If you want to determine whether a file has undergone format conversion, I'd venture that no algebraic approach (such as squaring over integers modulo $p$) is likely to be directly useful.
Assume the standard POW settings, so my understanding is that someone who has converted file.wav to file.mp3 is to use proof of work to demonstrate this conversion to another party.
Also, under the standard setting, one cannot just display the two files which a second party can check are two encodings of the same clip. The mechanism is used to stop spammers, so last thing we want is for them to submit the two files for someone (the spam target) to check.
There are at least two problems with this idea:
- POW can demonstrate the quantity of work done but not the aim of the work done.
- The actual algorithm for the conversion, regardless of what kind of encoding is used, cannot be usefully converted to an algebraic function with the properties required for POW, such as a Fiat-Shamir type of function, e.g., squaring modulo an integer.