1. An information gathering system comprising: a first processor, provided at a transmitter side node, configured to generate a collective identifier from one or a plurality of individual identifiers of respective management targets by performing a reduction operation, each of the individual identifiers being generated according to a state of a corresponding management target; and a second processor, provided at a receiver side node, configured to restore an individual identifier from the collective identifier and specify a management target based on the restored individual identifier, the first processor outputs a first parameter according to whether the transmitter side node is an origin node on a network, when the transmitter side node is the origin node on the network, the first parameter is an identity element in the reduction operation, and when the transmitter side node is not the origin node on the network and the transmitter side node receives an identifier from another node, the first parameter is the received identifier, the first processor outputs a second parameter according to whether a condition in which information should be reported is satisfied at a management target managed by the transmitter side node, when the condition is satisfied at the management target, the second parameter is an individual identifier specific to the management target, and when the condition is not satisfied at the management target, the second parameter is an identity element in the reduction operation, the first processor generates the collective identifier by performing the reduction operation on the first parameter and the second parameter, a length of the collective identifier is shorter than a sum of a length of the first parameter and a length of the second parameter, and the second processor restores the individual identifier that is a generation factor of the collective identifier from the collective identifier, and restores information of the management target from the restored individual identifier.