The Tree of Knowledge, Daniel Miller [unputdownable books txt] 📗

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 that 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.

The Trithemius cipher used what the inventor titled a “tabula recta,” which was a square table of alphabets, with each alphabet shifting one to the right. Using the tabula recta, a person