I'm not a hardware designer but I routinely deal with low level networking shenanigans and I must admit that I never considered that it would be possible to update a CRC without recomputing it fully (unless you were just appending data of course).

For people like me who aren't smart enough to figure it on their own, this stackexchange answer seem to explain how it's done: https://cs.stackexchange.com/questions/92279/can-one-quickly...