Checksumming filesystems and file transfer protocols cover many cases. SCP, rsync, btrfs, and zfs all fix this problem.
As for guaranteeing the computed data is correct: I know space systems often have two redundant computers that calculate everything and compare results. It's crazy expensive and power demanding, but it all but solves the problem.
Usually they have an odd number. The Space Shuttle had five, of which the fifth was running completely different software. In case of a 2/2 split the crew could shut down a pair (in case the failure was clear) or switch to the backup computer.
As for guaranteeing the computed data is correct: I know space systems often have two redundant computers that calculate everything and compare results. It's crazy expensive and power demanding, but it all but solves the problem.