A public-key-encryption data-communication system includes a public-key-certificate issuer authority. The public-key-certificate issuer authority performs the issuance of a public key certificate and management operations, certification of a subject to be certificated, which is a certificate issuing request, and management such as registration processing are executed by a root registration authority or each registration authority. The public-key-certificate issuer authority performs processing for validating, invalidating, and deleting the certificate in accordance with a request from the root registration authority. The root registration authority accepts a request for issuing a public key certificate corresponding to the subject to be certificated which is under the control of a certificated registration authority, and transfers it to the public-key-certificate issuer authority in a form in which a signature is added to it. Processes by the public-key-certificate issuer authority, the root registration authority, the registration authority are separated, whereby the need for new implementation of user recognition, certificate issuance, registration, and management is eliminated.