Attribute-Based Encryption for a Subclass of Circuits with Bounded Depth from Lattices

In this work, we present two Key-Policy Attribute-Based Encryption (ABE) schemes for some subclass of circuits based on the Learning with Error (LWE) assumption. Our constructions are selectively secure in the standard model. More specifically, our first construction supports a subclass of circuits with polynomially bounded depth. We call this subclass the OR-restricted circuits which means that for any input x, if f(x) = 0 then for all the OR gates in f , at least one of its incoming wires will evaluate to 0. The second one is a Key-Policy ABE scheme for shallow circuits whose depth is bounded by O(log log λ), where λ is the security parameter.