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In this paper,we present invalid-curve attacks that apply to the hyperelliptic curve scalar multiplication(HECSM)algorithm proposed by Avanzi et al.on the genus 2 hyperelliptic curve over binary field.We observe some new properties of the HECSM.Our attacks are based on these new properties and the observation that the parameters f0and f1of the hyperelliptic curve equation are not utilized for the HECSM.We show that with diferent“values”for curve parameters f0,f1,there exsit cryptographically weak groups in the Koblitz hyperelliptic curve.Also,we compute the theoretical probability of getting a weak Jacobian group of hyperelliptic curve whose cardinality is an smooth integer.
In this paper, we present invalid-curve attacks that apply to the hyperelliptic curve scalar multiplication (HECSM) algorithm proposed by Avanzi et al. On the genus 2 hyperelliptic curve over binary field. We observe some new properties of the HECSM. Our attacks are based on these new properties and the observation that the parameters f0 and f1 of the hyperelliptic curve equation are not utilized for the HECSM.We show that with diferent “values ” for curve parameters f0, f1, there exsit cryptographically weak groups in the Koblitz hyperelliptic curve.Also, we compute the theoretical probability of getting a weak Jacobian group of hyperelliptic curve whose cardinality is an smooth integer.