First, forget about the idea to use this approach for web-browsing.
If you want to circumvent censorship while browsing TOR is your way, but can't provide full censorship-freedom.
TOR works by establishing a tunnel through the internet (changed evey 10min) via three servers where the first received triple-encrypted contenet, the second double-encrypted and the last "only" single encrypted. The last one forwards the request to the clearnet.
Expect latencies for this around 500ms+ (Haven't done tests).
In fact, if you look for something like E-Mail-Style communication, there's a solution for you. Bitmessage. It works as follows:
- Obtain the address of the recipient, which is a public EC key.
- Encrypt the message using his public key and sign the message before using your private key (which is bound to your address).
- Send the message into the P2P network. It will stay there for 2-30 days.
- Every client will download your message and try to decrypt it using their private keys. If decryption fails, the message is considered "not for them" and discarded. Only the valid recipient can learn the message.
Now some notes to this: The sender by default isn't fully anonymous, as the message may be traced back, but TOR and dedicated address generation provides a high degree of privacy.
If you're interested in this, IIRC bitmessage uses ECIES + ECDSA on P-256.
And to address the DDoS issue raised in another answer, bitmessage is inspired by bitcoin and uses a proof-of-work system to prevent flooding of the network and to get a "message lifetime" (more PoW -> more lifetime).