Fault attacks on hyperelliptic curve discrete logarithm problem over binary field

Abstract

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. © 2014 Science China Press and Springer-Verlag Berlin Heidelberg.