Considerations about the future of ECC

Now that we have seen how a practical attack on ECDSA works, one of the most interesting questions we should ask for the future is the following:

Is elliptic curve cryptography resistant to classical and quantum attacks?

At a glance, the answer could be that most elliptic curves are not vulnerable (if well implemented) to most traditional attacks, except for the same ones we find against the classic discrete logarithm (such as Pollard Rho or a birthday attack) and man-in-the-middle attacks in D–H ECC.

In the quantum case, however, Shor’s algorithm can probably solve the elliptic curve problem, as we will see in the next chapter, dedicated to quantum cryptography.

Thus, if someone asks: Are my Bitcoins secured for the next 10 or 20 years? We can answer, Under determinate conditions, yes, but if the beginning of the quantum-computing era generates enough qubits to break the classical discrete logarithm problem, it...