| 摘要 |
The cryptographic scheme subdivides time into periods with an index j=0, 1, 2, etc. A public key indicates elements u and v of a first cyclic group G1 of prime order p and, for each period j, an integer sj between 0 and p−1 and elements g1,j of the group G1 and g2,j, wj and hj of another cyclic group G2 of order p. The private key of a member of the group indicates an integer xi between 0 and p−1 and, for each period j, an element Ai,j of the group G1 such that Ai,n=[Ai,n-1/g1,n-1]1/(xi−sn) for 1≦̸n≦̸j. To sign a message during a period j≧0, the member selects two integers α and &bgr; between 0 and p−1, calculates T1=uα, T2=Ai,j·vα, S1=g2,j&bgr; and S2=e(Ai,j, hj)&bgr; where e(., .) is a bilinear map of G1×G2 onto GT, and determines according to the message the data that justify the fact that the elements T1, T2, S1 and S2 are correctly formed with knowledge of the private key of the member for the period with index j. |
