Counting Points on Genus 2 Curves with Real Multiplication
  We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field (\F_{q}) of large characteristic from (\widetilde{O}(\log^8 q)) to (\widetilde{O}(\log^5 q)). Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian. 
Pierrick Gaudry (INRIA Nancy - Grand Est / LORIA), David Kohel (IML),   Benjamin Smith (INRIA Saclay - Ile de France)
math.NT