Shredded paper could be wetted and then put into a compost bin. It would need some green stuff with it to rot it quickly.
Smelly, but possibly effective answer. Soak it with water and chuck some pelleted chicken manure in there. It should only take a day or so for it to be sodden. Tip resultant mix into compost with as much green stuff as you can muster, cover it and see what happens. If you don't let the heap dry out, that will be beneficial. Chicken manure is very high in nitrogen and will help kick things off.
If you need green stuff to compost, you could cut any long grass around your allotment site and use that, or leafy tops of nettles, docks and the like. Soaking anything you have doubts about for a few weeks makes sure it doesn't sprout, but is smelly.
I have been known to scavenge off our communal dumping ground at my site as well. You often find people have dumped useful stuff. I got a whole barrow load of cleared crop material the other week. Before you write me off as completely sad, mad or dangerous to know, I was put onto it by a fellow plot holder, who has discovered the same trick and was filling his barrow with the same intentions of adding it to compost bins