功能加密的紧规约安全

Functional encryptions are much more expressive than traditional public key encryption and gradually become one of core techniques underlying future network security. With the introduction and development of lattice-based techniques and multi-linear maps, it is possible to give concrete constructions for a large class of functional encryptions. Therefore, it has become a hot topic to search for better solutions including the problem of investigating tightly secure functional encryptions. When proving the security of a certain functional encryption, it needs to construct a reduction algorithm that can solve some computational problem via invoking an attacker against the target functional encryption system. Typically, the success probability of the reduction algorithm is smaller than that of the attacker. We call the gap between them the loss of reduction. A tightly secure functional encryption has small loss of reduction when proving its security. A tight reduction not only means a better theoretical result, but also has positive impact on the implementation of the scheme. As the most fundamental type of functional encryptions, identity-based encryptions with tight reduction have appeared; however when we are talking about more complex functional encryptions (such as attribute-based encryptions, inner-product encryptions), current techniques fail to lead to an acceptable result. This paper focuses on the technique behind tightly secure identity-based encryptions, and discusses main drawbacks of current tightly secure functional encryptions for complex functionality. Finally, it is shown how the progresses on tight reduction made in the field of functional encryptions affect other cryptography fields.