Lattice-Based CP-ABE for Optimal Broadcast Encryption With Polynomial-Depth Circuits

Most current broadcast encryption with optimal parameters is limited to Nick’s class 1 (NC1) circuits and does not support polynomial-depth circuits (P-depth circuits), making it difficult to provide flexible access control in broadcast channels among vast user groups. To address this problem, we propose a ciphertext-policy attribute–based encryption (CP-ABE) that supports P-depth circuits on lattices, achieving fully collusion resistance with randomization via the matrix tensors, thereby, making it impossible for unauthorized users to get any details about the plaintext even though they join forces and reducing the security to the evasive learning with errors (evasive LWE). By using matrix tensor–based randomization and evasive LWE, we achieve a new optimal broadcast encryption scheme based on lattice specifically designed to support P-depth circuits. Since the matrices we choose as tensors have a low-norm block diagonal structure, the use of evasive LWE is sufficient to ensure security for our scheme. Compared with similar studies, it not only avoids being involved with low-norm matrices that restrict the system to NC1 circuits, but also eliminates the need for an additional assumption of the unproven tensor LWE. In addition, the use of matrix tensors further expands the dimensionality, which in turn enables the encryption of bit strings rather than a single bit, significantly reducing ciphertext expansion. Meanwhile, the CP-ABE that we use to achieve the broadcast encryption scheme has a more compact ciphertext with a parameter size of O(m² · d).