Compact Adaptively Secure ABE for $\mathsf {NC^1}$ from k-Lin

Abstract : We present compact attribute-based encryption (ABE) schemes for NC1 that are adaptively secure under the k-Lin assumption with polynomial security loss. Our KP-ABE scheme achieves ciphertext size that is linear in the atttribute length and independent of the policy size even in the many-use setting, and we achieve an analogous efficiency guarantee for CP-ABE. This resolves the central open problem posed by Lewko and Waters (CRYPTO 2011). Previous adaptively secure constructions either impose an attribute ``one-use restriction'' (or the ciphertext size grows with the policy size), or require q-type assumptions.