The question posed came about during a 2nd Year Comp Science lecture while discussing the impossibility of generating numbers in a deterministic computational device.
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I would sooner use something like ISAAC as a stronger PRNG before trusting round trip pings as entropy. As others have said, it would just be too easy for someone to not only guess your numbers, but also possibly control them to various degrees.
Other great sources of entropy exist, which others have mentioned. One that was not mentioned (which might not be practical) is sampling noise from the on board audio device.. which is usually going to be a little noisy even if no microphone is connected to it.
I went 9 rounds with trying to come up with a strong (and fast) PRNG for a client/server RPC mechanism I was writing. Both sides had an identical key, consisting of 1024 lines of 32 character ciphers. The client would send AUTH xx, the server would return AUTH yy .. and both sides knew which two lines of the key to use to produce the blowfish secret (+ salt). Server would then send a SHA-256 digest of the entire key (encrypted), client knew it was talking to something that had the correct key .. session continued. Yeah, very weak protection for man in the middle, but a public key was out of the question for how the device was being used.
So, you had a non blocking server that had to handle up to 256 connections .. not only did the PRNG have to be strong, it had to be fast. It wasn't such a hardship to use slower methods to gather entropy in the client, but that could not be afforded in the server.
So, I have to ask regarding your idea .. how practical would it be?