Is it legal to surf the web through these proxies?

As far as we can tell, the answer is yes.

The primary argument against open proxies is that their owners may not have intended for them to be used by the public. However, intent is a difficult thing to judge, especially when you're talking to a computer. By running a service on a machine accessible to the public, without restricting access to that service, a proxy's administrator is not explicitly denying that service to the public.

In a sense, a proxy server is just like a web server, an FTP server, or any other net service: if it's running and accepting connections, it's fair game. The internet is a public network, and if you're running a server you can hardly be surprised when someone uses it.

With regard to US law in particular, 18 USC 1030 (which covers computer-related fraud and theft) applies only when the user has knowingly accessed a computer without authorization or has knowingly exceeded his authorized access on that computer.

Because an open HTTP proxy allows connections and use of the service by anyone in the world, it would seem that the public at large has been "authorized" to use the service. There's no intentional bypassing of security taking place. Just as you don't need Google's express written permission to connect to google.com, you don't need a proxy admin's express written permission to use his open proxy server.

Naturally it's not legal to use a proxy for illegal purposes, but if that's your cup of tea, the proxy is probably the least of your worries.

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