Abstract: Plurality of users share a common key while permitting dynamic member change and computational complexity required for key exchange is reduced. The first key generation unit computes Ri and ci based on a twisted pseudo-random function. A session ID generation unit generates sid based on a target-collision resistant hash function and transmits (sid, R?, R?) to communication devices Ui. A second key generation unit of a representative communication device U1 computes T1 based on a pseudo-random function. A second key generation unit of general communication devices Uj computes Tj based on the pseudo-random function. A third key generation unit computes k? based on the twisted pseudo-random function and computes T?j with respect to each j. A session key generation unit of the general communication devices Uj computes Kjl and k1. The session key generation unit generates a common key K2 based on the pseudo-random function.