Functional signatures from indistinguishability obfuscation

Abstract

In PKC 2014, Boyle, Goldwasser, and Ivan introduced a cryptographic primitive called functional signatures. In a functional sig- nature scheme, in addition to a master key that can be used to sign any message, there are signing keys for a function f, which allow one to sign any message in the range of f. In the same paper, Boyle et al. pointed out that in order to obtain a functional signature scheme with short sig- natures, we must either rely on non-falsifiable assumptions (as in their succinct non-interactive arguments of knowledge construction) or make use of non black-box techniques. In this paper, we diverge from succinct non-interactive arguments of knowledge (SNARKs). We provide a construction of functional signature scheme satisfying both function privacy and succinctness under the existence of indistinguishability obfuscation for all polynomial-size circuits and one-way functions for the first time. Additionally, our scheme is under weaker assumption than SNARK -type assumptions for a class of functions and the size of signatures are independent of f, f (m), and m.