Predicate Encryption for Circuits from LWE, by Sergey Gorbunov and Vinod Vaikuntanathan and Hoeteck Wee

In predicate encryption, a ciphertext is associated with descriptive attribute values $x$ in addition to a plaintext $\mu$, and a secret key is associated with a predicate $f$. Decryption returns plaintext $\mu$ if and only if $f(x) = 1$. Moreover, security of predicate encryption guarantees that an adversary learns nothing about the attribute $x$ or the plaintext $\mu$ from a ciphertext, given arbitrary many secret keys that are not authorized to decrypt the ciphertext individually. We construct a leveled predicate encryption scheme for all circuits, assuming the hardness of the subexponential learning with errors (LWE) problem. That is, for any polynomial function $d = d(\secp)$, we construct a predicate encryption scheme for the class of all circuits with depth bounded by $d(\secp)$, where $\secp$ is the security parameter.