Skip to main content
SpringerLink
Log in
Book cover

International Conference on Cryptology and Information Security in Latin America

LATINCRYPT 2017: Progress in Cryptology – LATINCRYPT 2017 pp 23–43Cite as

Anonymous Single-Round Server-Aided Verification

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11368))

Abstract

Server-Aided Verification (SAV) is a method that can be employed to speed up the process of verifying signatures by letting the verifier outsource part of its computation load to a third party. Achieving fast and reliable verification under the presence of an untrusted server is an attractive goal in cloud computing and internet of things scenarios. In this paper, we describe a simple framework for SAV where the interaction between a verifier and an untrusted server happens via a single-round protocol. We propose a security model for SAV that refines existing ones and includes the new notions of SAV -anonymity and extended unforgeability. In addition, we apply our definitional framework to provide the first generic transformation from any signature scheme to a single-round SAV scheme that incorporates verifiable computation. Our compiler identifies two independent ways to achieve SAV-anonymity: computationally, through the privacy of the verifiable computation scheme, or unconditionally, through the adaptibility of the signature scheme.

Finally, we define three novel instantiations of SAV schemes obtained through our compiler. Compared to previous works, our proposals are the only ones which simultaneously achieve existential unforgeability and soundness against collusion.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   74.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    In [8, 26] the output of \(\mathsf{SAV.VSetup}\) is called \(\mathbf{Vstring}\).

  2. 2.

    To improve readability, we put the subscript \(\varSigma \) (resp. superscript \(\varGamma \)) to each algorithm related to the signature (resp. verifiable computation) scheme.

  3. 3.

    This claim will become clear after seeing examples of SAV signature schemes.

  4. 4.

    To provide an example, consider the BLS signature scheme [3]. Given \({\mathsf {pk}}=g^{\mathsf {sk}}\), \( m \in \{0,1\}^*\), \(\sigma \in {\mathbb G}_{p}\) and \({\mathsf {h}}\in {\mathbb Z}_{p}\), the output of \({\mathsf {Adapt}}\) can be defined as: \({\mathsf {pk}}' = {\mathsf {pk}}\cdot g^{\mathsf {h}}\) and \(\sigma '=\sigma \cdot H( m )^{\mathsf {h}}\). It is immediate to check that \((\sigma ', m )\) is a valid pair under \({\mathsf {pk}}'\).

  5. 5.

    To give benchmarks, let \(M_p\) denote the computational cost of a base field multiplication in \(\mathbb {F}_p\) with \(\log p = 256\), then computing \(z^a\) for any \(z\in \mathbb {F}_p\) and \(a\in [p]\) costs about \(256M_p\), while computing the Optimal Ate pairing on the bn curve requires about \(16000M_p\) (results extrapolated from Table 1 in [16]).

  6. 6.

    Efficiency gain is the ratio \(\big (cost(\mathsf{{ SAV.ProbGen}}) + cost(\mathsf{{ SAV.Verify}}) \big ) / cost(\mathsf {Verify}_\varSigma )\).

References

  1. Béguin, P., Quisquater, J.-J.: Fast server-aided RSA Signatures secure against active attacks. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 57–69. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-44750-4_5

    Chapter  Google Scholar 

  2. Benabbas, S., Gennaro, R., Vahlis, Y.: Verifiable delegation of computation over large datasets. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 111–131. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_7

    Chapter  Google Scholar 

  3. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. J. Cryptol. 17(4), 297–319 (2004)

    Article  MathSciNet  Google Scholar 

  4. Boneh, D., Shen, E., Waters, B.: Strongly unforgeable signatures based on computational diffie-Hellman. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 229–240. Springer, Heidelberg (2006). https://doi.org/10.1007/11745853_15

    Chapter  Google Scholar 

  5. Camenisch, J., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_4

    Chapter  Google Scholar 

  6. Canard, S., Devigne, J., Sanders, O.: Delegating a pairing can be both secure and efficient. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 549–565. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07536-5_32

    Chapter  MATH  Google Scholar 

  7. Cao, Z., Liu, L., Markowitch, O.: On two kinds of flaws in some server-aided verification schemes. Int. J. Netw. Secur. 18(6), 1054–1059 (2016)

    Google Scholar 

  8. Chow, S.S., Au, M.H., Susilo, W.: Server-aided signatures verification secure against collusion attack. Inf. Secur. Tech. Rep. 17(3), 46–57 (2013)

    Article  Google Scholar 

  9. Costello, C., et al.: Geppetto: versatile verifiable computation. In: 2015 IEEE Symposium on Security and Privacy (SP), pp. 253–270. IEEE (2015)

    Google Scholar 

  10. Derler, D., Slamanig, D.: Key-homomorphic signatures and applications to multiparty signatures. Technical report, IACR Cryptology ePrint Archive 2016, 792 (2016)

    Google Scholar 

  11. Ding, X., Mazzocchi, D., Tsudik, G.: Experimenting with server-aided signatures. In: NDSS (2002)

    Google Scholar 

  12. Fiore, D., Gennaro, R., Pastro, V.: Efficiently verifiable computation on encrypted data. In: Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, pp. 844–855. ACM (2014)

    Google Scholar 

  13. Fischlin, M.: Anonymous signatures made easy. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 31–42. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71677-8_3

    Chapter  Google Scholar 

  14. Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_25

    Chapter  Google Scholar 

  15. Girault, M., Lefranc, D.: Server-aided verification: theory and practice. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 605–623. Springer, Heidelberg (2005). https://doi.org/10.1007/11593447_33

    Chapter  Google Scholar 

  16. Guillevic, A., Vergnaud, D.: Algorithms for outsourcing pairing computation. In: Joye, M., Moradi, A. (eds.) CARDIS 2014. LNCS, vol. 8968, pp. 193–211. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16763-3_12

    Chapter  Google Scholar 

  17. Guo, F., Mu, Y., Susilo, W., Varadharajan,V.: Server-aided signature verification for lightweight devices. Comput. J. bxt003 (2013)

    Google Scholar 

  18. Lim, C.H., Lee, P.J.: Server(Prover/Signer)-aided verification of identity proofs and signatures. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 64–78. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-49264-X_6

    Chapter  Google Scholar 

  19. Pagnin, E., Mitrokotsa, A., Tanaka, K.: Anonymous single-round server-aided verification (2017). http://eprint.iacr.org/2017/794

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

    Google Scholar 

  21. Wang, B.: A server-aided verification signature scheme without random oracles. Int. Rev. Comput. Softw. 7, 3446 (2012)

    Google Scholar 

  22. Wang, Z.: A new construction of the server-aided verification signature scheme. Math. Comput. Model. 55(1), 97–101 (2012)

    Article  MathSciNet  Google Scholar 

  23. Wang, Z., Wang, L., Yang, Y., Hu, Z.: Comment on Wu et al’s server-aided verification signature schemes. IJ Netw. Secur. 10(2), 158–160 (2010)

    Google Scholar 

  24. Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_7

    Chapter  Google Scholar 

  25. Wu, W., Mu, Y., Susilo, W., Huang, X.: Server-aided verification signatures: definitions and new constructions. In: Baek, J., Bao, F., Chen, K., Lai, X. (eds.) ProvSec 2008. LNCS, vol. 5324, pp. 141–155. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88733-1_10

    Chapter  Google Scholar 

  26. Wu, W., Mu, Y., Susilo, W., Huang, X.: Provably secure server-aided verification signatures. Comput. Math. Appl. 61(7), 1705–1723 (2011)

    Article  Google Scholar 

  27. Yang, G., Wong, D.S., Deng, X., Wang, H.: Anonymous signature schemes. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 347–363. Springer, Heidelberg (2006). https://doi.org/10.1007/11745853_23

    Chapter  Google Scholar 

  28. Zhang, F., Safavi-Naini, R., Susilo, W.: An efficient signature scheme from bilinear pairings and its applications. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 277–290. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24632-9_20

    Chapter  Google Scholar 

Download references

Acknowledgements

We thank Dario Fiore (Assistant Research Professor) for providing useful comments on the contributions of this paper. This work was partially supported by the Japanese Society for the Promotion of Science (JSPS), summer program, the SNSF project SwissSenseSynergy and the STINT project IB 2015-6001.

Author information

Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Elena Pagnin & Aikaterini Mitrokotsa

  2. Tokyo Institute of Technology, Tokyo, Japan

    Keisuke Tanaka

Authors
  1. Elena Pagnin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aikaterini Mitrokotsa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Keisuke Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elena Pagnin .

Editor information

Editors and Affiliations

  1. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Tanja Lange

  2. University of Haifa, Haifa, Israel

    Orr Dunkelman

A Detailed Descriptions of Our SAV Schemes

A Detailed Descriptions of Our SAV Schemes

In this Appendix we present thorough descriptions of the new SAV scheme proposed in this paper (Sect. 6). The complete explanations of the algorithms in SAV\(^\mathsf{{CDS_1}}_{\mathsf{{BLS}}}\), SAV\(^\mathsf{{CDS_1}}_{\mathsf{Wat}}\) and SAV\(^{\mathsf{{CDS_2}}}_{\mathsf{{CL}}}\) are presented in Figs. 4, 5 and 6 respectively. For consistency, we adopt the multiplicative notation for describing the operation elliptic curve groups.

Fig. 4.
figure 4

SAV\(^\mathsf{{CDS_1}}_{\mathsf{{BLS}}}\) : Our SAV for the BLS Signature in [3].

Full size image
Fig. 5.
figure 5

SAV\(^\mathsf{{CDS_1}}_{\mathsf{Wat}}\): Our SAV for the Wat Signature in [24].

Full size image
Fig. 6.
figure 6

SAV\(^{\mathsf{{CDS_2}}}_{\mathsf{{CL}}}\) : Our SAV for the CL Signature in [5].

Full size image

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Pagnin, E., Mitrokotsa, A., Tanaka, K. (2019). Anonymous Single-Round Server-Aided Verification. In: Lange, T., Dunkelman, O. (eds) Progress in Cryptology – LATINCRYPT 2017. LATINCRYPT 2017. Lecture Notes in Computer Science(), vol 11368. Springer, Cham. https://doi.org/10.1007/978-3-030-25283-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-25283-0_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25282-3

  • Online ISBN: 978-3-030-25283-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation