Abstract for the seminar talk on 13.06.2008

Kate Stange (Brown University)
Elliptic Nets in Cryptography
Time: 11:00 / Place: HWZ (HG G43)

Elliptic divisibility sequences are integer recurrence sequences, eachof which is associated to an elliptic curve over the rationals together with a rational point on that curve. I'll give the background on these and present a higher-dimensional analogue over arbitrary fields. Suppose E is an elliptic curve over a field K, and P_1,...,P_n are points on E defined over K. To this information we associate an n-dimensional array of values of K satisfying a nonlinear recurrence relation. These are called elliptic nets. I'll talk about applications of elliptic nets to cryptography: specifically, I give a new algorithm for computing the Tate or Weil pairing for pairing-based cryptography. If time permits, I may briefly discuss recent work relating elliptic nets to the elliptic curve discrete logarithm problem.