Thanks for wording it more precisely than I did. Most people are assuming that the mapping tuple -> number is known, while I am not. I could come up with my own invertible mapping. The cool thing would be this:
- 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?
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.
You could choose to represent an image as image data + decoding scheme, using an agreed representation of the decoding scheme such as a computer program. Mathematically we get nowhere because we are simply moving the encoding scheme around, but in practice, since we possess concrete encoding schemes it means we can practically discuss the situation better.
This is a long-winded away of agreeing with you, BTW.