Invalid-curve attacks on (hyper)elliptic curve cryptosystems

Koray Karabina; Berkant Ustaoglu

doi:10.3934/amc.2010.4.307

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2010, Volume 4, Issue 3: 307-321. Doi: 10.3934/amc.2010.4.307

This issue Previous Article Next Article Linear programming bounds for unitary codes

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
2.
NTT Information Sharing Platform Laboratories, 3-9-11, Midori-cho Musashino-shi, Tokyo 180-8585

Received: May 2009

Revised: January 2010

Published online: August 2010

Abstract / Introduction Related Papers Cited by

Abstract

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:

Invalid-curve attacks,
hyperelliptic curves.

Mathematics Subject Classification: 94A60.

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