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 \(\varvec{x}\) and a new parameter, identity \(\mathrm {ID}\). Each secret key is also related to a vector \(\varvec{y}\) and an identity \(\mathrm {ID}'\). The decryption algorithm will output the inner-product value \(\langle \varvec{x},\varvec{y} \rangle \) only if \(\mathrm {ID}=\mathrm {ID}'\).