Any EXIF tag you set (including custom ones) can be altered by anyone who wants to. It's completely insecure and unreliable.
Typically in IT if you want to ensure the secure of a file (that it's not a tampered version), you'd use a file checksum, as explained briefly here. Essentially you create a separate file which lists computed values that have a high probability of being unique for each file. If you need to compare a file to your existing version, you can compute the checksum for the new file and see if it matches your existing values.
But that won't be useful to compare files which are e.g. resized. For that you need dedicated image processing tools and some clever thinking.
Using Imagemagick's compare functionality is probably the most easily available approach and you can get as complex or simple as you like with it.
If you scroll down that page you'll see quite a lot of info about various strategies and methods for comparing two images.