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Homomorphic message authentication codes (MACs) allow a user to outsource data to an untrusted server and verify the correctness of returned computation results over the outsourced data. Many cloud applications need delegation computations over outsourced data with dual capabilities. On one hand, they need to keep the outsourced data secret such that the server cannot trace and infer any sensitive information from the computation results. On the other hand, the user should be able to efficiently verify the computation results. Unfortunately, the state-of-the-art homomorphic MAC schemes are not so desirable due to either poor privacy or low verification efficiency. In this paper, we first put forward a new cryptographic primitive called privacy-preserving homomorphic MACs (PHMAC) that simultaneously provides data privacy and efficient verification. Then, we present a PHMAC construction capable for the evaluation of polynomials of fixed degree |$d\geq 1$|⁠ , in which the tag does not reveal any information of underlying authenticated data while being verifiable in constant time (in an amortized sense). As an application, we give a generic construction of homomorphic authenticated encryption (HAE) from proposed PHMAC and homomorphic encryption. Benefited from the functionalities of underlying PHMAC scheme, the derived HAE enjoys stronger authenticity and supports larger classes of functions than that of Lai et al. (Verifiable Computation on Outsourced Encrypted Data. In Computer Security—ESORICS 2014—19th European Symposium on Research in Computer Security , Wroclaw, Poland, September 7–11, Part I, pp. 273–291. Springer, Berlin). Such HAE enables verifiable delegation computations over growing outsourced encrypted data in an efficient way. [ABSTRACT FROM AUTHOR]

A tightly secure scheme has a reduction, where the reduction loss is a small constant. Identity-based signature (IBS) is an important cryptographic primitive, and tightly secure IBS schemes enjoy the advantage that the security parameter can be optimal to achieve a certain security level. General constructions of IBS schemes (Bellare, M. Namprempre, C. and Neven, G. (2004) Security Proofs for Identity-Based Identification and Signature Schemes. In Proc. EUROCRYPT 2004 , May 2–6, pp. 268–286. Springer, Berlin, Interlaken, Switzerland; Galindo, D. Herranz, J. and Kiltz, E. (2006) On the Generic Construction of Identity-Based Signatures With Additional Properties. In Proceedings of ASIACRYPT 2006 , December 3–7, pp. 178–193. Springer, Berlin, Shanghai, China) and their security have been extensively studied. However, the security is not tight and how to generally construct a tightly secure IBS scheme remains unknown. In this paper, we concentrate on the general constructions of IBS schemes. We first take an insight into previous constructions and analyze the reason why it cannot achieve tight security. To further study possible tightly secure constructions, we propose another general construction, which could be seen as a different framework of IBS schemes. Our construction requires two traditional signature schemes, whereas the construction by Bellare et al. uses one scheme in a two-round iteration. There are no additional operations in our general construction. Its main advantage is providing the possibility of achieving tight security for IBS schemes in the random oracle model. Combining two known signature schemes, we present an efficient IBS scheme with tight security as an example. [ABSTRACT FROM AUTHOR]

Linearly homomorphic signatures (LHSs) allow any entity to linearly combine a set of signatures and to provide authentication service for the corresponding (combined) data. The public key of the current known LHSs from lattices in the standard model requires |$O(l)$| matrices and |$O(k)$| vectors, where |$l$| is the length of file identifier and |$k$| is the maximum data set size that linear functions support. In this paper, we construct two lattice-based LHS schemes with provable security in the standard model and both schemes can authenticate vectors defined over finite field. First, we present a basic LHS scheme satisfying selective security, based on the full-rank difference hash functions. Second, we modify the chameleon hash function constructed by (Cash, D. Hofheinz, D. Kiltz, E. and Peikert, C. (2010) Bonsai Trees, or How to Delegate a Lattice Basis. In Proc. EUROCRYPT 10, Monaco/French Riviera, May 30 to June 3, pp. 523–552. Springer, Berlin) to construct a linearly homomorphic chameleon hash function (LHCHF), which can be applied to all transformations from selectively secure LHS scheme that authenticates vectors defined over finite field |$\mathbb{F}_{p}$| (⁠|$p=poly(n)$|⁠) to fully secure one, except for a new one that authenticates vectors defined over a small field. Starting from LHCFH and the basic scheme as above, we obtain a fully secure LHS scheme. Both schemes can be used to sign multiple files and have relatively short public keys consisting of |$O(1)$| matrices and |$O(k)$| vectors. [ABSTRACT FROM AUTHOR]