Can browsers connect to a proxy over SSL/TLS?

If I set up a proxy (such as Squid for example) configured with certs to listen for HTTPS are browsers able to connect to the proxy over TLS/SSL?

Example of what I'm asking:

Browse开发者_JAVA百科r Proxy Server yahoo.com -> TLS -> Squid -> HTTP -> yahoo.com

I've set up a proxy listening on 443, but am not having success getting browsers to use it (connecting to the http proxy on port 80 works fine).

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Chrome can do that: http://www.chromium.org/developers/design-documents/secure-web-proxy

It also supports a directive in PAC file to point to HTTPS proxy.

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If you want to secure your communication between browser and proxy, use STunnel (SSL tunneling) or VPN or SSH tunnel to the "proxy" server, then run your communication over this secure tunnel. I.e.:

Browser -> STunnel on the client -> STunnel on the server -> Squid Proxy -> Remote host

To answer your direct question - what you want is for the browser to act in a similar way to STunnel itself. I don't know a browser or even HTTP/HTTPS component (if we are on a programming site) to work this way.