Analysis of the fault attack ECDLP over prime field (Q410803)

Summary: \textit{I. Biehl} et al. [Crypto 2000, Lect. Notes Comput. Sci. 1880, 131--146 (2000; Zbl 0989.94505)] 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 \(\mathbb F_p\) with base point \(P \in E(\mathbb F_p)\). 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 \textit{H. W. Lenstra jun.} [Ann. Math. (2) 126, 649--673 (1987; Zbl 0629.10006)].