Skip to main content
SpringerLink
Log in
Book cover

Cryptographers’ Track at the RSA Conference

CT-RSA 2015: Topics in Cryptology –- CT-RSA 2015 pp 127–144Cite as

Revisiting Cryptographic Accumulators, Additional Properties and Relations to Other Primitives

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9048))

Abstract

Cryptographic accumulators allow to accumulate a finite set of values into a single succinct accumulator. For every accumulated value, one can efficiently compute a witness, which certifies its membership in the accumulator. However, it is computationally infeasible to find a witness for any non-accumulated value. Since their introduction, various accumulator schemes for numerous practical applications and with different features have been proposed. Unfortunately, to date there is no unifying model capturing all existing features. Such a model can turn out to be valuable as it allows to use accumulators in a black-box fashion.

To this end, we propose a unified formal model for (randomized) cryptographic accumulators which covers static and dynamic accumulators, their universal features and includes the notions of undeniability and indistinguishability. Additionally, we provide an exhaustive classification of all existing schemes. In doing so, it turns out that most accumulators are distinguishable. Fortunately, a simple, light-weight generic transformation allows to make many existing dynamic accumulator schemes indistinguishable. As this transformation, however, comes at the cost of reduced collision freeness, we additionally propose the first indistinguishable scheme that does not suffer from this shortcoming. Finally, we employ our unified model for presenting a black-box construction of commitments from indistinguishable accumulators as well as a black-box construction of indistinguishable, undeniable universal accumulators from zero-knowledge sets. Latter yields the first universal accumulator construction that provides indistinguishability.

The authors have been supported by the European Commission through project FP7-FutureID, grant agreement number 318424. An extended version of this paper is available in the IACR Cryptology ePrint Archive.

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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acar, T., Nguyen, L.: Revocation for delegatable anonymous credentials. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 423–440. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  3. Au, M.H., Tsang, P.P., Susilo, W., Mu, Y.: Dynamic universal accumulators for DDH groups and their application to attribute-based anonymous credential systems. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 295–308. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Barić, N., Pfitzmann, B.: Collision-free accumulators and fail-stop signature schemes without trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–494. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  5. Benaloh, J., de Mare, M.: One-way accumulators: a decentralized alternative to digital signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  6. Boneh, D., Corrigan-Gibbs, H.: Bivariate polynomials modulo composites and their applications. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 42–62. Springer, Heidelberg (2014). http://eprint.iacr.org/2014/719

    Chapter  Google Scholar 

  7. Buldas, A., Laud, P., Lipmaa, H.: Accountable certificate management using undeniable attestations. In: ACM CCS, pp. 9–17. ACM (2000)

    Google Scholar 

  8. Buldas, A., Laud, P., Lipmaa, H.: Eliminating Counterevidence with Applications to Accountable Certificate Management. Journal of Computer Security 10 (2002)

    Google Scholar 

  9. Camacho, P., Hevia, A.: On the impossibility of batch update for cryptographic accumulators. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 178–188. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Camacho, P., Hevia, A., Kiwi, M., Opazo, R.: Strong accumulators from collision-resistant hashing. In: Wu, T.-C., Lei, C.-L., Rijmen, V., Lee, D.-T. (eds.) ISC 2008. LNCS, vol. 5222, pp. 471–486. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Camenisch, J., Kohlweiss, M., Soriente, C.: An accumulator based on bilinear maps and efficient revocation for anonymous credentials. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 481–500. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Camenisch, J.L., Lysyanskaya, A.: Dynamic accumulators and application to efficient revocation of anonymous credentials. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 61–76. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Canard, S., Jambert, A.: On extended sanitizable signature schemes. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 179–194. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Catalano, D., Fiore, D.: Vector commitments and their applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 55–72. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Chase, M., Healy, A., Lysyanskaya, A., Malkin, T., Reyzin, L.: Mercurial Commitments with Applications to Zero-Knowledge Sets. Journal of Cryptology 26(2), 251–279 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  16. Damgård, I., Triandopoulos, N.: Supporting Non-membership Proofs with Bilinear-map Accumulators. Cryptology ePrint Archive, Report 2008/538 (2008). http://eprint.iacr.org/2008/538

  17. de Meer, H., Liedel, M., Pöhls, H.C., Posegga, J.: Indistinguishability of One-Way Accumulators. Technical Report MIP-1210, Faculty of Computer Science and Mathematics (FIM), University of Passau (2012)

    Google Scholar 

  18. de Meer, H., Pöhls, H.C., Posegga, J., Samelin, K.: Redactable signature schemes for trees with signer-controlled non-leaf-redactions. In: Obaidat, M.S., Filipe, J. (eds.) ICETE 2012. CCIS, vol. 455, pp. 155–171. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  19. Fauzi, P., Lipmaa, H., Zhang, B.: Efficient non-interactive zero knowledge arguments for set operations. In: Christin, N., Safavi-Naini, R. (eds.) FC 2014. LNCS, vol. 8437, pp. 214–231. Springer, Heidelberg (2014). http://eprint.iacr.org/2014/006

    Chapter  Google Scholar 

  20. Fazio, N., Nicolisi, A.: Cryptographic Accumulators: Definitions. Constructions and Applications, Technical report (2002)

    Google Scholar 

  21. Ghosh, E., Ohrimenko, O., Tamassia, R.: Verifiable Member and Order Queries on a List in Zero-Knowledge. Cryptology ePrint Archive, Report 2014/632 (2014). http://eprint.iacr.org/2014/632

  22. Goodrich, M.T., Tamassia, R., Hasic, J.: An efficient dynamic and distributed cryptographic accumulator. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 372–388. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  24. Li, J., Li, N., Xue, R.: Universal accumulators with efficient nonmembership proofs. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 253–269. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  25. Lipmaa, H.: Secure accumulators from euclidean rings without trusted setup. In: Bao, F., Samarati, P., Zhou, J. (eds.) ACNS 2012. LNCS, vol. 7341, pp. 224–240. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  26. Mashatan, A., Vaudenay, S.: A Fully Dynamic Universal Accumulator. Proceedings of the Romanian Academy 14, 269–285 (2013)

    MathSciNet  Google Scholar 

  27. Micali, S., Rabin, M.O., Kilian, J.: Zero-knowledge sets. In: FOCS, pp. 80–91 (2003)

    Google Scholar 

  28. Miers, I., Garman, C., Green, M., Rubin, A.D.: Zerocoin: anonymous distributed E-cash from bitcoin. In: IEEE Symposium on Security and Privacy, pp. 397–411. IEEE (2013)

    Google Scholar 

  29. Nguyen, L.: Accumulators from bilinear pairings and applications. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 275–292. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  30. Nyberg, K.: Commutativity in cryptography. In: 1st International Trier Conference in Functional Analysis. Walter Gruyter & Co (1996)

    Google Scholar 

  31. Nyberg, K.: Fast accumulated hashing. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 83–87. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  32. Peng, K., Bao, F.: Vulnerability of a non-membership proof scheme. In: SECRYPT, pp. 1–4, July 2010

    Google Scholar 

  33. Pöhls, H.C., Peters, S., Samelin, K., Posegga, J., de Meer, H.: Malleable signatures for resource constrained platforms. In: Cavallaro, L., Gollmann, D. (eds.) WISTP 2013. LNCS, vol. 7886, pp. 18–33. Springer, Heidelberg (2013)

    Google Scholar 

  34. Pöhls, H.C., Samelin, K.: On updatable redactable signatures. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 457–475. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  35. Sander, T.: Efficient accumulators without trapdoor extended abstract. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 252–262. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  36. Sander, T., Ta-Shma, A., Yung, M.: Blind, auditable membership proofs. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 53–71. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  37. Slamanig, D.: Dynamic accumulator based discretionary access control for outsourced storage with unlinkable access. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 215–222. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  38. Sudarsono, A., Nakanishi, T., Funabiki, N.: Efficient proofs of attributes in pairing-based anonymous credential system. In: Fischer-Hübner, S., Hopper, N. (eds.) PETS 2011. LNCS, vol. 6794, pp. 246–263. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  39. Tsudik, G., Xu, S.: Accumulating composites and improved group signing. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 269–286. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  40. Wang, P., Wang, H., Pieprzyk, J.: A new dynamic accumulator for batch updates. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 98–112. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Applied Information Processing and Communications (IAIK), Graz University of Technology (TUG), Inffeldgasse 16a, 8010, Graz, Austria

    David Derler, Christian Hanser & Daniel Slamanig

Authors
  1. David Derler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Hanser
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Slamanig
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Derler .

Editor information

Editors and Affiliations

  1. Aalto University School of Science, Espoo, Finland

    Kaisa Nyberg

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Derler, D., Hanser, C., Slamanig, D. (2015). Revisiting Cryptographic Accumulators, Additional Properties and Relations to Other Primitives. In: Nyberg, K. (eds) Topics in Cryptology –- CT-RSA 2015. CT-RSA 2015. Lecture Notes in Computer Science(), vol 9048. Springer, Cham. https://doi.org/10.1007/978-3-319-16715-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16715-2_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16714-5

  • Online ISBN: 978-3-319-16715-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation