Yeah, I'd strongly, strongly, in fact plead for people not to try this challenge. When it comes to 'compressing' random data: every single bit in random information is 'significant.' I am quite sure that the problem is logically meaningless, mathematically impossible, and a complete waste of effort. But more-so: if it weren't a waste of effort (it is) - I would still highly doubt any algorithm existed that was more efficient than brute force search. In this case -- the search for a function that solves the constraints is going to be like trying to brute force a cryptographic private key value. Simply because every 'bit' of entropy is valuable information.
Now lets look at how modern compression actually: works. Images, movies, text-documents, audio files... there is fundamental --structure-- in all this data. In text it might be using only a certain character range, a certain lexical word list, and so on. There may be geometric information in images and movies that could be turned into code to drastically cut down file size. With audio -- you can sample it and discard what you don't need. And so on and so fourth. Structure. But how do you apply any of these methods to random data? There is no structure, you can't sample it, reduce it, simplify it... Every bit has meaning.
So please, dear human thinking about compression of random data. It is an insane waste of intellectual effort. It's impossible. Don't do it. I made the same mistake (and setup vast amounts of HPC to work on algorithms.) COMPLETE. Waste of time.