Revisits and transformations among functional encryption systems

Functional encryption provides a general access control over the encrypted data, where only the receiver with attribute x→ that satisfies control policy function fv→ of policy parameter v→ (i.e. fv→x)= 1) can decrypt its ciphertext. Special cases of functional encryption include (anonymous-) (hierarchical) identity-based encryption, fuzzy identity-based encryption, attribute-based encryption, public key encryption with keyword search, spatial encryption, inner-product encryption, hidden-vector encryption and predicate encryption. In general functional encryption systems, the control policy function can be set flexibly. The main gap among these functional encryption schemes lies in the policy functions that associates with the secret keys. In this work, we first investigate several functional encryption schemes, and then formalize and unify the functionality description of the control policies for these schemes. After giving a general definition and security model, we present the relationship and transformations among functional encryption schemes when the equivalence of these different policy functions is employed.