If all they are looking for is unbreakable encryption...
...why don't they just fill a few G of durable ROM with random bytes. Duplicate it one time. Use the random bytes as mini keys. Encrypt each byte of the data stream with a different key (the next succesive one on the ROM).
As long as no one gets their hands on one of the ROMs, they can't break the code.
To make it even more secure, allow for key changes: signal the remote encryptor to skip to any particular location of the ROM and resume from there. Note that no actual key, encrypted or clear, need ever be transmitted.