Paper 2014/820 Original: eprint.iacr.org/2014/820 ↗

Operational Signature Schemes

Abstract

Functional encryption, as introduced by Boneh, Sahai, and Waters (TCC'11), generalizes public-key encryption systems to include functional decryption capabilities. Recently, Boyle et al. as well as Bellare and Fuchsbauer (both PKC'14) formalized analogous notions for signature schemes. Here we discuss that both their notions are limited in terms of expressiveness in the sense that they cannot cast known signature schemes supporting operations on data in their frameworks. We therefore propose a notion of what we call, for sake of distinctiveness, operational signature schemes which captures functional signatures, policy-based signatures, sanitizable signatures, P-homomorphic signatures, ring signatures, aggregate signatures etc., and also their message authentication code counterparts. We discuss possible instantiations for operational signatures. We give some positive result about achieving our general notion of operational signatures presenting a compact construction that relies on a new combination of indistinguishability obfuscation and random oracles. We then indicate that it is unlikely to be able to instantiate operational signature schemes in general using one-wayness and, under some circumstances, even using specific ``non-interactive'' assumptions like RSA.