The Tree of Knowledge

by Daniel G. Miller

  “OK, Dr. Puddles, I’ve got to go home and feed the dog. He gets cranky if I’m late.” The detective rose from his chair and lumbered toward the door. “But do me a favor. Don’t take too long, because this is just about the only evidence we’ve got on the killer. We got lucky.”

  Weatherspoon opened the door to exit.

  Albert nodded. “Oh, Detective, just out of curiosity, what did the thief steal?”

  The detective sighed. “Nothing special. The bank logs say that it was just something in a safe-deposit box. We’re trying to get in contact with the owner as we speak. But I’d remind you that there’s a woman who lost her husband of forty-five years last night, and she’s depending on you to figure out this problem. Like I said, don’t dawdle.”

  Chapter 4

  Eva set her red-ribboned fedora down on the entry table of her lavish Malibu home. She had loved this place from the moment she’d toured it. It was the first and only home she had lived in since leaving her mother’s house, and she knew that it would always be a part of her.

  The open, high-ceilinged space suggested transparency and order, while the carefully appointed minimalist décor echoed elegance and modernity. Steel appliances, white walls, and light wood were offset by dove-gray upholstery and marble. There were no pets, no plants, no clutter. The floor-to-ceiling windows and wraparound deck overlooking the Pacific Ocean spoke to her of limitless possibilities. Beyond the aesthetic trappings, however, her Southern California enclave represented something even more inspiring: freedom.

  Eva’s father had succumbed to a heart attack when she was an infant. Consequently, she had lived alone with a powerful and domineering mother for her entire childhood. Eva loved her mother and deeply appreciated all of the sacrifices that she had made in raising her, but her strict rules and boundless expectations had always made the girl feel more like a student in a reform school than a loved only child.

  She remembered how one day in the fourth grade she had run home from school infused with joy at the “99/100” she had received on her recent math test. She burst through the door of her mother’s study and giddily told her of the triumph. Her mother slowly looked up, took her glasses off, and said, “That’s great, Evalita. What was the one you got wrong?”

  Eva could still feel the pangs of frustration and subordination that she experienced that day. This feeling worsened as she grew into womanhood and assumed her mother’s beauty. She felt empowered by the way boys worshipped and girls envied her tanned Latin skin and long black hair, and she longed to test the limits of that power. But her mother insisted on a regimen of early curfews, conservative clothing, and scheduled study that served as a constant reminder of her captivity.

  Freedom finally came a decade ago on her eighteenth birthday when, in celebration, her mother announced that it was time for Eva to have her own place and handed over the keys to the stunning house right off the Pacific Coast Highway. In addition to her dream house, Eva had received formal entrance into the Society. And as she rose in the Society’s ranks, this house had served as the last bastion of independence in her life.

  But today, even the replenishing effects of the Pacific Ocean could not rinse away the wretched feeling in Eva’s chest.

  Fresh air. That’s what I need.

  Eva unbuttoned her double-breasted black pinstriped blazer and opened the sliding glass door. As the cool ocean air slid past her damp skin, bringing the smell of salt and marine life, she stared out at the glittering water and thought about the previous night.

  “Not your best work, soldier,” hissed a voice on the balcony behind her.

  Eva jumped back, startled.

  “General? What are you doing here?”

  The general eased forward. Tall and lean, with a bullet head and a nose that jutted forward like the prow of a ship, the general was an impressive figure. Smoke slithered up from his unfiltered cigarette and drifted across his face. His voice was quiet and penetrating. “Tell me, what is the third rule?”

  “Wha-what?” stammered Eva.

  The general slid forward further, backing Eva up against a railing.

  “What is the third rule of the Society?”

  Eva swallowed hard. “Our reasoning is only as strong as our information. But, General . . . I mapped out every possible scenario. The security guard, security system . . . everything.”

  The general stared past Eva out at the Pacific and took a long drag from his cigarette, exhaling smoke through pursed lips like a blow dart. “Not everything.”

  Eva shrugged. “But I did. I got every piece of information.”

  The general turned and leaned in closer to Eva, practically pushing her over the railing with his lithe body. She could smell the nicotine on his breath as his tongue slid across his lips.

  “Then why is there a dead security guard in the lobby of Bank of Princeton with a logic tree in his hand?”

  “What? What are you talking about?” Eva reached into her blazer pocket and rifled through the papers inside. “I just chloroformed him. I didn’t kill him.”

  The general’s face grew red, and a powerful vein bulged from the center of his forehead underneath his cropped, receding silver hair. He pulled a folder out from under his arm and slapped her chest with it to punctuate each sentence. “If you had properly researched the security guard, you would know his name is Wally McCutcheon.” Slap. “He had a heart condition, which is why the chloroform killed him.” Slap. “And he is also a former state wrestling champion, which would explain how he pulled a logic tree from out of your pocket!” Slap.

  Eva ripped through the pages.

  No, no, no!

  “Oh God, the prima facie. He must have grabbed it. What time is it? Five p.m. That means the police have it.”

  The general clasped Eva’s shoulder with his long, bony hand. She looked back at the waves crashing behind her. She felt his grip digging into her clavicle.

  “As you well know, Eva, the Society frowns on murder. It is impractical and expensive. Now I have to deal with the police, the media, and several other nuisances that I have zero tolerance for.”

  “I know. I’ll fix this.”

  “You better, or the security guard won’t be the only dead body I’ll be dealing with this week.”

  Chapter 5

  “What do we do now?” asked Ying, still carrying the smile that had been tattooed on her face since news of the case had arrived.

  Ying Koh had lived most of her life in Singapore and was the youngest child in her family, coming after four brothers. Being both the youngest and the only girl, Ying endlessly fought to be included in her siblings’ activities. Unfortunately, from her first days, the round-faced girl was plagued by multiple ailments that served as a physical and emotional barrier to her inclusion. As a child, she suffered from an intense form of scoliosis, which required her to wear a large plastic brace around her torso eight hours a day. The stress on her back caused her to walk on her tiptoes, which required additional braces around her ankles and calves. Her body, enveloped in braces, gave Ying the appearance of a robot-person, an image that caused both her parents and her siblings much agony and shame. The physical threat of her four protective brothers prevented any of the schoolchildren from teasing her, but the sense of alienation, exclusion, and pity that hung over her during her formative years exceeded any physical pain that bullying could have inflicted. This sense of isolation was exacerbated by Ying’s intelligence. Her ability to calculate complex mathematical calculations in her head, and her participation in international math competitions, confirmed the feeling among her classmates that Ying was somehow different.

  So it was with great joy that at the age of seventeen Ying kissed her parents and brothers goodbye and fled to America for college. As she journeyed on the epic plane flight from Singapore to the United States, for the first time she understood the phrase “land of opportunity.” Not in
the traditional economic sense, but in a spiritual and emotional sense. Coming to this new land meant that Ying could remake herself. No longer would she be the brace-ridden girl that people looked at with sorrow even after the braces were gone. She would be Ying, the smiley-faced, intelligent, joyful woman that she had always been but no one could see. It was this woman, imbued with optimism and adventure, who sat bright-eyed and grinning in Professor Puddles’s office, soaking up the exciting and terrifying details of the police investigation into which she had just been thrust.

  Professor Puddles raised an eyebrow and shook his head at the smiling Ying. “We aren’t going to do anything. You are going to the lecture hall to inform the class that we’ll resume our session tomorrow, and I am going to see if I can break down this cipher.”

  “Oh, come on,” implored Ying, her big brown eyes blinking furiously. “You know that it’s probably some type of Caesar cipher, and we’ll be able to do it much faster together than if you do it on your own.”

  When she smiled, her cheeks formed two shiny round balls that kept her thick-rimmed glasses from sliding down her undersized nose.

  Albert hated to admit it, but Ying was right. Ciphers dated back to the Roman Empire. The Caesar cipher took its name from the emperor Julius Caesar, who used a basic substitution cipher in which each letter of the alphabet was substituted with the letter three places down in the alphabet. For example, the letter A would be replaced with the letter D, the letter B with the letter E, and so on. While the Caesar cipher was relatively rudimentary, it proved extremely effective in its day because the vast majority of the known world was illiterate, and knowledge of linguistics and code-breaking was in its infancy.

  While Caesar ciphers served their purposes during the time of the Roman Empire, their simple construction eventually proved too vulnerable for military use. In the ninth century, al-Kindi, an Arab linguist, published a tome on deciphering codes, which introduced the concept of frequency analysis. Using the Koran as his inspiration, al-Kindi documented the frequency of occurrence of each letter in the Arabic language. He discovered that certain letters occurred with much greater frequency than others. The power of this discovery lay in the fact that, for the first time, cryptographers could look at a given cipher and, by identifying symbols that occurred with greater frequency, begin to crack the code. Linguists in other countries soon discovered that these differences in the distribution of letters existed in all languages, thus signaling the death of the Caesar cipher in serious communications.

  In 1553, the Vigenère cipher was created to address the weaknesses attributed to the Caesar cipher. In an ironic twist of history, what is now known as the Vigenère cipher was created by an Italian cryptologist named Giovan Battista Bellaso in 1553, but later misattributed to Vigenère, who had developed an even stronger cipher that built on Bellaso’s work. The Vigenère cipher used a Caesar cipher, but instead of a constant substitution shift such as three letters to the right, the shift changed at each position according to a keyword. If the keyword was as long as the text of the message itself, then the code was considered unbreakable. However, in practice, due to the difficulty of remembering lengthy keywords, shorter keywords were often used, making the cipher vulnerable to advanced cryptography. In fact, during the Civil War, the Confederacy regularly used a Vigenère cipher with the key “Complete Victory,” which was eventually cracked by the Union.

  Albert prayed that the cipher that lay before them was not a Vigenère. He removed his glasses and massaged the bridge of his nose. “OK, Ying, go tell the class that we’re done for the day and that we will resume tomorrow.”

  “Yaaaaay,” Ying exclaimed as she scampered out the office door.

  “Tell them to finish the first two chapters of Introduction to Logic,” shouted Albert, hoping that she was still within earshot.

  Albert stared deeply at the encoded numbers in front of him.

  Where to begin?

  It had been years since he had performed any decryption. As a teenager, he had loved trying to decode mathematical puzzles and cryptograms, but things were different now. The demands of modern professorship were constant: publishing new papers, teaching, attending faculty meetings. Albert remembered his father’s words to him whenever he was stuck on a difficult problem.

  “Just start trying things to get your mind moving.”

  His father, a world-class teacher and mathematician in his own right, referred to the paralysis that students often felt when tackling a math problem as “the freeze,” and felt that if you just began to “talk to the problem,” your brain would begin to thaw and a solution would present itself.

  With that in mind, Albert assessed the logic tree before him.

  The letters in each box were a random jumble. Then he spotted something. In the shaded box second from the right was a code with not one but two repeating letters in it: “PPKVSS.”

  This could be a vulnerability.

  Albert attempted to crack the word using the easiest solution.

  Let’s assume that each letter is just substituted for one letter down in the alphabet. A would be B; B would be C, etcetera.

  Albert performed the analysis: “QQLWTT.”

  “OK, I’m pretty sure that’s not it,” he said to himself.

  As Albert began to think of another approach, Ying returned from telling the class the good news.

  “Any progress?” she inquired hopefully.

  “Nope. I tried a simple substitution, and unless ‘QQLWTT’ is a word I don’t know about, I’m pretty sure we need to try something else.”

  Ying laughed and looked over the logic map as Albert stood up from his chair.

  She pushed her glasses up her nose. “You know, I’ve been thinking about it, and I really don’t think this cipher can be that complicated. The code is done by hand and on a pretty simple game tree, so I just don’t see the thief using anything too advanced. Should we try a brute-force attack?”

  A brute-force attack was cryptography slang for solving a cipher by trying all possible variations according to a given hypothesis. In the case of a Caesar cipher, the attacker would simply rewrite the cipher twenty-six times for each potential number of shifts in the alphabet.

  “Yeah, that makes sense. I’ll take the first half, you take the second.”

  Albert and Ying rewrote the cipher, each time shifting down one letter of the alphabet. Albert began by making the A into a B, the B into a C, and so on, but that produced nothing. He then made the A into a C and continued, but still nothing. After fifteen minutes, he and Ying had completed their respective tables. The two combined the tables, and hunched over the finished product hoping to see something of meaning:

  Albert stared in disbelief at the jumbled list of letters in front of him and growled, “Are you kidding me? I can’t believe that this is more than just a basic substitution cipher.”

  “I know. It seems like a lot of effort to go through to hide a game tree.”

  “I hope this is a Vigenère cipher, because if it’s not, then it’s probably unbreakable unless we have the keyword, which we don’t. Will you do me a favor and hop on the computer? There’s a guy at MIT who’s created an automated program for cracking a Vigenère cipher. I’m not sure if it will work since each cipher in each box of the game tree is so short, but it’s worth a shot.”

  Ying darted over to the computer on Albert’s large, carefully ordered desk while he stood in front of the chalkboard thinking of alternatives. He found the chalkboard uniquely calming and illuminating. The feel of the soft, powdery chalk in his hands triggered memories of learning going back to childhood and provided a unique sensation of order and clarity. The clear, dark blackboard energized his mind like the endless expanse of space. Albert grabbed his familiar eraser and slid it back and forth across the board until the last particle of chalk was gone.

  “I just can’t accept that this is t
hat complex a cipher,” insisted Albert. “I mean, think about it logically. You’re a thief about to break into a bank. You’re a freakishly logical thief with some training in mathematics, so in preparation for the theft, you create a game tree—by hand, mind you—that requires a complex encryption process or device. That seems so illogical and tedious given the incredible unlikelihood that it’s going to wind up in someone else’s hands.”

  “Yeah, when I was in Professor Turner’s cryptography class, he just said that if we ever wanted to encrypt something by hand quickly, we should just use a Trithemius cipher,” said Ying.

  Albert chuckled. “He said the same thing when I was in his class.”

  Professor Turner was an institution at Princeton. He had won every mathematics prize ever invented, had taught nearly every aspiring mathematician of the last half century, and had launched the very Mental Calculation World Cup that Albert and Ying had won.

  Albert’s eyes brightened at the thought.

  “That’s it! It’s a Trithemius cipher!”

  Johannes Trithemius was a German abbot in the late fifteenth and early sixteenth centuries. During his lifetime, Trithemius published numerous works on history, language, and cryptography. In 1499, he completed his most famous work, Steganographia, the first book published on cryptography. To the layman, Steganographia appeared to be a work outlining a system of angel magic. However, in a clever inside joke, the text on magic was encoded, and upon breaking the code, it showed itself to be a book on cryptography and stenography. The book included what is now known as the Trithemius cipher, a more practical but less secure predecessor to the Vigenère cipher.