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Fault attacks on hyperelliptic curve discrete logarithm problem over binary field
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DOI：10.1007/s11432-013-5048-6.png)
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Abstract
En 中文
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 f(0) and f(1) of the hyperelliptic curve equation are not utilized for the HECSM. We show that with different values for curve parameters f(0), f(1), 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.
Keywords:
hyperelliptic curve
discrete logarithm
binary field
genus
cryptosystem
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