Move data from NIOS to hardware and then back to NIOS

It depends on the kind of performance that you want. You can create an Avalon slave interface and have the CPU write all the integers one by one to your hardware. But if the only thing your hardware does is a multiplication I don't think it ill be a lot faster than doing it in software.

If you want a bettor performance it makes sense to use a DMA that will read the integers from your memory and give them to your custom hardware.

I'm not a Verilog expert, but I think that if you do a search on the forum you should find some Verilog templates for Avalon slave interfaces.