It is fairly easy to find such mappings. Call the carried data the key. XOR the key data with any other image to get the encrypted file. Simply XOR the encrypted file with the key file to get the desired image.
Finding small mappings is another matter.
- I carry a large number y with me
- the police demands that I disclose y, and I do; they apply inverse mapping f^{-1} and obtain x = f^{-1}(y) which is a porn image
- then I show the police that applying inverse mapping g^{-1}, one obtains a totally legit image z = g^{-1}(y)
Of course, finding such a mapping g could be extremely difficult, but if the same number can be obtained from two different images, how would the police be able to accuse me of anything?