Homomorphic Signature Schemes

A Survey
1. Auflage 2016
ISBN: 978-3-319-32114-1
Verlag: Springer International Publishing

Buch, Englisch, 64 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1299 g

Reihe: SpringerBriefs in Computer Science

Homomorphic signature schemes are an important primitive for many applications and since their introduction numerous solutions have been presented. Thus, in this work we provide the first exhaustive, complete, and up-to-date survey about the state of the art of homomorphic signature schemes. First, the general framework where homomorphic signatures are defined is described and it is shown how the currently available types of homomorphic signatures can then be derived from such a framework. In addition, this work also presents a description of each of the schemes presented so far together with the properties it provides. Furthermore, three use cases, electronic voting, smart grids, and electronic health records, where homomorphic signature schemes can be employed are described. For each of these applications the requirements that a homomorphic signature scheme should fulfill are defined and the suitable schemes already available are listed. This also highlights the shortcomings of current solutions. Thus, this work concludes with several ideas for future research in the direction of homomorphic signature schemes.

Zielgruppe

Research

Autoren/Hrsg.

Traverso, Giulia

Buchmann, Johannes

Demirel, Denise

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

1 From Digital to Homomorphic Signature Schemes 1.1 Digital Signatures1.2 Digital Signature Schemes Security Definition1.2.1 Known-Message Attack1.2.2 Chosen-Message Attack 1.2.3 Adaptive Chosen-Message Attack1.3 Homomorphic Signature Schemes 1.4 Homomorphic Signature Schemes Security Definition2 Homomorphic Signature Schemes2.1 Homomorphic Signature Schemes for the Single-User Scenario2.1.1 Linearly Homomorphic Signature Schemes2.1.2 Homomorphic Signature Schemes for Polynomial Functions 2.1.3 Fully Homomorphic Signatures2.2 Homomorphic Signature Schemes for the Multi-Users Scenario2.2.1 Multiple Sources Homomorphic Signature Schemes2.2.2 Homomorphic Aggregate Signature Schemes3 Evaluation of Homomorphic Signature Schemes3.1 Hardness Assumptions3.1.1 Bilinear Groups3.1.2 RSA3.1.3 Lattices 3.2 Efficiency and Size3.3 Security3.3.1 Weak Adversary3.3.2 Strong Adversary3.4 Privacy3.5 Random Oracle Model vs. Standard Model
4  State of the Art of Homomorphic Signature Schemes4.1 Linearly Homomorphic Signature Schemes Defined Over Bilinear Groups4.1.1 Signing a Linear Subspace: Signature Schemes for Network Coding, by Boneh etal. (2009)4.1.2 Homomorphic Network Coding Signatures in the Standard Model, by Attrapadungand Libert (2011)4.1.3 Computing on Authenticated Data: New Privacy Definitions and Constructions, byAttrapadung et al. (2012)4.1.4 Efficient Network Coding Signatures in the Standard Model, by Catalano et al. (2012) 4.1.5 Improved Security for Linearly Homomorphic Signatures: A Generic Framework,by Freeman (2012)<4.1.6 Efficient Completely Context-Hiding Quotable and Linearly HomomorphicSignatures, by Attrapadung et al. (2013)4.1.7 Secure Network Coding Against Intra/Inter-Generation Pollution Attacks, byGuangjun et al. (2013)4.1.8 Summary of Linearly Homomorphic Signature Schemes Defined Over BilinearGroups4.2 RSA-Based Linearly Homomorphic Signature Schemes4.2.1 Secure Network Coding Over the Integers, by Gennaro et al. (2010)4.2.2 Adaptive Pseudo-Free Groups and Applications, by Catalano et al. (2011)4.2.3 Efficient Network Coding Signatures in the Standard Model, by Catalano et al. (2012) 4.2.4 Improved Security for Linearly Homomorphic Signatures: A Generic Framework,by Freeman (2012)4.2.5 Summary of RSA-Based Linearly Homomorphic Signature Schemes4.3 Lattice-Based Linearly Homomorphic Signature Schemes 4.3.1 Linearly Homomorphic Signatures over Binary Fields and New Tools forLattice-Based Signatures, by Boneh and Freeman (2011) 4.3.2 Lattice-Based Linearly Homomorphic Signature Scheme over Binary Fields, byWang et al. (2013)4.3.3 Summary of Lattice-Based Linearly Homomorphic Signature Schemes 4.4 Homomorphic Signature Schemes for Polynomial Functions 4.4.1 Homomorphic Signatures for Polynomial Functions, by Boneh and Freeman (2011)4.4.2 Homomorphic Signatures for Polynomial Functions with Shorter Signatures, byHiromasa et al. (2013)4.4.3 Homomorphic Signatures with Efficient Verification for Polynomial Functions, byCatalano et al. (2014)4.4.4 Summary of Homomorphic Signature Schemes for Polynomial Functions4.5 Fully Homomorphic Signature Schemes4.5.1 Leveled Fully Homomorphic Signatures from Standard Lattices, by Gorbunov etal. (2014)4.5.2 Adaptively Secure Fully Homomorphic Signatures Based on Lattices, by Boyen etal. (2014) 4.5.3 Leveled Strongly-Unforgeable Identity-Based Fully Homomorphic Signatures, byWang et al. (2015)4.5.4 Summary of Fully Homomorphic Signature Schemes 4.6 Multiple Sources Linearly Homomorphic Signature Schemes 
4.6.1 Signatures for Multi-Source Network Coding, by Czap and Vajda (2010) 4.6.2 Short Signature Scheme for Multi-Source Network Coding, by Yan et al. (2011)4.6.3 Efficient Multiple Sources Network Coding Signature in the Standard Model, byZhang et al. (2014) 4.6.4 Summary of Multiple Sources Linearly Homomorphic Signature Schemes 4.7 Linearly Homomorphic Aggregate Signature Schemes 4.7.1 A Homomorphic Aggregate Signature Scheme Based on Lattice, by Zhang et al.(2012)4.7.2 An Efficient Homomorphic Aggregate Signature Scheme Based on Lattice, by Jing(2014) 4.7.3 Summary of Linearly Homomorphic Aggregate Signature Schemes 5 Suitable Homomorphic Signature Schemes for eVoting, Smart Grids, and eHealth5.1 Electronic Voting5.2 Smart Grids 5.3 Electronic Health Records6 ConclusionReferences