TheUneasyRelationship BetweenMathematicsand Cryptography

Short Description
the cryptography chapter of his forthcoming book Ran-. dom Curves: Journeys of a Mathematician, ….. ticular application of cryptography. From the early …

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Content
972 Notices of the AMS Volume 54, Number 8
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…