Homomorphic Signature Schemes - A survey

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.

[1]  Reza Curtmola,et al.  Practical defenses against pollution attacks in wireless network coding , 2011, TSEC.

[2]  Jonathan Katz,et al.  Compact Signatures for Network Coding , 2008 .

[3]  Tatsuaki Okamoto,et al.  Homomorphic Signatures for Polynomial Functions with Shorter Signatures , 2013 .

[4]  Ronald Cramer,et al.  Signature schemes based on the strong RSA assumption , 2000, TSEC.

[5]  Bogdan Warinschi,et al.  Homomorphic Signatures with Efficient Verification for Polynomial Functions , 2014, CRYPTO.

[6]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[7]  Brent Waters,et al.  Short and Stateless Signatures from the RSA Assumption , 2009, CRYPTO.

[8]  Thomas Peters,et al.  Efficient Completely Context-Hiding Quotable and Linearly Homomorphic Signatures , 2013, Public Key Cryptography.

[9]  Craig Gentry,et al.  Trapdoors for hard lattices and new cryptographic constructions , 2008, IACR Cryptol. ePrint Arch..

[10]  Fengjun Li,et al.  Preserving data integrity for smart grid data aggregation , 2012, 2012 IEEE Third International Conference on Smart Grid Communications (SmartGridComm).

[11]  Huajing Fang,et al.  Short signature scheme for multi-source network coding , 2012, Comput. Commun..

[12]  Brent Waters,et al.  Efficient Identity-Based Encryption Without Random Oracles , 2005, EUROCRYPT.

[13]  Daniele Micciancio,et al.  Asymptotically Efficient Lattice-Based Digital Signatures , 2018, Journal of Cryptology.

[14]  Shai Halevi,et al.  Secure Hash-and-Sign Signatures Without the Random Oracle , 1999, EUROCRYPT.

[15]  Bogdan Warinschi,et al.  Efficient Network Coding Signatures in the Standard Model , 2012, Public Key Cryptography.

[16]  Caroline Fontaine,et al.  A Survey of Homomorphic Encryption for Nonspecialists , 2007, EURASIP J. Inf. Secur..

[17]  Dan Boneh,et al.  Short Signatures Without Random Oracles , 2004, EUROCRYPT.

[18]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.

[19]  Yong Guan,et al.  An Efficient Signature-Based Scheme for Securing Network Coding Against Pollution Attacks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[20]  Ronald L. Rivest.  On the Notion of Pseudo-Free Groups , 2004, TCC.

[21]  Zhengjun Jing,et al.  An Efficient Homomorphic Aggregate Signature Scheme Based on Lattice , 2014 .

[22]  Andreas Peter,et al.  Privacy-Preserving Verification of Clinical Research , 2013, Sicherheit.

[23]  Jeremy Clark,et al.  Scantegrity: End-to-End Voter-Verifiable Optical- Scan Voting , 2008, IEEE Security & Privacy.

[24]  Kamal Jain,et al.  Signatures for Network Coding , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[25]  David Mandell Freeman,et al.  Improved Security for Linearly Homomorphic Signatures: A Generic Framework , 2012, Public Key Cryptography.

[26]  Fang Zhao,et al.  Signatures for Content Distribution with Network Coding , 2007, 2007 IEEE International Symposium on Information Theory.

[27]  Silvio Micali,et al.  A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks , 1988, SIAM J. Comput..

[28]  Dimitra I. Petrakaki,et al.  Implementation and adoption of nationwide electronic health records in secondary care in England: qualitative analysis of interim results from a prospective national evaluation , 2010, BMJ : British Medical Journal.

[29]  Christian Hanser,et al.  Structure-Preserving Signatures on Equivalence Classes and their Application to Anonymous Credentials , 2014, IACR Cryptol. ePrint Arch..

[30]  Jean-Sébastien Coron,et al.  New Multilinear Maps Over the Integers , 2015, CRYPTO.

[31]  Lei Yang,et al.  Detecting false data injection in smart grid in-network aggregation , 2013, 2013 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[32]  Jonathan Katz,et al.  Signing a Linear Subspace: Signature Schemes for Network Coding , 2009, IACR Cryptol. ePrint Arch..

[33]  Hovav Shacham,et al.  Aggregate and Verifiably Encrypted Signatures from Bilinear Maps , 2003, EUROCRYPT.

[34]  István Vajda,et al.  Signatures for Multisource Network Coding , 2010 .

[35]  Bogdan Warinschi,et al.  Adaptive Pseudo-Free Groups and Applications , 2011, IACR Cryptol. ePrint Arch..

[36]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[37]  Dawn Xiaodong Song,et al.  Homomorphic Signature Schemes , 2002, CT-RSA.

[38]  Jonathan Katz,et al.  Secure Network Coding Over the Integers , 2010, IACR Cryptol. ePrint Arch..

[39]  Nuttapong Attrapadung,et al.  Homomorphic Network Coding Signatures in the Standard Model , 2011, Public Key Cryptography.

[40]  Dipak Kalra,et al.  Electronic Health Records , 2006 .

[41]  Zhe Xia,et al.  Versatile Prêt à Voter: Handling Multiple Election Methods with a Unified Interface , 2010, INDOCRYPT.

[42]  Hugo Krawczyk,et al.  Performance Evaluation of Secure Network Coding Using Homomorphic Signature , 2011, 2011 International Symposium on Networking Coding.

[43]  Yongge Wang,et al.  Insecure "Provably Secure Network Coding" and Homomorphic Authentication Schemes for Network Coding , 2010, IACR Cryptol. ePrint Arch..

[44]  Zhang Peng,et al.  A Homomorphic Aggregate Signature Scheme Based on Lattice , 2012 .

[45]  Jung Hee Cheon,et al.  On Homomorphic Signatures for Network Coding , 2010, IEEE Transactions on Computers.

[46]  Abhi Shelat,et al.  Computing on Authenticated Data , 2012, Journal of Cryptology.

[47]  Dan Boneh,et al.  Homomorphic Signatures for Polynomial Functions , 2011, EUROCRYPT.

[48]  Thomas Peters,et al.  Computing on Authenticated Data: New Privacy Definitions and Constructions , 2012, ASIACRYPT.

[49]  Dario Catalano,et al.  Homomorphic Signatures and Message Authentication Codes , 2014, SCN.

[50]  D. Blumenthal,et al.  The "meaningful use" regulation for electronic health records. , 2010, The New England journal of medicine.

[51]  Yupu Hu,et al.  Lattice-based linearly homomorphic signature scheme over binary field , 2012, Science China Information Sciences.

[52]  Michael E. Miller,et al.  Electronic Health Records , 2014, Annals of Internal Medicine.

[53]  Daniel Wichs,et al.  Leveled Fully Homomorphic Signatures from Standard Lattices , 2015, IACR Cryptol. ePrint Arch..

[54]  Dan Boneh,et al.  Linearly Homomorphic Signatures over Binary Fields and New Tools for Lattice-Based Signatures , 2011, Public Key Cryptography.

[55]  Dan Boneh,et al.  Efficient Selective Identity-Based Encryption Without Random Oracles , 2011, Journal of Cryptology.

[56]  Elaine Shi,et al.  Adaptively Secure Fully Homomorphic Signatures Based on Lattices , 2014, IACR Cryptol. ePrint Arch..

[57]  Ronald L. Rivest,et al.  Scratch & vote: self-contained paper-based cryptographic voting , 2006, WPES '06.