To obtain a safe and highly convenient computer communication system by which it is recognized whether communication is the one by means of a legal subscriber or not and illegal communication is prevented by updating communication recognizing signals which are respectively held in first and second communication systems at every prescribed unit of communication in accordance with a fixed algorithm.

The first communication system is constituted of a personal computer having a means for reading/writing in a portable storage medium and the second communication system is constituted of a center having the storage means of the communication recognizing signals together with an ID number and a password. The center generates the communication recognizing signal at every communication and re-writes the communication recognizing signal of the portable storage medium at the side of the personal computer and the communication recognizing signal of the storage means at the side of the center. The communication recognizing signals are calculated based on a last-time communication result. For example, the personal computer and the center can independently update the communication recognizing signals through the use of the last communication time and communication start time.