In a food processor, finely chop the ginger. Transfer to a saucepan, add the salt and water and bring to a boil. Simmer over moderate heat for 10 minutes. Strain the ginger broth through a fine sieve, discarding the ginger. Return the broth to the saucepan and bring to a boil. Add the shrimp and cook over high heat just until opaque, about 1 minute. Remove the shrimp to a plate with a slotted spoon and let cool. Let the cooking liquid cool too, then add the shrimp and refrigerate until chilled, at least 30 minutes. Drain the shrimp and pat dry.