Mathematician Finds Math + Cryptography = Drama + Conflict

August 22, 2007

"Drama and conflict are inherent in cryptography," mathematician Neal Koblitz of the University of Washington writes in his article "The Uneasy Relationship between Mathematics and Cryptography." He continues, "The 'spy vs. spy' mentality of constant competition and rivalry extends to the disciplinary culture of the field." The article appears in the September issue of the Notices of the American Mathematical Society.

Among other things, Koblitz describes the pernicious effects of this mixing of various interests. One result he calls the "bandwagon effect," whereby some mathematicians slant their research grant proposals to curry favor with funding entities such as the National Security Agency.

The other result involves efforts on the part of cryptographers to demonstrate that their systems are "provably" secure — that is, there exist ironclad mathematical proofs of their systems' inviolability. However, Koblitz and others have demolished such claims of "provable security," often eliciting heated and bizarre reactions from defensive cryptographers.

As one case study, Koblitz recounts the development and use of a technique known as "elliptic curve cryptography," or EEC, which involves planar curves that have properties central to modern number theory. Elliptic curves, he points out, played a significant role in Andrew Wiles's proof of Fermat's Last Theorem. Koblitz includes a discussion of an algorithm dubbed "xedni calculus" ("index" spelled backwards) that initially seemed to promise a fast way to crack ECC systems, but ultimately proved to be too slow.

The constant competition and pressure, Koblitz writes, "can get to be excessive — and even childish at times — but it also explains in part why it can be so much fun to do research in cryptography."

Source: American Mathematical Society, Aug. 7, 2007.