The invention provides a method for verification having a structure that reflects reliability of a signature history properly for a hysteresis signature used for verification based on the signature history, and provides a method for arbitration and an arbitrator apparatus that solve a dispute on correctness of a signature based on the method for verification. Furthermore, the invention provides a method for managing history that mitigates the signature history management burden on a signer. Reliability is set on a signature forming record that is a component of a signature history, reliability of the signature history is calculated based on the set reliability, and the calculated reliability is output as reliability of a verification result. The invention provides a method for verification having a structure that reflects the reliability of a signature history properly and a method for arbitration and an arbitrator apparatus that solve a dispute on correctness of a signature. Furthermore, providing a signature history storage service apparatus mitigates the signature history storage burden on a signer.