Fault attacks on hyperelliptic curve discrete logarithm problem over binary field

• Main Authors: WANG, Mingqiang, XUE, Haiyang, ZHAN, Tao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2014
• Subjects: hyperelliptic curve; discrete logarithm; binary field; genus; cryptosystem; Information Security; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/9189; https://ink.library.smu.edu.sg/context/sis_research/article/10194/viewcontent/s11432_013_5048_6.pdf
• Institution: Singapore Management University

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.