Supplies of deficiency of a key in information on a set of keys

A method for supplying deficiency of a key in information on a set of keys stored in a device, the method comprising:

• receiving the information on a set of keys from each of a plurality of devices, wherein the information on the set of keys includes a plurality of key values, each key in the set of keys being assigned to a node among nodes in a tree structure, and the set of keys having one or more missing keys;
• in a case where a position of a key or each key in the tree structure in a first set of keys stored in a first device among the plurality of devices and a value of this key correspond to a position of a key or each key in the tree structure in a second set of keys stored in a second device among the plurality of devices and a value of this key, respectively, grouping the first device and the second device together;
• and
• in a case where there is a missing key in the first set of keys, finding a key corresponding to the missing key from the second set of keys or finding a key common in the first set of keys and the second set of keys.