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With Merlutti’s napkins and concert programs as her chalkboard, Susan set out to give her charming new pedagogue a mini course in cryptography. She began with Julius Caesar’s “perfect square” cipher box.
Caesar, she explained, was the first code‑writer in history. When his foot‑messengers started getting ambushed and his secret communiques stolen, he devised a rudimentary way to encrypt this directives. He rearranged the text of his messages such that the correspondence looked senseless. Of course, it was not. Each message always had a letter‑count that was a perfect square‑sixteen, twenty‑five, one hundred‑depending on how much Caesar needed to say. He secretly informed his officers that when a random message arrived, they should transcribe the text into a square grid. If they did, and read top‑to‑bottom, a secret message would magically appear.
Over time Caesar’s concept of rearranging text was adopted by others and modified to become more difficult to break. The pinnacle of non computer‑based encryption came during World War II. The Nazis built a baffling encryption machine named Enigma. The device resembled an old‑fashioned typewriter with brass interlocking rotors that revolved in intricate ways and shuffled cleartext into confounding arrays of seemingly senseless character groupings. Only by having another Enigma machine, calibrated the exact same way, could the recipient break the code.
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At first, the pass‑keys being used were short enough for the NSA’s computers to “guess.” If a desired pass‑key had ten digits, a computer was programmed to try every possibility between 0000000000 and 9999999999. Sooner or later the computer hit the correct sequence. This method of trial‑and‑error guessing was known as “brute force attack.” It was time‑consuming but mathematically guaranteed to work.
As the world got wise to the power of brute‑force code‑breaking, the pass‑keys started getting longer and longer. The computer time needed to “guess” the correct key grew from weeks to months and finally to years.
By the 1990s, pass‑keys were over fifty characters long and employed the full 256‑character ASCII alphabet of letters, numbers, and symbols. The number of different possibilities was in the neighborhood of 10120 ‑ ten with 120 zeros after it. Correctly guessing a pass‑key was as mathematically unlikely as choosing the correct grain of sand from a three‑mile beach. It was estimated that a successful brute‑force attack on a standard sixty‑four‑bit key would take the NSA’s fastest computer‑the top‑secret Cray/Josephson II‑over nineteen years to break. By the time the computer guessed the key and broke the code, the contents of the message would be irrelevant.
Susan’s mind was racing‑Ensei Tankado wrote a program that creates unbreakable codes! She could barely grasp the thought.
“Digital Fortress,” Strathmore said. “That’s what he’s calling it. It’s the ultimate counterintelligence weapon. If this program hits the market, every third grader with a modem will be able to send codes the NSA can’t break. Our intelligence will be shot.”
But Susan’s thoughts were far removed from the political implications of Digital Fortress. She was still struggling to comprehend its existence. She’d spent her life breaking codes, firmly denying the existence of the ultimate code. Every code is breakable‑the Bergofsky Principle! She felt like an atheist coming face to face with God.
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Strathmore shrugged. “Either way, it’s too late now. He’s posted a complimentary copy of Digital Fortress at his Internet site. Everyone in the world can download it.”
Susan went white. “He what!”
“It’s a publicity stunt. Nothing to worry about. The copy he posted is encrypted. People can download it, but nobody can open it. It’s ingenious, really. The source code for Digital Fortress has been encrypted, locked shut.”
Susan looked amazed. “Of course! So everybody can have a copy, but nobody can open it.”
“Exactly. Tankado’s dangling a carrot.”
“Have you seen the algorithm?”
The commander looked puzzled. “No, I told you it’s encrypted.”
Susan looked equally puzzled. “But we’ve got TRANSLTR; why not just decrypt it?” But when Susan saw Strathmore’s face, she realized the rules had changed. “Oh my God.” She gasped, suddenly understanding. “Digital Fortress is encrypted with itself?”
Strathmore nodded. “Bingo.”
Susan was amazed. The formula for Digital Fortress had been encrypted using Digital Fortress. Tankado had posted a priceless mathematical recipe, but the text of the recipe had been scrambled. And it had used itself to do the scrambling.
“It’s Biggleman’s Safe,” Susan stammered in awe.
Strathmore nodded. Biggleman’s Safe was a hypothetical cryptography scenario in which a safe builder wrote blueprints for an unbreakable safe. He wanted to keep the blueprints a secret, so he built the safe and locked the blueprints inside. Tankado had done the same thing with Digital Fortress. He’d protected his blueprints by encrypting them with the formula outlined in his blueprints.