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Someone please correct me if I'm wrong, but there's no proof that a general solution to elliptic curve discrete logarithm problem can't be found.

It's reasonable to assume that a solution hasn't been found yet though, otherwise that would be the world's best kept secret.

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Shor's algorithm, originally designed for integer factorization, can also be adapted to solve the discrete logarithm problem in polynomial time on a quantum computer. There is also the less efficient Grover's algorithm can also be used for unstructured search problems on a quantum computer.

I was thinking more along the lines of solving in polynomial time on a conventional computer.

That's downstream of P vs NP.

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