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.

功能加密（FE）为加密数据提供细粒度的访问控制，正成为密码学领域的新热点。最近的应用，如外包计算、可搜索加密等，表明有限元具有无限的可能性。尤其显示出构建不可区分混淆和可重用乱码电路的巨大可行性。此外，有界共谋功能加密是有限元的一种扩展，它针对多个密钥查询，保护多个功能密钥下的消息安全。在本文中，我们根据 Agrawal 和 Rosen 在 TCC 2017 上的工作提出了三次多项式的有界共谋有限元。我们的构造仅调用 Regev 公钥加密和避免递归定义的复杂编码的线性有限元方案。全 SIM 卡安全。最后，我们还实现了这些方案，并对参数的大小、时间和空间性能进行了一些分析。