Leakage-Resilient Attribute-Based Encryption with Fast Decryption: Models, Analysis and Constructions

Traditionally, in attribute-based encryption (ABE), an access structure is constructed from a linear secret sharing scheme (LSSS), a boolean formula or an access tree. In this work, we encode the access structure as their minimal sets, which is equivalent to the existence of a smallest monotonic span program for the characteristic function of the same access structure. We present two leakage-resilient attribute-based encryption schemes, ciphertext-policy ABE (LR-CP-ABE) and keypolicy ABE (LR-KP-ABE), that can tolerate private key and master key to be partially leaked. By using our encoding mechanism, we obtain short ciphertext in LR-CP-ABE and short key in LR-KP-ABE. Also, our schemes have higher decryption efficiency in that the decryption cost is independent to the depth of access structures. Meanwhile, our proposed schemes provide the tolerance of both master key leakage and continual leakage in the sense that there are many master keys for universal set Σ and many private keys per attribute set S. We explicitly employ a refresh algorithm to update a (master) key while the leakage information will beyond the allowable leakage bound. The schemes are proven to be adaptively leakage-resilient secure in the standard model under the static assumptions in composite order bilinear groups.