Skip to main content
SpringerLink
Log in

A Survey of Verifiable Computation

  • Published:
Mobile Networks and Applications Aims and scope Submit manuscript

Abstract

Internet of Things (IoT) has taken place to motivate various intelligent applications with the data collected by the things”. Meanwhile, Cloud computing offers an efficient and convenient way to store, process and analyze huge amount of data. Because a Cloud Service Provider (CSP) that is employed to store and process user private data is actually not in the trust domains of cloud users, data security becomes a serious issue in cloud computing. One crucial problem in cloud is the cloud data processing result may be incorrect, thus cannot be fully trusted. This calls for research to verify the correctness of data processing at the cloud in order to enhance its trustworthiness, especially for encrypted data processing. At present, various cryptosystems have been proposed to achieve verifiability with different characteristics and quality. However, the literature still lacks a thorough survey to review the current state of art in order to get a comprehensive view of this research field, named verifiable computation. In this paper, we review existing work of verifiable computation by comparing and discussing pros and cons according to performance requirements, highlight open research issues through serious review and analysis and propose a number of research directions in order to guide future research.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Jing Q, Vasilakos AV, Wan J, Lu J, Qiu D (2014) Security of the internet of things: perspectives and challenges. Wirel Netw 20(8):2481–2501

    Article  Google Scholar 

  2. Shu Z, Wan J, Li D, Lin J, Vasilakos AV, Imran M (2016) Security in software-defined networking: threats and countermeasures. Mobile Networks and Applications 21(5):764–775

    Article  Google Scholar 

  3. Parno B, Raykova M, Vaikuntanathan V (2012) How to delegate and verify in public: verifiable computation from attribute-based encryption. Proc of the 9th international conference on Theory of Cryptography (TCC’12), Springer Berlin Heidelberg, pp 422–439

  4. Dijk M, Clarke D, Gassend B, Edward Suh G, Devadas S (2006) Speeding up exponentiation using an untrusted computational resource. Journal Designs, Codes and Cryptography 39:253–273

    Article  MathSciNet  MATH  Google Scholar 

  5. Catalano D, Fiore D (2013) Practical homomorphic macs for arithmetic circuits. In: Advances in Cryptology–EUROCRYPT, Springer, pp. 336–352

  6. Gennaro R, Wichs D (2013) Fully homomorphic message authenticators. In: Advances in Cryptology-ASIACRYPT, Springer, pp 301–320

  7. Backes M, Fiore D, Reischuk RM (2013) Verifiable delegation of computation on outsourced data. In: ACM conference on Computer and communications security. ACM, pp 863–874

  8. Boneh D, Freeman DM (2011) Homomorphic signatures for polynomial functions. In: Advances in Cryptology– EUROCRYPT, Springer, pp 149–168

  9. Chung KM, Kalai Y, Vadhan S (2010) Improved delegation of computation using fully homomorphic encryption. In: Advances in Cryptology–CRYPTO, Springer, pp 483–501

  10. Thaler JR (2013) Practical verified computation with streaming interactive proofs. Ph.D. dissertation, Harvard University

  11. Fiore D, Gennaro R (2012) Publicly verifiable delegation of large polynomials and matrix computations, with applications. In: ACM conference on Computer and communications security, ACM, pp 501–512

  12. Parno B, Howell J, Gentry C, Raykova M (2013) Pinocchio: nearly practical verifiable computation. In: IEEE Symposium on Security and Privacy, IEEE, pp 238–252

  13. Papadopoulos S, Cormode G, Deligiannakis A, Garofalakis M (2013) Lightweight authentication of linear algebraic queries on data streams. In: International conference on Management of data, ACM, pp 881–892

  14. Canetti R, Riva B, Rothblum GN (2012) Two protocols for delegation of computation. In: Proceedings of the 6th international conference on information theoretic security, ser. ICITS’12. Springer-Verlag, Berlin pp 37–61

  15. Papamanthou C, Shi E, Tamassia R (2013) Signatures of correct computation. In: Proceedings of the 10th theory of cryptography conference on theory of cryptography, ser. TCC’13. Springer-Verlag, Berlin, pp 222–242

  16. Kate A, Zaverucha GM, Goldberg I (2010) Constant-size commitments to polynomials and their applications. In: Advances in cryptology-ASIACRYPT 2010, Springer, pp 177–194

  17. Shamir A (1979) How to share a secret. Commun ACM 22(11):612–613

    Article  MathSciNet  MATH  Google Scholar 

  18. Blakley G (1979) Safeguarding cryptographic keys. In: Proceedings of the 1979 AFIPS National Computer Conference, AFIPS Press, Monval, pp. 313–317

  19. Mignotte M (1983) How to share a secret. In: Proceedings of the 1982 Conference on cryptography, Springer-Verlag, Berlin, Heidelberg, pp. 371–375

  20. Asmuth C, Bloom J (2006) A modular approach to key safeguarding. IEEE Trans Inf Theor 29:208–210

    Article  MathSciNet  Google Scholar 

  21. Setty S, McPherson R, Blumberg AJ, Walfish M (2012) Making argument systems for outsourced computation practical (sometimes). In: Pceedings of the ISOC NDSS

  22. Yan Z, Yu XX, Ding WX (2017) Context-aware verifiable cloud computing. IEEE Access 5:2211–2227

    Article  Google Scholar 

  23. M. Cafaro and P. Pelle, Space-efficient Verifiable Secret Sharing Using Polynomial Interpolation. IEEE Transactions on Cloud Computing, PP(9), 1–1, 2015.

  24. H. Ma, R. Zhang, Z. Wan, Y. Lu, and S. Lin, “Verifiable and Exculpable Outsourced Attribute-Based Encryption for Access Control in Cloud Computing.” IEEE Transactions on Dependable and Secure Computing, PP(99), 1–1, 2015.

  25. Renjith P, Sabitha S (2013) Verifiable el-gamal re-encryption with authenticity in cloud. Computing, communications and networking technologies (ICCCNT), 2013 fourth international conference on, pp 1–5, 4-6 July 2013

  26. Sun W, Wang B, Cao N, Li M, Lou W, Hou YT, Li H (2014) Verifiable privacy-preserving multi-keyword text search in the cloud supporting similarity-based ranking. IEEE Transactions on Parallel and Distributed Systems 25(11):3025–3035

    Article  Google Scholar 

  27. Wang J, Chen X, Huang X, You I, Xiang Y (2015) Verifiable auditing for outsourced database in cloud computing. IEEE Trans Comput 64(11):3293–3303

    Article  MathSciNet  MATH  Google Scholar 

  28. Wen Z, Luo J, Chen H, Meng J, Li X, Li J, A Verifiable Data Deduplication Scheme in Cloud Computing. Intelligent Networking and Collaborative Systems (INCoS), 2014 International conference on, pp 85–90, 10-12, Sept 2014

  29. Xu J, Wen Q, Li W, Jin Z (2016) Circuit Ciphertext-policy attribute-based hybrid encryption with verifiable delegation in cloud computing. IEEE Transactions on Parallel and Distributed Systems 27(1):119–129

    Article  Google Scholar 

  30. Yadav H, Dave M (2014) Secure data storage operations with verifiable outsourced decryption for mobile cloud computing. Recent Advances and innovations in Engineering (ICRAIE), pp 1–5, 9-11 may 2014

  31. Guo L, Fang Y, Li M, Li P (2015) Verifiable privacy-preserving monitoring for cloud-assisted mHealth systems. 2015 I.E. conference on computer communications (INFOCOM), pp 1026–1034, April 26 2015-may 1 2015

  32. X. Chen, J. Li, X. Huang, J. Ma, and W. Lou, “Verifiable Computation over Large Database with Incremental Updates.” IEEE Transactions on Computers, PP(99), 1–1, 2016.

  33. Li W, Xue K, Xue Y, Hong J (2016) TMACS: a robust and verifiable threshold multi-authority access control system in public cloud storage. IEEE Transactions on Parallel and Distributed Systems 27(5):1484–1496

    Article  Google Scholar 

  34. X. Liu, W. Sun, H. Quan, W. Lou, Y. Zhang, and H. Li, “Publicly Verifiable Inner Product Evaluation over Outsourced Data Streams under Multiple Keys.” IEEE Transactions on Services Computing, PP(99), 1–1, 2016.

  35. Park KW, Han J, Chung J, Park KH (2013) THEMIS: a mutually verifiable billing system for the cloud computing environment. IEEE Trans Serv Comput 6(3):300–313

    Article  Google Scholar 

  36. Santos WM, DE Queiroz RJGB, Saraiva CER, Junior GPV (2013) Toward coercion-resistant end-to-end verifiable electronic voting systems. 2013 12th IEEE international conference on trust, security and privacy in computing and communications, pp 1696–1703, 16-18 July 2013

  37. Schiffman J, Sun Y, Vijyakumar H, Jaeger T (2013) Cloud verifier: verifiable auditing service for IaaS clouds. 2013 I.E. Ninth World Congress on Services, pp 239–246, June 28 2013–July 3 2013

  38. Vu V, Setty S, Blumbery AJ, Walfish M (2013) A hybrid architecture for interactive verifiable computation. Security and privacy (SP), 2013 I.E. Symposium on, pp 223–237, 19-22 may 2013

  39. Goldwasser S, Kalai YT, Rothblum GN (2008) Delegating computation: interactive proofs for muggles. In: Proc ACM Symp Theory Comput, pp. 113–122

  40. Lai J, Deng RH, Pang H, Weng J (2014) Verifiable computation on outsourced encrypted data. In: Proc Eur Symp Res Comput Security, pp 273–291

  41. Vu V, Setty S, Blumberg AJ, Walfish M (2013) A hybrid architecture for interactive verifiable computation. In: Proc IEEE Symp Security Privacy, pp 223–237

  42. Zhang L, Safavi-Naini R (2014) Verifiable delegation of computations with storage-verification trade-off. In: Proc 19th Eur Symp res Comput security, pp 112–129

  43. Lai J, Deng RH, Guan C, Weng J (2013) Attribute-based encryption with verifiable outsourced decryption. IEEE Trans Inf Forensics Security 8(8):1343–1354

    Article  Google Scholar 

  44. Atallah MJ, Frikken KB (2010) Securely outsourcing linear algebra computations. Proc ACM Symposium on information, computer and communications security (ASIACCS 2010), ACM, pp 48–59

  45. Benjamin D, Atallah MJ (2008) Private and cheating-free outsourcing of algebraic computations. Proc of the 6th Annual Conference on Privacy, Security and Trust (PST ‘08), IEEE Computer Society, pp 240–245

  46. Gennaro R, Gentry C, Parno B (2010) Non-interactive verifiable computation: outsourcing computation to untrusted workers. Proc of the 30th annual conference on Advances in cryptology (CRYPTO’10), Springer Berlin Heidelberg, pp 465–482

  47. Hohenberger S, Lysyanskaya A (2005) How to securely outsource cryptographic computations. Proc of the Second international conference on Theory of Cryptography (TCC’05), Springer Berlin Heidelberg, pp 264–282

  48. Choi SG, Katz J, Kumaresan R, Cid C (2013) Multi-Client non-interactive verifiable computation. Proc of the 10th theory of cryptography conference on Theory of Cryptography (TCC’13), Springer Berlin Heidelberg, pp 499–518

  49. Benabbas S, Gennaro R, Vahlis Y (2011) Verifiable delegation of computation over large datasets. Proc of the 31st annual conference on Advances in cryptology (CRYPTO’11), Springer Berlin Heidelberg, pp 111–131

  50. Papamanthou C, Shi E, Tamassia R (2013) Signatures of correct computation. Proc of the 10th theory of cryptography conference on Theory of Cryptography (TCC’13), Springer Berlin Heidelberg, pp 222–242

  51. Haeberlen A (2010) A case for the accountable cloud. SIGOPS Operating Systems Rev 44:52–57

    Article  Google Scholar 

  52. Koeppe F, Schneider J (2010) Do you get what you pay for? Using proof-of-work functions to Verify performance assertions in the cloud. In: Proc. of the IEEE Second Int’l Conf. Cloud computing technology and Science (CloudCom), pp 687–692

  53. Peng K, Bao F (2009) Efficient publicly verifiable secret sharing with correctness, soundness and zk privacy. In: Information security applications (eds) Youm H, Yung M, vol. 5932 of lecture notes in computer Science, pp 118–132, Springer, Berlin Heidelberg

  54. Yan Z, Ding W, Yu X, Zhu H, Deng RH (2016) Deduplication on encrypted big data in cloud. IEEE Transactions on Big Data 2(2):138–150

    Article  Google Scholar 

  55. Yan Z, Wang M, Li Y, Vasilakos AV (2016) Encrypted data management with deduplication in cloud computing. IEEE Cloud Computing 3(2):28–35

    Article  Google Scholar 

  56. Yang K, Jia X, Ren K (2015) Secure and verifiable policy update outsourcing for big data access control in the cloud. Parallel & Distributed Systems IEEE Transactions on 26(12):3461–3470

    Article  Google Scholar 

  57. Qin BD, Deng RH, Liu SL, Ma SQ (2013) Attribute-based encryption with verifiable outsourced decryption. IEEE Transactions on Information Forensics & Security 8(8):1343–1354

    Article  Google Scholar 

  58. Chaum D (2004) Secret-ballot receipts: true voter-verifiable elections. IEEE Secur Priv 2(1):38-47

  59. Chaum D, Ryan PYA, Schneider SA (2005) A practical voter-verifiable election scheme. In: Proc of the 10th European Symposium on research in Cumputer Science (ESORICS´05), pp 118–139

  60. Adida B, Rivest RL (2006) Scratch & vote: self-contained paper-based cryptographic voting. WEPS´06: in Proc. of the 5th ACM workshop on privacy in electronic society, New York

  61. Setty S, Braun B, Vu V, Blumberg AJ, Parno B, Walfish M (2013) Resolving the conflict between generality and plausibility in verified computation. In: Proc of the ACM European Conference on Computer Systems (EuroSys), Apr. 2013

  62. Almeida JB, Bangerter E, Barbosa M, Krenn S, Sadeghi A-R, Schneider T (2010) A certifying compiler for zero-knowledge proofs of knowledge based on s-protocols. In: Proc of ESORICS

  63. Meiklejohn S, Erway CC, Küpc A, Hinkle T, Lysyanskaya A (2010) ZKPDL: a language-based system for efficient zero-knowledge proofs and electronic cash. In: Proc of USENIX

  64. Papamanthou C, Shi E, Tamassia R (2011) Publicly verifiable delegation of computation. Cryptology ePrint Archive, report 2011/587

  65. Yao A (1982) Protocols for secure computations. In: Proc of the IEEE Symposium on Foundations of Computer Science, pp 160–164

  66. Yao A (1986) How to generate and exchange secrets. In: Proc of the IEEE Symposium on Foundations of Computer Science, pp 162–167

  67. Setty S, Vu V, Panpalia N, Braun B, Blumberg AJ, Walfish M (2012) Taking proof-based verified computation a few steps closer to practicality. In: Proc. of USENIX Security

  68. Canetti R, Riva B, Rothblum GN (2011) Two 1-round protocols for delegation of computation. Cryptology ePrint Archive, report 2011/518

  69. Gentry C, Wichs D (2011) Separating succinct non-interactive arguments from all falsifiable assumptions. In: Proceedings of the ACM Symposium on Theory of Computing, STOC

  70. Papamanthou C, Tamassia R, Triandopoulos N (2011) Optimal verification of operations on dynamic sets. In: Rogaway P (ed) CRYPTO 2011. LNCS, vol. 6841. Springer, Heidelberg, pp 91–110

    Google Scholar 

  71. Rivest RL, Adleman L, Dertouzos ML (1978) On data banks and privacy homomorphisms. Foundations of Secure Computation, pp 169–180

  72. Cramer R, Damgård I, Schoenmakers B (1994) Proofs of partial knowledge and simplified design of witness hiding protocols. In: Proc of CRYPTO

  73. Backes M, Maffe M, Pecina K (2012) Automated synthesis of privacy preserving distributed applications. In: Proc of ISOC NDSS

  74. Groth J, Sahai A (2008) Efficient non-interactive proof systems for bilinear groups. In: Proc of EUROCRYPT

  75. Rial A, Danezis G (2011) Privacy-preserving smart metering. In: Proc of the ACM WPES

  76. Gentry C (2009) A fully homomorphic encryption scheme. Ph.D. dissertation, Stanford University

  77. Johnson R, Molnar D, Song D, Wagner D (2002) Homomorphic signature schemes. In: CT-RSA 2002. LNCS, vol. 2271, pp 244–262, Springer, Heidelberg

  78. Catalano D, Marcedone A, Puglisi O (2013) Linearly homomorphic structure preserving signatures: new methodologies and applications. IACR Cryptology ePrint Archive 2013:801

  79. Ahn JH, Boneh D, Camenisch J, Hohenberger S, Shelat A, Waters B (2012) Computing on authenticated data. In: TCC 2012. LNCS, vol. 7194, pp 1–20, Springer, Heidelberg

  80. Attrapadung N, Libert B, Peters T (2012) Computing on authenticated data: new privacy definitions and constructions. In: ASIACRYPT 2012, LNCS, vol. 7658, pp 367–385, Springer, Heidelberg

  81. Attrapadung N, Libert B, Peters T (2013) Efficient completely context-hiding quotable and linearly homomorphic signatures. In: PKC 2013. LNCS, vol. 7778, pp 386–404, Springer, Heidelberg

  82. Boneh D, Freeman DM (2011) Homomorphic signatures for polynomial function. In: EUROCRYPT 2011. LNCS, vol. 6632, pp 149–168, Springer, Heidelberg

  83. Libert B, Peters T, Joye M, Yung M (2013) Linearly homomorphic structurepreserving signatures and their applications. In: CRYPTO 2013, Part II. LNCS, vol. 8043, pp 289–307, Springer, Heidelberg

  84. Gennaro R, Wichs D (2013) Fully homomorphic message authenticators. In: ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp 301–320, Springer, Heidelberg

  85. Joo C, Yun A (2013) Homomorphic authenticated encryption secure against chosenciphertext attack. IACR Cryptology ePrint Archive 2013:726

    Google Scholar 

  86. Catalano D, Fiore D (2013) Practical homomorphic MACs for arithmetic circuits. In: EUROCRYPT 2013. LNCS, vol. 7881, pp 336–352, Springer, Heidelberg

  87. Shi E, Chan TH, Rieffel EG, Chow R, Song D (2011) Privacy-preserving aggregation of time-series data. In: NDSS 2011, the internet society, February 2011

  88. Goldwasser S, Gordon SD, Goyal V, Jain A, Katz J, Liu FH, Sahai A, Shi E, Zhou HS (2014) Multi-input functional encryption. In EUROCRYPT 2014, LNCS, vol. 8441, Springer, Heidelberg, pp 578–602

  89. Gordon SD, Katz J, Liu FH, Shi E, Zhou HS (2015) Multi-client verifiable computation with stronger security guarantees. In: 12th theory of cryptography conference, TCC 2015, Proceedings: LNCS 9015, pp 144–68

  90. Sakka MA, Defude B (2012) Towards a scalable semantic provenance management system. Transactions on Large-Scale Data- and Knowledge-Centered Systems VII, Springer Verlag, Berlin, pp 96–127

  91. Sakka MA, Defude B (2012) Scalability issues in designing and implementing semantic provenance management systems. In: Proc. of data Management in Cloud, grid and P2P systems. 5th international conference, globe 2012, Springer Verlag, Berlin, Germany, pp 49–61, 5-6 sept. 2012

  92. Marinho A, Murta L, Werner C et al (2012) ProvManager: a provenance management system for scientific workflows. Concurrency and Computation: Practice and Experience 24(13):1513–1530

    Article  Google Scholar 

  93. Buneman P, Chapman A, Cheney J (2006) Provenance management in curated databases. 2006 ACM SIGMOD international conference on Management of Data, Chicago, pp 539–550, 27-29, June 2006

  94. Zheng H, Zhu QH, Wu K (2012) Provenance management for data quality assessment. Journal of Software 7(8):1905–1910

    Article  Google Scholar 

  95. Sabaa H, Panda B (2007) data authentication and provenance management. In: Prof of Second IEEE International Conference on Digital Information Management, Piscataway, pp 309–14, Oct. 2007

  96. Li T, Liu L, Zhang XL et al (2014) ProvenanceLens: service provenance management in the cloud. Collaborative computing: networking, applications and Worksharing (CollaborateCom), 2014 international conference on, pp 275–284

  97. Young M (1989) The technical Writer’s handbook. University Science, Mill Valley

    Google Scholar 

Download references

Acknowledgments

This work is sponsored by the National Key Research and Development Program of China (grant 2016YFB0800704), the NSFC (grants 61672410 and U1536202), the Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2016ZDJC-06), the PhD grant of the Ministry of Education, China (grant 20130203110006), the 111 project (grants B08038 and B16037), and Aalto University.

Author information

Authors and Affiliations

  1. The State Key Laboratory on Integrated Services Networks, School of Cyber Engineering, Xidian University, Xi’an, China

    Xixun Yu & Zheng Yan

  2. Department of Communications and Networking, Aalto University, Espoo, Finland

    Zheng Yan

  3. Department of Computer Science, Electrical and Space Engineering, Lulea University of Technology, Lulea, Sweden

    Athanasios V. Vasilakos

Authors
  1. Xixun Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Athanasios V. Vasilakos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zheng Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, X., Yan, Z. & Vasilakos, A.V. A Survey of Verifiable Computation. Mobile Netw Appl 22, 438–453 (2017). https://doi.org/10.1007/s11036-017-0872-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11036-017-0872-3

Keywords

Search

Navigation