With the massive diffusion of cloud computing, more and more sensitive data is being centralized into the cloud for sharing, which brings forth new challenges for the security and privacy of outsourced data. To address these challenges, the server-aided access control(SAAC) system was proposed. The SAAC system builds upon a variant of conditional proxy re-encryption(CPRE) named threshold conditional proxy re-encryption(TCPRE). In TCPRE, t out of n proxies can re-encrypt ciphertexts(satisfying some specified conditions) for the delegator(while up to t-1 proxies cannot), and the correctness of the re-encrypted ciphertexts can be publicly verified. Both features guarantee the trust and reliability on the proxies deployed in the SAAC system. The security models for TCPRE were formalized, several TCPRE constructions were proposed and that our final scheme was secure against chosen-ciphertext attacks was proved.
