop, and to prevent me from digging any deeper.”

“He’s in for a disappointment then.”

“Let’s at least hope so. But I can’t see how to break through. The N.S.A. is a closed door.”

“Even for an old bloodhound like Mikael Blomkvist?”

“Even for him.”

Chapter 30

25. xi

The text message had said <Until next time, sister!> Salander could not work out if it had been sent three times in error or if it was an absurd attempt to be over-explicit. It made no difference now anyway.

The message was evidently from Camilla, but it added nothing to what Salander already knew. The events on Ingarö had only deepened the ancient hatred — she was certain Camilla would come after her again, having got so close.

It was not the wording of the texts that had upset Salander so much as the thoughts it had brought to mind, the memory of what she had seen on the steep rock slope in the early morning light when she and August had crouched on the narrow ledge in falling snow, gunfire rattling above them. August had not been wearing a jacket or shoes and was shivering violently as the seconds went by and Salander realized how desperately compromised their situation was. She had a child to take care of and a pathetic pistol for a weapon, while the bastards up there had assault rifles. She had to take them by surprise, otherwise she and August would be slaughtered like lambs. She listened to the men’s footsteps and the direction they were shooting in, even their breathing and the rustle of their clothes.

But the strange thing was, when she finally saw her chance, she hesitated. Crucial moments went by as she broke a small twig into pieces on the rock ledge in front of them. Only then did she spring to her feet right in front of the men and, taking advantage of that brief millisecond of surprise, she fired right away, two, three times. From experience she knew that moments like these burned an indelible impression on your mind, as if not only your body and muscles are sharpened, but also your perception.

Every detail shone with a strange precision and she saw each ripple in the landscape in front of her, as if through a camera zoom. She noted the surprise and fear in the men’s eyes, the wrinkles and irregularities in their faces and clothes, and the weapons which they were waving and firing off at random, narrowly missing their targets.

But her strongest impression did not come from any of that. It came from a silhouette further up the slope which she caught out of the corner of her eye, not menacing in itself, but it made more of an impact on her than the men she had shot. The silhouette was that of her sister. Salander would have recognized her a kilometre away, even though they had not seen each other for years. The air itself was poisoned by her presence and afterwards Salander wondered if she should have shot her too.

Camilla stood there a moment too long. It was careless of her to be out on the rock slope in the first place, but presumably she could not resist the temptation of seeing her sister being executed. Salander recalled how she half squeezed the trigger and felt a holy rage beating in her chest. Yet she hesitated for a split second, and that was enough. Camilla threw herself behind a rock and a scrawny figure appeared on the terrace and started shooting. Salander jumped back onto the ledge and tumbled down the slope with August.

Now, walking away from the boxing club, thinking back to it all, Salander’s body tightened in readiness for a new battle. It struck her that perhaps she should not go home at all, but leave the country for a while. But something else drove her back to her desk; what she had seen in her mind’s eye in the shower, before reading Camilla’s texts, and which was now occupying her thoughts more and more. August’s equation:

N = 3034267
E: y2 = x3 — x - 20; P = (3.2)

From a mathematical point of view, there was nothing unique or extraordinary about it. But what was so remarkable was that August had started with the random number she had given him at Ingarö and taken that further to develop a considerably better elliptic curve than the one she herself had made. When the boy had not wanted to go to sleep, she had left it on the bedside table. She had not got any answer then, nor even the slightest reaction, and she had gone to bed convinced that August understood nothing about mathematical abstractions, that he was only a kind of human calculator of prime-number factorizations.

But, my God... she had been wrong. August had stayed up in the night not just drawing; he had also perfected her own mathematics. She did not even take off her boots or leather jacket, she just stomped into her apartment and opened the encrypted N.S.A. file along with her program for the elliptic curves.

Then she rang Hanna Balder.

Hanna had scarcely slept because she had not brought any of her pills with her. Yet the hotel and its surroundings still cheered her. The breathtaking mountain scenery reminded her of how cramped her own existence had become. Slowly she began to unwind, and even the deep-seated fear in her body was beginning to let go. But that could have been wishful thinking. She also felt slightly at sea in such extravagant surroundings.

There had been a time when she would sail into rooms like these with perfect self-assurance: Look at me, here I come. Now she was timid and trembling and had difficulty eating anything even though the breakfast was lavish. August sat beside her, compulsively writing out his series of numbers, and he was not eating either, but he drank unbelievable volumes of freshly pressed orange juice.

Her new mobile rang, startling her. But it had to be the woman who had sent them here. Nobody else had the number, so far as she knew, and no doubt she just wanted to know if they had arrived safely. So Hanna answered cheerfully and launched into an effusive description of how wonderful everything at the hotel was. She was brusquely interrupted:

“Where are you?”

“We’re having breakfast.”

“In that case stop now and go up to your room. August and I have work to do.”

“Work?”

“I’m going to send over some equations I want him to take a look at. Is that clear?”

“I don’t understand.”

“Just show them to August, and then call me and tell me what he’s written.”

“O.K.,” Hanna said, nonplussed.

She grabbed a couple of croissants and a cinnamon bun and walked with August to the lifts.

It was only at the outset that August helped her. But it was enough. Later she would see her mistakes more clearly and make new improvements to her program. Deep in concentration she worked on for hour after hour, until the sky darkened outside and the snow began to fall again. Then suddenly — in one of those moments she would remember for ever — something strange happened to the file. It fell apart. A shock ran through her. She punched the air.