In a mixing bowl, combine the salt, sugar, and white pepper. Place the salmon on a wire rack, skin side down. Place a sheet tray under the rack. Pack the salt mixture over the salmon fillet and place heavier amounts of the salt on the thicker part of the fillet and lesser amounts on the tail section. Pack the chopped dill on top of the salt mixture. Let the salmon chill, covered, for 48 hours.

Remove dill and salt mixture from salmon fillet. Do not rinse with water. Slice the cured salmon thinly and serve on toasted bread as an appetizer or on a sandwich.