Quantum algorithm for elliptic curve's private keys Is there a quantum algorithm to find private keys generated using elliptic curves ?
Shor's algorithm, which runs only on quantum computers, solves all discrete-logarithm problem instances over all groups.

This obviously includes the elliptic curve discrete logarithm problem at the heart of ECDH, ECDSA and ECIES. For a more detailed discussion of the details, see this recent paper.

However, there are things we can do with elliptic curves that are believed to which we don't know better quantum algorithms, like elliptic curve supersingular isogeny-based key exchanges.