Homomorphic-Policy Attribute-Based Key Encapsulation Mechanisms

Attribute-Based Encryption (ABE) allows to target the recipients of a message according to a policy expressed as a predicate among some attributes. Ciphertext-policy ABE schemes can choose the policy at the encryption time, contrarily to key-policy ABE schemes that specify the policy at the key generation time, for each user. In this paper, we define a new property for ABE, on top of a ciphertext-policy ABE scheme: homomorphic-policy. A combiner is able to (publicly) combine ciphertexts under different policies into a ciphertext under a combined policy (AND or OR). This allows to specify even much later the policy for a specific ciphertext: the sender encrypts, and the combiner specifies the policy, without knowing the plaintext. More precisely, using linear secret sharing schemes (LSSS), we design Attribute-Based Key Encapsulation Mechanisms (ABKEM) with our new Homomorphic-Policy property. Technically, by exploiting a specific property in the structure of LSSS matrix, we can show that, given several encapsulations of the same keys under various policies, anyone can derive an encapsulation of the same key under any combination of the policies. As a consequence, from encapsulations under many single attributes, one can build an encapsulation under a complex policy over the attributes. Similarly to the case of encryption with homomorphic properties, where malleability weakens confidentiality, homomorphic-policy ABE also weakens the security of an ABE when the combiner colludes with legitimate users. On the other hand, homomorphic-policy provides additional flexibility and nice features when one targets some practical application: in Pay-TV, this allows to separate the content providers that can generate the encapsulations of a session key under every attributes, this key being used to encrypt the payload, and the service providers that build the decryption policies according to the subscriptions. The advantage is that the aggregation of the encapsulations by the service providers does not contain any secret information.