LSSS Matrix-Based Attribute-Based Encryption on Lattices

Attribute-Based Encryption (ABE) schemes show unprecedented flexibility and expressiveness through the introduction of access policies. Compared to ABE schemes for thresholds or circuits from lattices, Linear Secret Sharing Schemes (LSSS) matrix-based ABE is more difficult to design for its abstract mathematical structure. We propose an ABE scheme for LSSS matrix from lattices in this work. The prior lattice-based ABE scheme for LSSS matrix constructed a large virtual encryption matrix to embed the LSSS matrix in secret key. We use a completely different but common method in lattice-based encryption schemes to achieve the same task. Moreover, we prove that our scheme is secure against chosen plaintext attack in the selective security model under the Learning with Errors (LWE) assumptions.