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Science/Tech See other Science/Tech Articles Title: The Uneasy Relationship Between Mathematics and Cryptography The Uneasy Relationship Between Mathematics and Cryptography Neal Koblitz During the first six thousand years—until the invention of public key in the 1970s—the mathematics used in cryptography was generally not very interesting. Well into the twentieth century cryptographers had little use for any of the concepts that were at the cutting edge of mathematics. Indeed, mathematicians looking at cryptography in those years might have found justification for Paul Halmos’ infamous title “Applied Mathematics Is Bad Mathematics.” There were some exceptions. In the 1940s Alan Turing, the father of computer science, worked extensively in cryptography and, in particular, showed how to use sophisticated statistical techniques to crack a code; and Claude Shannon, the father of information theory, worked on the foundations of cryptography. In the same decade G. H. Hardy wrote in A Mathematician’s Apology that “both Gauss and lesser mathematicians may be justified in rejoicing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean.” In Hardy’s day most applications of mathematics were military, and as a pacifist he was pleased that number theory was studied not for its practical uses, but only for its intrinsic aesthetic appeal. This image of number theory as “gentle and clean” took a big hit in 1977 when three computer scientists at the Massachusetts Institute of Technology—Ron Rivest, Adi Shamir, and Len Adleman—invented a radically new cryptographic system. An article in Scientific American by Martin Gardner described the RSA idea, explained its significance, and caused a sudden upsurge in popular interest in both cryptography and number theory. Post Comment Private Reply Ignore Thread
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