Abstract
AbstractWe 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 à 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.KeywordsFinite FieldCharacteristic PolynomialElliptic CurfAbelian VarietyPrime PowerThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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