American Institute of Mathematical Sciences

Advanced
August  2010, 4(3): 307-321. doi: 10.3934/amc.2010.4.307

Invalid-curve attacks on (hyper)elliptic curve cryptosystems

Koray Karabina 1, and  Berkant Ustaoglu 2,

1. 

Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada, N2L 3G1, Canada
2. 

NTT Information Sharing Platform Laboratories, 3-9-11, Midori-cho Musashino-shi, Tokyo 180-8585, Japan

Received  May 2009 Revised  January 2010 Published  August 2010

We extend the notion of an invalid-curve attack from elliptic curves to genus 2 hyperelliptic curves. We also show that invalid singular (hyper)elliptic curves can be used in mounting invalid-curve attacks on (hyper)elliptic curve cryptosystems, and make quantitative estimates of the practicality of these attacks. We thereby show that proper key validation is necessary even in cryptosystems based on hyperelliptic curves. As a byproduct, we enumerate the isomorphism classes of genus g hyperelliptic curves over a finite field by a new counting argument that is simpler than the previous methods.
Keywords: hyperelliptic curves., Invalid-curve attacks.
Mathematics Subject Classification: 94A6.
Citation: Koray Karabina, Berkant Ustaoglu. Invalid-curve attacks on (hyper)elliptic curve cryptosystems. Advances in Mathematics of Communications, 2010, 4 (3) : 307-321. doi: 10.3934/amc.2010.4.307
[1]

Knut Hüper, Irina Markina, Fátima Silva Leite. A Lagrangian approach to extremal curves on Stiefel manifolds. Journal of Geometric Mechanics, 2020  doi: 10.3934/jgm.2020031
[2]

Yuxi Zheng. Absorption of characteristics by sonic curve of the two-dimensional Euler equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 605-616. doi: 10.3934/dcds.2009.23.605
[3]

Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388
[4]

Petr Pauš, Shigetoshi Yazaki. Segmentation of color images using mean curvature flow and parametric curves. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1123-1132. doi: 10.3934/dcdss.2020389
[5]

Huanhuan Tian, Maoan Han. Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020368
[6]

Kuo-Chih Hung, Shin-Hwa Wang. Classification and evolution of bifurcation curves for a porous-medium combustion problem with large activation energy. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020281
[7]

Karol Mikula, Jozef Urbán, Michal Kollár, Martin Ambroz, Ivan Jarolímek, Jozef Šibík, Mária Šibíková. Semi-automatic segmentation of NATURA 2000 habitats in Sentinel-2 satellite images by evolving open curves. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1033-1046. doi: 10.3934/dcdss.2020231

2019 Impact Factor: 0.734

Tools

Metrics

  • PDF downloads (130)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences