An equivalence between attribute-based signatures and homomorphic signatures, and new constructions for both

Abstract

In Attribute-Based Signatures (ABS; first defined by Maji, Prabhakaran and Rosulek, CT-RSA 2011) an authority can generate multiple signing keys, where each key is associated with an attribute x. Messages are signed with respect to a constraint f, such that a key for x can sign messages respective to f only if f(x) = 0. The security requirements are unforgeability and key privacy (signatures should not expose the specific signing key used). In (single-hop) Homomorphic Signatures (HS; first defined by Boneh and Freeman, PKC 2011), given a signature for a data-set x, one can evaluate a signature for the pair (f(x), f), for functions f. In context-hiding HS, evaluated signatures do not reveal information about the original (pre-evaluated) signatures. In this work we start by showing that these two notions are in fact equivalent. The first implication of this equivalence is a new lattice-based ABS scheme for polynomial-depth circuits, based on the HS construction of Gorbunov, Vaikuntanathan and Wichs (GVW; STOC 2015). We then construct a new ABS candidate from a worst case lattice assumption (SIS), with different parameters. Using our equivalence again, now in the opposite direction, our new ABS implies a new lattice-based HS scheme with different parameter trade-off, compared to the aforementioned GVW.