Abstract: A client's secret key is Ki=(s+Ii)?1P where Ii is obtained by using a collision-resistant hash function h to process client IDs with respect to the secret numbers s and r and the parameters P and Q of a secret on an elliptic curve E. The session key Ks that encrypts the message m is Ks=enc(P,Q)rk and the header is constituted by H1=k ?i=1?N(s+Ii)R=k?i=0?NcisiR, H2=k(rP), S={I1,I2, . . . , IN}. The client restores the session key by means of A/B=en(P,Q)rk?j=1?N,j?iIj, (A/B)?j=1?N,j?iIj?1=Ks from A=en(Ki,H1)=en((s+Ii)?1P,k?i=1?N(s+Ii)R) and B=en(H2,?j=1?N,j?i(s+Ij)Q??j=1?N,j?iIjQ)=en(P,Q)rk?j=1?N,j?i Ij.

Abstract: Mapping is carried out at a point on an elliptic curve to be utilized for elliptic encryption based on identity information (ID information) of each entity and a mapping value is set to be a public key of the entity. By using the mapping value and secret information, a secret key of each entity is generated. The entity generates a common key to be used for an encrypting process and a decrypting process by utilizing the self-secret key and the public key to be the mapping value obtained by mapping at a point on the elliptic curve based on ID information of a communication participate. In this case, pairing on the elliptic curve is utilized.