Ciphertext-Policy Attribute-Based Encryption for Circuits from Lattices Under Weak Security Model

The existing Ciphertext-Policy Attribute-Based Encryption (CP-ABE) scheme from lattices can only support a simple threshold access structure, resulting in its limited application scenario. In order to improve the flexibility and expressiveness of the CP-ABE scheme, we present a CP-ABE for circuits from lattices in this paper. The new scheme generates secret key for each attribute of the attribute set by invoking the sampling algorithm from lattices and embeds the attribute set into the secret keys. Meanwhile, to associate the ciphertext with a circuit, we design a Secret Matrix Distribution Mechanism (SMDM) for circuits, which distributes a matrix with specific form to each node of the circuit, and the scheme can generate the ciphertexts by combining the matrices of the leaf nodes. In the decryption phase, the SMDM guarantees the user who satisfies the access structure can decrypt the ciphertexts correctly. Finally, we prove that our scheme is secure against chosen plaintext attack in the selective weak security model under the Learning with Errors (LWE) assumptions.