Section: New Results

Point counting

In joint work with Pierrick Gaudry (CARAMEL) and David Kohel (Marseille), B. Smith developed an accelerated Schoof-type point counting algorithm for genus 2 curves with efficiently computable real multiplication endomorphisms. This project has made the computation of cryptographic-sized group orders practical for curves of genus 2 over prime finite fields. Going way beyond the current cryptographic range, the algorithm has been used to compute the group order of a 1024-bit Jacobian (smashing the previous 256-bit record of Gaudry and Schost). The article describing this algorithm has been awarded the Best Paper prize at ASIACRYPT 2011 [26] , and an extended version has been invited for submission to Journal of Cryptology (the leading journal in the field).