Revocable identity-based fully homomorphic signature scheme with signing key exposure resistance

Abstract

Fully homomorphic signature schemes in identity-based settings can provide authenticity, homomorphism, and non-repudiation as do traditional digital signatures, while simplifying the public key infrastructure (PKI) requirements, in which each user in the system can use his or her identity as a public key. As identity-based systems (IBS) have a natural link between unique identity information and the user, allowing user revocation is usually more difficult in IBS than in PKI settings. Although several revocable identity-based fully homomorphic signature (RIBFHS) schemes have been proposed, these schemes are vulnerable to signing key exposure. With this study, we are the first to consider a realistic threat signing key exposure in RIBFHS systems. In addition, we introduce a new security definition of RIBFHS with signing key exposure resistance. Then, we employ Agrawal’s left–right lattices and delegation technology in fixed dimensions to construct a new RIBFHS scheme over the lattice with regularly broadcasted update keys, which not only resists signing key exposure, but also meets scalability and context hiding properties. Finally, we prove that our construction is existentially unforgeable against chosen message attacks under the standard short integer solution (SIS) assumption in the random oracle model.