The does-not-leak-information property doesn't depend on the discrete log assumption, but the binding property does. I.e., if you have an oracle that solves the

The does-not-leak-information property doesn't depend on the discrete log assumption, but the binding property does. I.e., if you have an oracle that solves the discrete log problem you can now open commitments in different ways, but if someone else generates a commitment you still can't tell what their secret input was. One thing I found useful is section 2.2 of https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf https://crypto.stanford.edu/~dabo/papers/RSA-survey.pdf, on blinding in RSA.