Publication Type
Journal Article
Version
publishedVersion
Publication Date
6-2014
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.
Keywords
hyperelliptic curve, discrete logarithm, binary field, genus, cryptosystem
Discipline
Information Security | Theory and Algorithms
Research Areas
Cybersecurity
Areas of Excellence
Digital transformation
Publication
SCIENCE CHINA Information Sciences
Volume
57
Issue
3
First Page
1
Last Page
17
ISSN
1674-733X
Identifier
10.1007/s11432-013-5048-6
Publisher
Springer
Citation
WANG, Mingqiang; XUE, Haiyang; and ZHAN, Tao.
Fault attacks on hyperelliptic curve discrete logarithm problem over binary field. (2014). SCIENCE CHINA Information Sciences. 57, (3), 1-17.
Available at: https://ink.library.smu.edu.sg/sis_research/9189
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1007/s11432-013-5048-6