A program with complete conditions for a usable mask yields a unitary mask, each try. A ticket issuance device computes document private information from a private function f of an interaction device owned by a user and document m to be transferred to the interaction device when generating interaction, and issues ticket t generated from authentication characteristic information x and the document private information to the user. A novel scanning algorithm, which performs multiple scans at different velocities, enables accurate PMD measurements, even of moving optical cable.