Authentication method and apparatus using pairing functions for the elliptic curves based cryptosystems

摘要

A first party (60) has a first (s1) and a second (P,RTA1) cryptographic key. A second party (70) has a third ("TA2") and a fourth (s1QTA2) cryptographic key, the fourth cryptographic key (s1QTA2) being derived from the first (s1) and third ("TA2") cryptographic keys thereby providing an association between the parties (60,70). To enable a third party (90) to verify the existence of an association between the first and second parties (60,70), the second party generates a number (r) that in association with the second cryptographic key (P,RTA1), the third cryptographic key ("TA2") and the fourth (s1QTA2) cryptographic key define a first cryptographic parameter (X), a second cryptographic parameter (Y) and a third cryptographic parameter (Z) respectively. By using these parameters and the second and third cryptographic keys, the third party (90) can verify if the first and second parties (60,70) are associated.