Predicate Encryption For Circuits From Lwe

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(lambda), we construct a predicate encryption scheme for the class of all circuits with depth bounded by d(lambda), where lambda is the security parameter.