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AMC

We extend the notion of an invalid-curve attack from elliptic curves
to genus 2 hyperelliptic curves. We also show that invalid singular (hyper)elliptic
curves can be used in mounting invalid-curve attacks on (hyper)elliptic curve
cryptosystems, and make quantitative estimates of the practicality of these
attacks. We thereby show that proper key validation is necessary even in cryptosystems
based on hyperelliptic curves. As a byproduct, we enumerate the
isomorphism classes of genus g hyperelliptic curves over a finite field by a new
counting argument that is simpler than the previous methods.

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