Paper 2016/1106

Functional Encryption for Quadratic Functions, and Applications to Predicate Encryption

Romain Gay

Abstract

We present a functional encryption scheme based on standard assumptions where ciphertexts are associated with a tuple of values $(x_1,\dots ,x_n)\in {\mathbb{Z}}_p^n$, secret keys are associated with a degree-two polynomial, and the decryption of a ciphertext ${\mathsf{ct}}_{(x_1,\dots ,x_n)\in {\mathbb{Z}}_p^n}$ with a secret key ${\mathsf{sk}}_{P\in {\mathbb{Z}}_p[X_1,\dots ,X_n],\mathsf{deg}(P)\le 2}$ recovers $P(x_1,\dots ,x_n)$, where the ciphertext contains only $O(n)$ group elements. Our scheme, which achieves selective security based on pairings, also yields a new predicate encryption scheme that supports degree-two polynomial evaluation, generalizing both [KSW 08] and [BSW 06].