A radio communications system includes radio devices, and antenna and an array antenna. The radio devices communicate a prescribed signal via the antenna and the array antenna in a system of transmission and reception at a single frequency, such as time division duplex, as the array antenna changes the in directivity to form a plurality of directivities. The radio devices detect a plurality of received radio waves' strength to produce receive signal profiles, respectively, indicating a plurality of strength profiles. The radio devices multivalue strength of the receive signal profiles, respectively, and generate private keys having the multivalued plurality of values serving as a bit pattern.