If you dig up and store in your basement, check them a couple of times over winter. I do this with all my stored bulbs, corms, tubers etc. If they are rotting - toss em. If they look like they are drying out, mist them lightly and let them set out for a day or so, then re-store them. Some people store them in slightly moist media such as peat moss. I don't do this. I have historically had more problem with rot than drying out.
I store mine in either chopped up paper, vermiculite, perlite or peat moss. Some people just store them in paper bags.
Do NOT sore in plastic bags or plastic containers. They need to have circulation.
Mine were still doing well til I cut them down on Sunday when I also cut and dug my Elephant Ears and Hardy Banana. They were gonna get nailed this week-end anyway - low of 21 forecast.