This paper presents a fully secure (adaptively secure) practical functional encryption scheme for a large class of relations, that are specified by non-monotone access structures combined with inner-product relations. The security is proven under a standard assumption, the decisional linear assumption, in the standard model. Our scheme is constructed on the concept of dual pairing vector spaces and a hierarchical reduction technique on this concept is employed for the security proof. The proposed functional encryption scheme covers, as special cases, (1) key-policy, ciphertext-policy and unified-policy attribute-based encryption with non-monotone access structures, (2) (hierarchical) attribute-hiding functional encryption with inner-product relations and functional encryption with nonzero inner-product relations and (3) spatial encryption and a more general class of encryption than spatial encryption.

中文翻译：

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来自决策线性假设的具有大量关系的完全安全的功能加密

本文针对一大类关系提出了一种完全安全（自适应安全）实用的函数加密方案，这些关系由结合内积关系的非单调访问结构指定。在标准模型中的标准假设（决策线性假设）下证明了安全性。我们的方案是基于双配对向量空间的概念构建的，并且在此概念上采用了分层归约技术来进行安全证明。作为特殊情况，所提出的功能加密方案包括（1）具有非单调访问结构的基于密钥策略、密文策略和统一策略属性的加密，