Speaking of secrecy, do you think there are advances in cryptography at the moment way beyond what's public knowledge?

The whole book is really about the ongoing battle between code makers and code breakers. At the moment most people would say that the code makers are clearly ahead. So it doesn't really matter if people are coming up with new codes because the ones we have are already very strong. The question is whether there is someone who's made a big breakthrough in code breaking that we don't know about -- so that the assumption that there's this big lead isn't actually true. You can never be sure, but I think it's unlikely. Although the NSA [National Security Agency] is the world's largest employer of mathematicians, there are lots of brilliant mathematicians elsewhere who haven't found any major new algorithms.

So in fact public knowledge at this point in time may be a real reflection of the secret knowledge, so to speak?

Yes, I think that's the case.

The subtitle of the book is "The Evolution of Secrecy from Mary, Queen of Scots, to Quantum Cryptography," and early on you make the point that cryptography proceeds in a very Darwinian fashion with a kind of information arms race propelling developments on each side.

It is an evolutionary process, with code makers continually coming up with new developments, and then the code breakers having to respond by evolving new methods for penetrating those defenses. It is like the evolution of predator-prey relationships. It's interesting too because there are selection pressures. Sometimes it's only when you're desperate enough that new breakthroughs happen. For example, when the Germans developed the Enigma code between the wars and ultimately it was the Poles -- who were sandwiched between both the Germans and the Russians, and were therefore desperately worried about their national security -- who made the first big breakthroughs in cracking these codes. The work was then smuggled out to the British. The Poles are often forgotten in the story, but it really was extraordinary work they did, driven by this pressure of adversity.

We seem to be living at a time when there is a general obsession with codes: not just cryptographic codes, but computer codes and genetic codes -- we've got the Human Genome Project on the verge of sequencing the entire DNA code of human beings. You also have books like Neal Stephenson's "Cryptonomicon."

It's funny, but when "Fermat's Enigma" came out there was also "Good Will Hunting" (which was wonderful) and "Pi" (which was terrible), and there were books like "The Man Who Loved Only Numbers" [by Paul Hoffman] and "A Beautiful Mind" [by Sylvia Nasar]. There was a whole series of math films and math books that seemed to enter popular culture at the same time. And now you have a Hollywood film like "Enemy of the State" with Will Smith, and last year's "Mercury Rising" with Bruce Willis, about the NSA. Also "Cryptonomicon" in literature. I'm sure this won't be the only book on codes. I'm not sure what triggered this.

Just one of those things that's in the air. It seems to me that an interest in codes is actually pretty widespread. Children love making up codes and creating secret little languages. Lots of people love the idea of being part of some select group with its own secret passwords, like the Freemasons.

As soon as you express yourself in words, and especially once you start putting words down on paper -- whether it's 10,000 years ago or children today -- there's a realization that you may need to keep these things secret, whether it's your personal diary or a military strategy. So it's quite natural that children do this. And it's empowering. One of the reasons children make codes is to hide things from their parents. To children, parents are almost like Big Brother. We worry about the CIA and the NSA; children worry about their parents. We both use codes to try and protect ourselves.

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