Analysis of the Fault Attack ECDLP over Prime Field

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 p with base point P∈E(p). Applying the fault attack on these curves, the discrete logarithm on the curve can be computed in subexponential time of Lp(1/2,1+o(1)). The runtime bound relies on heuristics conjecture about smooth numbers similar to the ones used by Lenstra, 1987