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I need a checksum/fingerprint function for short strings (say, 16 to 256 bytes) which fits in a 24 bits word. Is there any well known algorithm for that?
I propose to use a 24-bit CRC as an easy solution. CRCs are available in all lengths and always simple to compute. Wikipedia has a matching entry. The quality is far better than a modulo-reduced sum, because swapping characters will most likely produce a different CRC.
The next step (if it is a real threat to have a wrong string with the same checksum) would be a cryptographic MAC like CMAC. While this is too long out of the book, it can be reduced by taking the first 24 bits.