|Title||Counting Points on Hyperelliptic Curves over Finite Fields|
|Author(s)|| Pierrick Gaudry, Robert Harley|
|Type||Article in Conference Proceedings|
|Abstract||We describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They|
include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm `a la Schoof for genus 2 using Cantor's division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and
we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature.