Fully Collusion Resistant Traceable Identity-Based Inner Product Functional Encryption

We present the first fully collusion resistant traceable functional encryption (TFE) scheme for identity-based inner product FE (IBIPFE) that directly traces user identities through an efficient tracing procedure. We name such a scheme as embedded identity TIBIPFE (EI-TIBIPFE) where secret keys and ciphertexts are computed for vectors, and decryption recovers the inner product between the vectors given the key and ciphertext are associated with the same group identity. Additionally, a secret key corresponds to a user identity for the purpose of tracing. Suppose some of the users linked to a particular group team up and create a pirate decoder that is capable of decrypting the content of the group, then the tracing algorithm extracts the identities of the dishonest users' given black-box access to the decoder. Previously, such schemes were designed for usual public key encryptions. In this work, we construct a fully collusion resistant EI-TIBIPFE scheme from pairings in the standard model. The ciphertext size of our scheme grows sub-linearly with the number of users in the system. We achieve many-target security of tracing, namely the adversary is allowed to ask for multiple secret keys corresponding to many functions, which notably solves an open problem raised by Do, Phan, and Pointcheval [CT-RSA'2020].