Elliptic curves are uniformly hard. If you could solve the elliptic curve discrete log problem (ECDLP) on any non-negligible fraction of inputs, then you'd break a lot of cryptography. In fact, the use of Pedersen commitments is based on nobody knowing the logarithm log(H) of a specific curve point H with respect to the standard base G. An efficient algorithm for solving ECDLP on a non-negligible fraction of inputs, could fail on input H, but one would eventually work on some random input r * H for a randomly picked scalar r, giving log(H) as log(r * H) / r.