Genus-2 Curves and Jacobians with a given Number of Points
نویسندگان
چکیده
We study the problem of efficiently constructing a curve C of genus 2 over a finite field F for which either the curve C itself or its Jacobian has a prescribed number N of F-rational points. In the case of the Jacobian, we show that any ‘CM-construction’ to produce the required genus-2 curves necessarily takes time exponential in the size of its
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