Adaptive-Secure Identity-Based Inner-Product Functional Encryption and Its Leakage-Resilience.

There are lots of applications of inner-product functional encryption (IPFE). In this paper, we consider two important extensions of it. One is to enhance IPFE with access control such that only users with a pre-defined identity are allowed to compute the inner product, referred as identity-based inner-product functional encryption (IBIPFE). We formalize the definition of IBIPFE, and propose the first adaptive-secure IBIPFE scheme from Decisional Bilinear Diffie-Hellman (DBDH) assumption. In an IBIPFE scheme, the ciphertext is related to a vector x and a new parameter, identity ID. Each secret key is also related to a vector y and an identity ID'. The decryption algorithm will output the inner-product value < x, y > only if ID = ID'. The other extension is to make IBIPFE leakage resilient. We consider the bounded-retrieval model (BRM) in which an adversary can learn at most l bits information from each secret key. Here, l is the leakage bound determined by some external parameters, and it can be set arbitrarily large. After giving the security definition of leakage-resilient IBIPFE, we extend our IBIPFE scheme into a leakage-resilient IBIPFE scheme in the BRM by hash proof system (HPS).