Functional Encryption for Set Intersection in the Multi-Client Setting
Functional encryption for set intersection (FE-SI) in the multi-client environment is that each client i encrypts a set Xi associated with time T by using its own encryption key and uploads it to a cloud server, and then the cloud server which receives a function key of the client indexes i, j from a trusted center can compute the intersection Xi ∩X j of the two client ciphertexts. In this paper, we first newly define the concept of FE-SI suitable for the multi-client setting. Then, we propose an efficient FE-SI scheme in asymmetric bilinear groups and prove the static security of our scheme under newly introduced assumptions. In our FE-SI scheme, a ciphertext consists of O(`) group elements, a function key consists of a single group element, and the decryption algorithm has O(`2) complexity where ` is the size of a set in the ciphertext. Next, we propose another FE-SI scheme with time-constrained keys that limits the ability of function keys to be valid only for a specified time period T , and proves the static security of our scheme. Finally, we prove that the two assumptions hold in the general group model to provide confidence in the two newly introduced assumptions.