To provide an image processor capable of increasing the number of updates compared with the conventional one even when a periodic update processing interval of a unique key is prolonged compared with the conventional one.

(1) When a device generates or installs a paired key in the case of no key pair, it generates a unique key and stores a secret key of the key pair by encrypting it. (2) When the device generates or installs the second or later key pair, it stores the secret key by encrypting it with the unique key prepared in (1). (3) Paired keys of the device can be deleted by user operation and periodic processing. The unique key can be also deleted at the timing of deleting the last one key pair.