|The Paula Gordon Show|
|Math, Codes & Quantum States|
Secrets are key to the Information Revolution, according to Simon Singh. They are required for the secure exchange of information, as they have been since the beginning of recorded history, code-makers squaring off against code-breakers. It's a race which stretches back into the mists of recorded history and forward to become the foundation of e-commerce. Mr. Singh has broken the code on cryptography for lay people in The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography.
In the past 25 years, pure and applied mathematics have found a common home in the world of cryptography, Mr. Singh reports. The best codes today are based in pure mathematics. Consider public key encryption, crucial to the security of the Internet. It was created in the 1960's by young Americans fluent in the language of mathematics. Whitfield Diffie, Ralph Merkle and Martin Hellman (who described themselves "God's Fools") became famous for inventing public key cryptography's mathematical padlock. Ron Rivest, Adi Shamir and Leonard Adleman put those padlocks to work (and built an enormous business) with RSA, asymmetric cryptography.
Now the irony. Virtually simultaneously, in Britain, James Ellis, Clifford Cocks and Malcolm Williamson also figured out how to do public key encryption. But as employees of Government Communications Headquarters (formed from the remnants of the famed top-secret WW2 Blenchley Park,) their work was ... top secret. Ellis went to his grave unrecognized.
There's a lot of room for creativity in this strange world, a world accessible only to those fluent in the language of mathematics. It's usually (but not always) very young people who solve very old problems, Mr. Singh says, people whose thinking is not calcified. God's fools. They seem oblivious to others' certainty that a task is impossible. Imagination provides most mathematicians with the first leap of enthusiasm to pursue a line of argument. Often, solving the big problems does not, in fact, come while the person is working on that problem. Ideas don't just appear -- they require hard work. But breakthroughs typically do not come when they're doing the hard work. The "aha" happens when mathematicians look away.
Today's codes are effectively unbreakable, says Mr. Singh. That's good for private conversations on line and for e-commerce. The flip side, of course, is that this provides effective cover for terrorists and criminals. Turns out, solving the monumental social problems we've engendered with these codes may rival the undeniable accomplishments of scaling pure math's intellectual Everests.
[This program was recorded on September 27, 2000, in Atlanta, GA.]
Simon Singh tells Paula
Gordon and Bill
Russell how present day cryptography united applied mathematics and
pure mathematics. Mr. Singh puts cryptography in the context of the Information
Age and the security required for the e-commerce revolution. He describes
the rich and rapidly-growing arena of mathematics.
Spurred on by Carl Sagan, James Burke and science popularizers
on television, Mr. Singh describes how mathematics stories he tells on
television influence the stories in his books. He compares mathematics
to music, eager to give people a glimpse of the beauty many of us cannot
see in mathematical notations. He gives examples. Mr. Singh describes
the creative process involved in solving a mathematical problem, relating
this to the "Creating Sparks" festival held in London in September,
2000. He explains why it is often very young people who advance mathematics.
For centuries, cryptography had an apparently impossible
problem. Mr. Singh describes how Whitfield Diffie, Ralph Merkle and Martin
Hellman solved it by inventing public key cryptography and why they described
themselves as "God's Fools." Mr. Singh explains the heart of
their mathematical padlocks which are central to Internet security. He
recalls how Ron Rivest, Adi Shamir and Leonard Adleman implemented public
key cryptography with "RSA" (asymmetric cryptography.) He explains
why the vast majority of financial transactions on the Internet depend
on these interconnected concepts. Mr. Singh gives pluses and minuses for
effectively unbreakable codes. He recommends a forthcoming book on cryptography
and tells why.
Mr. Singh tells the story of the simultaneous (secret)
development of mathematical padlocks in Britain, citing the work of James
Ellis, Clifford Cocks and Malcolm Williamson. Mr. Singh details the enormity
of Mr. Cocks' mathematical achievement. The process of solving mathematical
problems is considered, using the example of solving Fermat's Last Theorem.
Mathematics and physics are compared, with Mr. Singh offering examples
of the enormous diversity there is in approaches within science. Math's
collaborative nature is described with the story of an Hungarian-American
Mr. Singh considers why he can tell scientists' stories
and they can't. He agrees with the scientist who contended that the most
incomprehensible thing about our universe is that it is comprehensible.
He relates that to how the mathematics for today's modern encryption system
were available long before people needed to use that math to solve Information
Revolution problems. He expands, showing how important timing is. Mr.
Singh describes quantum cryptography, presenting the history of codes
as a battle between code-makers and code-breakers with a series of examples.
Continuing with quantum cryptography, Mr. Singh explains
the quantum concepts behind it and assures us that it is here today, though
still limited in reach. The power of Mr. Singh's stories is explored.
He demonstrates how careful one must be in taking the ideas of math and
science into everyday language.
Our thanks to Yuko Miki at Anchor Books/Random House for her help in making the arrangements for this conversation.