The 2010 version of the ECC workshop was held at Microsoft Research in Redmond the week of October 18. Usually ECC stands for Elliptic Curve Cryptography, but this year it stood for Elliptic Curves in Computation. The advertised reason is that this is the 25th anniversary of a “period in which a number of influential papers initiated a fundamental connection between elliptic curves, cryptology and the theory of computation.” The rumor I heard* is that the name was changed so that they could get funding from certain Agencies that don’t like to overtly support cryptography. Believe what you will.
The first day of the workshop had “old-timers” (Frey, Miller, Morain, Schoof, Goldwasser, Koblitz) talking (mostly) about their fundamental contributions from the 80s. It was fun to hear how these new ideas were developed. Rene Schoof was particularly entertaining, describing how he had developed his point counting algorithm nearly 5 years before it appeared, during which period everyone he talked to was convinced that the algorithm was useless. It was also fun to watch Neil Koblitz and Shafi Goldwasser “debating” the merits of provable security.
The next 2.5 days were a standard ECC workshop, presenting recent crypto-related work. A highlight (for me) was William Stein’s talk on SAGE, which convinced me that not only is SAGE a powerful platform for computing with elliptic curves (which I already knew), but also that it is quite easy to start using. Another highlight was Kristin Lauter’s talk on computing genus 2 class polynomials using a new set of invariants.
The fourth afternoon consisted of three talks tribute to Oliver Atkin, whom I never had the opportunity to meet. The final day collected additional recent results from cryptography and computation. I particularly liked Melanie Matchett Wood’s talk on composition laws;. It seems she has uncovered a new universe of algebraic structures amenable to computation; the big question is whether these structures can provide anything new and useful for cryptography.
* Victor Miller asserts that this rumor is false. He writes, “Since there’s always been a lot of serious computation surrounding elliptic curves, modular forms and abelian varieties with no apparent connection to cryptography I thought that it would be good to get the two groups together, and thus the name change. It never occurred to me that it might help funding.”
Still, it makes a good story.