Journal of Applied Mathematics
Volume 2011 (2011), Article ID 580749, 11 pages
http://dx.doi.org/10.1155/2011/580749
Research Article

Analysis of the Fault Attack ECDLP over Prime Field

Mingqiang Wang and Tao Zhan

School of Mathematics, Shandong University, Jinan 250100, China

Received 17 May 2011; Revised 27 August 2011; Accepted 12 September 2011

Academic Editor: Tak-Wah Lam

Copyright © 2011 Mingqiang Wang and Tao Zhan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In 2000, Biehl et al. proposed a fault-based attack on elliptic curve cryptography. In this paper, we refined the fault attack method. An elliptic curve 𝐸 is defined over prime field 𝔽 𝑝 with base point 𝑃 ∈ 𝐸 ( 𝔽 𝑝 ) . Applying the fault attack on these curves, the discrete logarithm on the curve can be computed in subexponential time of 𝐿 𝑝 ( 1 / 2 , 1 + 𝑜 ( 1 ) ) . The runtime bound relies on heuristics conjecture about smooth numbers similar to the ones used by Lenstra, 1987.