Say Alice have 4GB USB flash memory and Peter also have 4GB USB flash memory. They once meet and save on both of memories two files named alice_to_peter.key (2GB) and peter_to_alice.key (2GB) which is randomly generated bits. Then they never meet again and communicate electronicaly. Alice also maintains variable called alice_pointer and Peter maintains variable called peter_pointer which is both initially set to zero.

Then when Alice needs to send message to Peter they do:

encrypted_message_to_peter[n] = message_to_peter[n] XOR alice_to_peter.key[alice_pointer + n]

Where n i n-th byte of message. Then alice_pointer is attached at begining of the encrypted message and (alice_pointer + encrypted message) is sent to Peter and then alice_pointer is incremented by length of message (and for maximum security can be used part of key erased)

Peter receives encrypted_message, reads alice_pointer stored at beginning of message and do this:

message_to_peter[n] = encrypted_message_to_peter[n] XOR alice_to_peter.key[alice_pointer + n]

And for maximum security after reading of message also erases used part of key. - EDIT: In fact this step with this simple algorithm (without integrity check and authentication) decreases security, see Paulo Ebermann post below.

When Peter needs to send message to Alice they do analogical steps with peter_to_alice.key and with peter_pointer.

With this trivial schema they can send for next 50 years each day 2GB / (50 * 365) = cca 115kB of encrypted data in both directions. If they need more data to send, they simple use larger memory for keys for example with today 2TB harddiscs (1TB keys) is possible to exchange next 50years 60MB/day ! (thats practicaly lots of data for example with using compression its more than hour of high quality voice communication)

It Seems to me there is no way for attacker to read encrypted message without keys even if they have infinitely fast computer. because even with infinitely fast computer with brute force they get ever possible message that can fit to length of message, but this is astronomical amount of messages and attacker dont know which of them is actual message.

I am right? Is this communication schema really absolutely secure? And if its secure, has this communication method its own name? (I mean XOR encryption is well-known, but whats name of this concrete practical application with use large memories at both communication sides for keys? I am humbly expecting that this application has been invented someone before me :-) )

Note: If its absolutely secure then its amazing because with today low cost large memories it is practicaly much cheeper way of secure communication than expensive quantum cryptography and with equivalent security!

EDIT: I think it will be more and more practical in future with lower a lower cost of memories. It can solve secure communication forever. Today you have no certainty if someone succesfuly atack to existing ciphers one year later and make its often expensive implementations unsecure. In many cases before comunication exist step where communicating sides meets personaly, thats time to generate large keys. I think its perfect for military communication for example for communication with submarines which can have installed harddrive with large keys and military central can have harddrive for each submarine they have. It can be also practical in everyday life for example for control your bank account because when you create your account you meet with bank etc.