As an experiment I divided the product of two images (A and B) by one of the factor images (A) to unlock the other factor image (B)
I grabbed the images from my own web site, so they were 8-bit sRGB
compressed jpegs to begin with.
You can see some round-off error
in the quotient image.
I keep meaning to use this to divide a photo by a white diffuse Maxwell simulation of the photo in order to derive a good texture map that when lit will look pretty much like the original photo. The goal is to avoid re-lighting the lighting already in the photo.
You could heavily watermark your images on your web site and provide
certain people with the key image that unlocks the watermark.
Can you think of any other blend modes for which this would work? This entry uses Multiply / Divide.
Linear Dodge (ADD) / Subtract would be a logical choice if Photoshop allowed negative color numbers like Nuke or Shake does.
Any other mutually undoable blend mode pairs?