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As far as I know, and please correct me if I'm wrong, I can connect to an https site (assuming the whole page is https) while using a free proxy server I find on the web (and entered into Firefox's proxy settings), completely securely. The only thing the proxy will know is the domain I'm connecting to. Nothing else. It won't know the passwords I'm typing, nor even the exact page or query string following the domain.
Is there ANYTHING that I need to do to ensure that is the case, or is that automatic by the nature of https?