Efficient RKA-secure KEM and IBE schemes against invertible functions

We propose efficient KEM and IBE schemes secure under the related-key attacks RKAs against almost all invertible related-key derivation RKD functions under the DBDH assumption. The class of RKD functions we consider is broader than the best known RKD function class: For example, the class contains polynomial functions of bounded polynomial degrees and the XOR functions simultaneously.