Abstract: In the present invention, scope search can be effectively performed in a database having encrypted registration information. A plurality of values, first identification information to identify the plurality of values, and a key are accepted as input. A value group is generated from the plurality of values. The value group is treated as a word group, and a secure index is generated from the word group, the first identification information, and the key. On the basis of a value to be retrieved and a key, trapdoor information for the value to be retrieved is generated. With respect to the generated secure index, a secure index assessment process is performed using the trapdoor information. When the value to be retrieved is assessed to be contained in the secure index as a result of the assessment process, second identification information to identify the secure index is output.

Abstract: The system of the present invention includes a first radio station and a plurality of second radio stations that communicate via a limited radio resource having a limited time slot and a limited frequency band allocated in advance. The first radio station performs control not to request the plurality of second radio stations to re-transmit transmission data when detecting a receive error in the transmission data from the plurality of second radio stations to the first radio station. Each of the plurality of second radio stations performs control, when detecting a receive error in transmission data from the first radio station to the second radio station, not to request the first radio station to re-transmit the transmission data in which the receive error has been detected, but to receive the transmission data re-transmitted according to a upper layer protocol from a communication partner radio station with which communication on the upper layer has already been established.