Place cubed daikon in a bowl. Add kosher salt and toss to coat. Pour water carefully down the side of the bowl just to the level of the radishes; take care not to rinse all of the salt off. Cover with plastic wrap and set in a cool place for 12 to 24 hours.
Drain the radishes and rinse thoroughly. Add Korean red pepper paste, ginger, Korean red pepper powder, fish sauce, sugar, and garlic. Mix thoroughly. Cover the container with plastic wrap or a lid and put it in a cold place. Allow to ferment for 4 to 6 weeks.
