Methods for supplying deficiency of a key in a set of keys stored in devices includes receiving information (key values) on the keys from each device. Each key is assigned to a node or pair of nodes in a tree structure(s). If a position of a key in the tree structure in a first set of keys is stored in a first device with its value and corresponds to a position of a key in the tree structure in a second set of keys stored in a second device with its value, the first device and the second device are grouped together. Where there is a missing key in the first set of keys, a key corresponding to the missing key from the second set of keys is found, or a key common in the first set of keys and the second set of keys is found.