The primary suspect in the Unabomber case was revealed to have a background in mathematics and not a background in sociology, but the 7/20/96 San Francisco Examiner article [=LINK] provided some interesting insights into the FBI's investigative procedures. The question the article implicitly raised was, How, precisely, is the FBI reading the Unabomber's missives? Were they searching for encrypted messages? Most certainly they were looking for clues suggesting the existence of a specialized langauge in the writer.

About the same time the aforementioned San Francisco Examiner article appeared, there appeared an article in the Omaha World-Herald ("Released Cables Tie Rosenbergs to Soviets," Thursday, July 13, 1995, p. 9) about the Rosenbergs and the Venona group of cryptologists who broke the Soviets "one time pad," which was the way the Rosenbergs and the Soviets were communicating with each other. What sorts of decryptive techniques (if any) were the FBI cryptologists using on the Unabomber's letters?

A one-time pad is a code that grants perfect secrecy­but at a severe cost. Here is how it works: First, number the letters of your alphabet. Next, produce a string of numbers, S=N1, N2, N3 . . . Nm by some random process (e.g., by blindly selecting numbered balls, with replacement, from a well-mixed urn) such that each of the numbers (Ni takes on some numerical value corresponding to that of one of these letters, and such that m is a number at least as large as the sum of the lengths of all of the messages you intend to send on the pad. (Thus m must be some prespecified integer­a severe problem with this kind of system.) S is the key that will encrypt the transmitter's plaintext into ciphertext, and will then decode this ciphertext back into plaintext for its receiver. To encode a message on the pad, simply add together the ith values of plaintext and key for each i, utilizing clock (or modular) arithmetic (e.g., in English alphabet 25+2=1), while to decode it reverse the process, subtracting from this sum the ith values of the key for each i, yielding the plaintext.

Another severe problem with this system is how to get the key to the receiver, since the former problem guarantees it will eventually exhaust itself and have to be replaced, the Achilles heel of the one-time pad concept. Question: Why should the security of conveying a key from point A to point B, over and over again, be any greater than that of transmitting ciphertext by some more sophisticated algorithm employing a fixed key, or for that matter simply sending the plaintext itself by secret courier? Where's the payoff?

There is an answer, though a somewhat ambiguous one: If you send very long keys you will not have to send them very often. Nonetheless, with a large volume of cryptological traffic you will have to replace them sooner or later, while this volume must also create a new problem of its own. (Claude Shannon had proved that cryptosystems based on random keys longer than their message lengths grant perfect computational security.)

On at least one occasion in the 1940s the Soviet must have blundered and used the same sub-sequence of their key to encrypt two or more different messages­a grave mistake. The blunder was all the cryptologists needed. As soon as the Soviets introduced checkable repetitions or periodicities into the encryptions scheme they were asking for trouble, since the frequencies of the place-values in their ciphertext began to reflect frequencies naturally occurring in the language, allowing their code to be picked apart in a statistical analysis. My assumption is that as more and more Soviet agents began to transmit messages on the key, they began to lose track of where previous messages had ended, hence what part of the key had already been used. This led to frustrating discordances between transmitters and receivers, with couriers constantly forced to liase between the parties (itself reducing the security, hence the whole point of the system), until finally they figured the process was more trouble than it was worth and began to double up their messages on the key. That is when they got caught by the (presumably) sophisticated statistical tests the American cryptanalysists in Venona were throwing at every ciphertext that came their way.

One-time pads are not good for general cryptological traffic but only for special occasions, and only then when great care is taken. For this reason cryptologists have devoted a great deal of energy to finding deterministic systems that are able to approach the absolute (textual) security of the one-time pad and its randomized key while at the same time managing the key distribution problem in a rational way. The second half of this problem, at least, was solved in the 70s with the advent of public key cryptosystems based on one-way trap-door functions (e.g., the prime factoring of large integers). But again, all of these systems are based on the hope that complex deterministic systems can mimic random processes with a high degree of fidelity. That's the catchword: mimic. No simulation is perfect.

This, in a related way, was the Unabomber's predicament: as the quantity and length of his communications expanded, the language in which they were verbalized became at a certain point over-determined. That is, the specialized language component of his vocabulary­the expression of his ideas­began to reveal itself even as he was trying to simulate (randomize) a non-specialized vocabulary. It finally caught up with him. How? Because he had left behind some earlier writings, the substance of which the FBI began to check against his signed (authorized) statements. How many of us could write even the briefest of messages without using the vocabulary of our professional training? It becomes second nature to us, and I suspect that even if we would make a concerted effort of avoid using it, it would "slip through" on rare occasions. The FBI assumed that eventually their sophisticated statistical analysis would one day catch up with the Unabomber's mimicry of randomness (used both in his messages and in the random locations of his attacks).

Randomness probes the structure of the real. What randomness reveals is how the proportion of nonsense to sense inevitably increases as things get big, while the rate at which this happens itself tends to accelerate with increasing size. Murry Gell- Mann puts the matter this way in The Quark and the Jaguar (36):

Discussions of simplicity and complexity tend to become more and more meaningful as the bit strings become longer and longer. At the other extreme, say for a string of one bit, it is evidently meaningless to differentiate between simplicity and complexity.

To prove this, below is an experiment: three sentences picked at random from three literary texts which were also picked at random. The experiment is to write a small story that incorporates each of these sentences, not necessarily in the order in which they are listed (that would be six times as hard!).

Try to make your creation as concise and coherent as possible. When you are finished, note the time it took you and the total number of words you required. Then, add a fourth sentence from a fourth source to the mix and start over again. What happens? Try again with a new set of sentences.

Note the conflicting priorities in the scenario envisioned: For example, we can cut down on our composition time radically by simply concatenating events without relating them intrinsically: "First X happened and then Y happened and then Z happened." But this is a cinder, not a diamond! The point is to get the terms within sentence A to refer to those in B and C via a chain of intermediaries. How shall we go about quantifying these conflicting constraints?

Here are the three sentences, chosen at random from three texts that were also chosen at random:

"Oh, how shameless!" Michael cried, "But this is outright blasphemy!" (Eco's The Name of the Rose)

"But what it is all about exactly I could no more say, at the present moment, than take up my bed and walk." (Beckett, Malone Dies)

"In those years it was unheard of that groceries should be delivered to anyone at home" (I. B. Singer, "Zeitel and Richel," The Seance)

Don't worry if the result seems slightly absurd or dreamlike, a problem that may be eliminateable only in an extensive an elaborate treatment. (A related question, then, is What does this experiment tell us about the nature of dreaming?
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