I have a device that signs (symmetrically) very short messages, and I would like to sign a long one.
I split it into several short messages, signed each one separately, and now combine all the signatures. Of course, the trivial way is to concatenate them, but is there a way to have the combined signature of the same length as the individual ones?
It doesn't seem easy to protect from rearranging the pieces in a different order (hashing the whole sequence of sequences is not considered easy in my case).
However, the device covers by the signature not only the message but also the running index of the messages it signs. Now, it is evident that the straightforward xor of the piecewise signatures is a perfect signature of the whole message.
Has anybody encountered anything like this in theory or practice?