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

Abstract

We present compact attribute-based encryption (ABE) schemes for $${\textsf {NC}}^{1}$$ 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 attribute 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.