Checksum algorithm is typically used to ensure that the binary of the files downloaded over the net matches the original ones. I am not quite familiar with its details but you can look it up on google.
However, checksum does not prevent people from altering your files.
You can also digitally sign the files. Use PGP or GNU's GPG programs. The recipients can check for the files signature, and it will flag if the files are altered or corrupted.
By "watermarking" do you mean adding an invisible signature added to the media, imperceptible to the eye, but made so that an algorithm can detect it? This is a method of marking something so that you can detect later if someone steals it for their own published or commercial use.
The methods to watermark video and audio are very different because to make such a mark imperceptible you have to alter the data in a way that is specific to the type of the media. If you tried to put a video watermark on an audio file, you would probably perceive the alteration.
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