Functional encryption for cubic polynomials and implementation

Abstract Functional encryption (FE), which provides fine-grained access control on encrypted data, is becoming a new hot spot in the field of cryptography. Recent applications, such as outsourcing computation, searchable encryption and so on, suggest that FE has unlimited possibilities. It especially shows great feasibility to construct indistinguishability obfuscation and reuseable garbled circuits. Furthermore, bounded collusion functional encryption is an extension of FE which is against more than one key query and protects the security of messages under more than one function keys. In this paper, we proposed a bounded collusion FE for cubic polynomials, which follows from Agrawal and Rosen's work on TCC 2017. Our construction only invokes the Regev public key encryption and a linear FE scheme which avoids complex encodings defined recursively. What's more, we proposes an FE scheme for all circuit with FULL-SIM security. Finally, we also implement these schemes and do some analyses on parameters' size, time and space performance.