Identity-based functional encryption for quadratic functions from lattices

Abstract

We present a functional encryption scheme for quadratic functions from lattices under identity-based access control. This represents a practical relevant class of functions beyond multivariate quadratic polynomials and may adapt to many scenarios. Recently, Baltico et al. [10] in Crypto 2017 presented two constructions from pairings which enable efficient decryption only when xTFy is contained in a sufficiently small interval to finally compute a discrete logarithm, and one construction is proved selectively secure under standard assumptions and the other adaptively secure in the generic group model (GGM). Our construction is no pairings and no small interval restriction. We formalize the definition of identity-based functional encryption and its indistinguishability security and achieve adaptive security against unbounded collusions under standard assumptions in the random oracle model.