"When one letter is substituted for another?" Archie guessed. "So A becomes F, B becomes G, and so on."
"Exactly. Enigma is just a very complex substitution system."
"Complex in what way?" asked Tom.
"The key to breaking any code is spotting a pattern," Dominique replied, taking over from Viktor. "The beauty of the Enigma was that it changed the pattern after each individual letter."
"Through these?" Tom asked, taking a metal disc with teeth and electrical circuits from the small wooden box that had been brought in with the machine.
"The rotors," Dominique confirmed. "Every time a letter was encoded, the rotors would change position and so would the pattern. And as a further safeguard each original letter was mapped to a totally different starting letter through the wires on the plug board before it even went through the rotors, and then the entire process was repeated in reverse before the encoded letter would light up." Her fingernail tapped against one of the glass windows. "They say there are one hundred and fifty-nine million million million possible combinations in all."
"So, to decode a message, you would need to know exactly how the original machine had been set up," Tom surmised.
"Exactly." Viktor stepped forward. "They used to issue codebooks so that, on any particular day, everyone would know what setting to use. If we don't have the settings, we're going to have to involve some expert help."
"Which will take time. Something we don't have," Tom said.
"Well, Renwick must know, or he wouldn't have gone to all this bother, would he?" Archie observed. "There must be some way to work it out."
"You're right," said Tom. "Maybe we missed something. Let's have another look at those photos." They turned to the screen once again and examined the painting's edges.
"How many of these wires did you say there were?" Archie asked eventually.
"It varied," Viktor replied. "Between ten and thirteen, depending on the setting. Any unwired letters were passed through the rotors without having been substituted first. It was another way of confusing eavesdroppers. Why?"
"It's just that there are twenty-six letters along the top edge of the painting," said Archie. "And they look like they've been written in pairs."
Viktor nodded. "Thirteen pairs of letters. That could easily be the setting for the plug board — U to A. P to F …" She quickly reconfigured the wires to match the pairs of letters along the top of the frame. "There."
"Which leaves us with what?" Tom inquired, his voice animated by their apparent progress.
"The choice of rotors and their settings," Viktor replied. "We need to know which three to select and what ring settings to give them." She took the remaining four rotors out of their greaseproof paper and pointed at a small ring that seemed to have been stuck to the side of each rotor. "These rotate and are then locked into a starting position. Without these, we've got nothing."
CHAPTER EIGHTY-SEVEN
They had taken turns in front of the computer, each trying to make sense of the jumbled mass of letters that decorated the painting's edges like elaborate black lace. But no matter how hard they looked at the photos, whatever clever tricks they came up with to count the letters or divide them by the number on the other side, or subtract one from the other, they were no closer to discovering the rotor settings or which rotors they should use.
They had even, in desperation, brought in the items they had recovered — the photos of the Bellak paintings, the Bel-lak painting of the synagogue itself, the walnut box that had contained Lammers's medal, the medals, the safety-deposit box key, and the leather pouch and map hidden within the box — to see if they could provide some inspiration or reveal some hidden clue or message. But after six hours of fruitless inquiry, the letters had begun to cobweb across their vision.
Archie had long since left the room, complaining of a headache, while Viktor had gone to arrange some food for them. For Dominique, however, solving this puzzle had developed into a personal battle. She knew that Tom and Archie made fun of her for getting like this, often over quite trivial things, but she couldn't help herself, especially when, as in this case, it was almost as if they had been set a formal challenge. It aroused her deepest competitive instincts, which were further fueled by her desire not to let the others down.
She had therefore stayed at the desk, her eyes glued to the screen, pausing every so often only to flex her fingers where they had been gripping the mouse. Tom was sitting behind her, eyes closed, and she couldn't tell if he was sleeping or thinking until he broke the silence with a question.
"Do you think we should call it a day? Maybe we need to take a fresh look in the morning?"
"The morning will be too late," she replied matter-of-factly, without even looking around. She was getting frustrated at herself and was having difficulty masking it.
She sensed Tom was about to say something, but he must have thought better of it because no words came. An awkward silence settled until Dominique looked around with a frown.
"You know, the camera wasn't empty."
"Hmm?" Tom's eyes were shut again in thought. "Your camera — it had other photos on it when you gave it to Kristenko."
"Oh yeah," said Tom. "I guess I forgot to wipe it. Nothing there that shouldn't have been, was there?"
"Don't think so, no," she said, scrolling through the images on the disk.
First the shots of the synagogue in Prague, the walls scrawled with hate-filled graffiti, the floor carpeted with children's drawings, the painting's empty frame. Then shots of the stained-glass window from the church in Kitzbiihel that Lammers had had installed. A castle. A circle of trees. Some birds taking wing through an azure sky. Finally the shots of the Bellak portrait.
Dominique paused, frowning. She scrolled back through to the pictures of the stained-glass window, then picked up the faded black-and-white photo of the same scene that Archie had found in Weissman's secret room. She looked up at the window, then down at the photo.
"Tom?" she called in an uncertain voice.
"Mmmm?" he answered, keeping his eyes shut. "I think I've found something."
"Really?"
"They're not the same."
"What's not the same?" His eyes snapped open.
"The painting and the window. The photos of each one. They're not the same. Look."
She pointed at the photo of the window on the screen as he sprang to her side, then passed the photo of the painting into his eager hands.
"Let me see." Tom held the photo up to the screen. "Christ, you're right!" He breathed excitedly. "The window's different. He must have changed it."
"It's quite subtle. Here the castle has two turrets, but in the window it has three. Here there are seven trees in the foreground, in the window five."
"And look, four birds in the painting, two in the window. That means we've got two sets of three numbers."
"But which ones should we use?"
"The ones in the window," Tom said confidently. "Don't forget, Bellak didn't know anything about the Order or their plans; he finished that painting years before the Gold Train set out on its journey. But the window was produced after the war and could easily have been designed to include the Enigma settings. The painting is only useful insofar as the discrepancies with the window tell people where to look for the numbers. Reading left to right there are three turrets, five trees, and two birds in the window. That's three, five, two."
"It could be the rotors!" Dominique exclaimed, her earlier frustration evaporating in the excitement of the moment. "There are only five of those. This could be telling us which rotors to use."