I am building a small embedded system of two nodes that communicate wirelessly. The microcontrollers I'm using are very limited: they only have 256 bytes of RAM. I would like to be able to authenticate messages sent and received between the nodes, but traditional methods such as HMAC aren't possible because of the constraints of the system (lack of RAM).
I do have a large (2 megabit) EEPROM that is largely unused. I would like to use this space to store a (relatively) large one-time pad that could be used to authenticate the messages, which are only a few bytes long. I do not care about the secrecy of the messages, only their unforgeability and integrity. If only, say, 4 bytes of pad are used per message, the pad should far outlast the system's expected usefulness. Finally, messages are not guaranteed to be received by the other node (for example, due to interference, malicious or not).
Are there any schemes that use a one-time pad for message authentication? Assume the one-time pad is truly random. Or is this an entirely hair-brained idea that is inherently insecure?