Skip to main content
SpringerLink
Log in

Selectively Linkable Group Signatures—Stronger Security and Preserved Verifiability

  • Conference paper
  • First Online:
Cryptology and Network Security (CANS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13099))

Included in the following conference series:

Abstract

Group signatures allow group members to sign on behalf of the group anonymously. They are therefore well suited to storing data in a way that preserves the users’ privacy, while guaranteeing its authenticity. Garms and Lehmann (PKC’19) introduced a new type of group signatures that balance privacy with utility by allowing to selectively link subsets of the group signatures via an oblivious entity, the converter. The conversion takes a batch of group signatures and blindly transforms signatures originating from the same user into a consistent representation. Their scheme essentially targets a setting where the entity receiving fully unlinkable signatures and the converted ones is the same: only pseudonyms but not full signatures are converted, and the input to the converter is assumed to be well-formed. Thus, the converted outputs are merely linkable pseudonyms but no longer signatures.

In this work we extend and strengthen such convertibly linkable group signatures. Conversion can now be triggered by malicious entities too, and the converted outputs can be publicly verified. This preserves the authentication of data during the conversion process. We define the security of this scheme and give a provably secure instantiation. Our scheme makes use of controlled-malleable NIZKs, which allow proofs to be mauled in a controlled manner. This allows signatures to be blinded, while still ensuring they can be verified during conversions.

A. Fraser—The author was supported by the EPSRC Next Stage Digital Economy Centre in the Decentralised Digital Economy (DECaDE) under grant number EP/T022485/1.

L. Garms—The author was supported by the EPSRC and the UK government as part of the Centre for Doctoral Training in Cyber Security at Royal Holloway, University of London (EP/K035584/1) and by the InnovateUK funded project AQuaSec, as well as by a research grant from Nomadic Labs and the Tezos Foundation.

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

Access this chapter

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 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
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

Institutional subscriptions

References

  1. Helping public health officials combat covid-19. https://blog.google/technology/health/covid-19-community-mobility-reports/

  2. Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-preserving signatures and commitments to group elements. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 209–236. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_12

    Chapter  Google Scholar 

  3. Abe, M., Hofheinz, D., Nishimaki, R., Ohkubo, M., Pan, J.: Compact structure-preserving signatures with almost tight security. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 548–580. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_19

    Chapter  Google Scholar 

  4. Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_38

    Chapter  Google Scholar 

  5. Bellare, M., Shi, H., Zhang, C.: Foundations of group signatures: the case of dynamic groups. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 136–153. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30574-3_11

    Chapter  Google Scholar 

  6. Bernhard, D., Fuchsbauer, G., Ghadafi, E., Smart, N.P., Warinschi, B.: Anonymous attestation with user-controlled linkability. Int. J. Inf. Secur. 12(3), 219–249 (2013). https://doi.org/10.1007/s10207-013-0191-z

    Article  Google Scholar 

  7. Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_3

    Chapter  Google Scholar 

  8. Bootle, J., Cerulli, A., Chaidos, P., Ghadafi, E., Groth, J.: Foundations of fully dynamic group signatures. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 117–136. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_7

    Chapter  Google Scholar 

  9. Brickell, E., Camenisch, J., Chen, L.: Direct anonymous attestation. In: ACM CCS (2004)

    Google Scholar 

  10. Camenisch, J., Drijvers, M., Lehmann, A.: Anonymous attestation using the strong Diffie Hellman assumption revisited. In: Franz, M., Papadimitratos, P. (eds.) Trust 2016. LNCS, vol. 9824, pp. 1–20. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45572-3_1

    Chapter  Google Scholar 

  11. Camenisch, J., Drijvers, M., Lehmann, A.: Universally composable direct anonymous attestation. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9615, pp. 234–264. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49387-8_10

    Chapter  Google Scholar 

  12. Camenisch, J., Kiayias, A., Yung, M.: On the portability of generalized Schnorr proofs. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 425–442. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_25

    Chapter  Google Scholar 

  13. Camenisch, J., Stadler, M.: Efficient group signature schemes for large groups. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 410–424. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052252

    Chapter  Google Scholar 

  14. Canard, S., Schoenmakers, B., Stam, M., Traoré, J.: List signature schemes. Discrete Appl. Math. 154(2), 189–201 (2006)

    Article  MathSciNet  Google Scholar 

  15. Canetti, R., Krawczyk, H., Nielsen, J.B.: Relaxing chosen-ciphertext security. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 565–582. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_33

    Chapter  Google Scholar 

  16. Chase, M., Kohlweiss, M., Lysyanskaya, A., Meiklejohn, S.: Malleable proof systems and applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 281–300. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_18

    Chapter  Google Scholar 

  17. Chatterjee, S., Menezes, A.: On cryptographic protocols employing asymmetric pairings- the role of \(\psi \) revisited. Discrete Appl. Math. 159(13), 1311–1322 (2011)

    Article  MathSciNet  Google Scholar 

  18. Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_22

    Chapter  Google Scholar 

  19. Chow, S., Lee, J., Subramanian, L.: Two-party computation model for privacy-preserving queries over distributed databases. In: NDSS (2009)

    Google Scholar 

  20. Chow, S.S.M., Susilo, W., Yuen, T.H.: Escrowed linkability of ring signatures and its applications. In: Nguyen, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 175–192. Springer, Heidelberg (2006). https://doi.org/10.1007/11958239_12

    Chapter  Google Scholar 

  21. De Santis, A., Di Crescenzo, G., Ostrovsky, R., Persiano, G., Sahai, A.: Robust non-interactive zero knowledge. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 566–598. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_33

    Chapter  Google Scholar 

  22. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31(4), 469–472 (1985)

    Article  MathSciNet  Google Scholar 

  23. Emura, K., Hayashi, T.: Road-to-vehicle communications with time-dependent anonymity: a lightweight construction and its experimental results. IEEE Trans. Veh. Technol. 67(2), 1582–1597 (2017)

    Article  Google Scholar 

  24. Franklin, M., Zhang, H.: Unique group signatures. In: Foresti, S., Yung, M., Martinelli, F. (eds.) ESORICS 2012. LNCS, vol. 7459, pp. 643–660. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33167-1_37

    Chapter  Google Scholar 

  25. Fraser, A., Garms, L., Lehmann, A.: Selectively linkable group signatures - stronger security and preserved verifiability. Cryptology ePrint Archive 2021/1312 (2021). https://eprint.iacr.org/2021/1312.pdf

  26. Fuchsbauer, G.: Automorphic signatures in bilinear groups and an application to round-optimal blind signatures. Cryptology ePrint Archive 2009/320 (2009)

    Google Scholar 

  27. Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008)

    Article  MathSciNet  Google Scholar 

  28. Garms, L., Lehmann, A.: Group signatures with selective linkability. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11442, pp. 190–220. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17253-4_7

    Chapter  Google Scholar 

  29. Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006). https://doi.org/10.1007/11935230_29

    Chapter  Google Scholar 

  30. Groth, J.: Fully anonymous group signatures without random oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_10

    Chapter  Google Scholar 

  31. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24

    Chapter  Google Scholar 

  32. Hwang, J.Y., Lee, S., Chung, B.H., Cho, H.S., Nyang, D.: Short group signatures with controllable linkability. In: Workshop on Lightweight Security & Privacy: (LightSec) (2011)

    Google Scholar 

  33. Hwang, J.Y., Lee, S., Chung, B.H., Cho, H.S., Nyang, D.: Group signatures with controllable linkability for dynamic membership. Inf. Sci. 222, 761–778 (2013)

    Article  MathSciNet  Google Scholar 

  34. Kiayias, A., Tsiounis, Y., Yung, M.: Traceable signatures. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 571–589. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_34

    Chapter  Google Scholar 

  35. Kim, S.J., Park, S.J., Won, D.H.: Convertible group signatures. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 311–321. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0034857

    Chapter  Google Scholar 

  36. Krenn, S., Samelin, K., Striecks, C.: Practical group-signatures with privacy-friendly openings. In: ARES (2019)

    Google Scholar 

  37. Libert, B., Peters, T., Yung, M.: Scalable group signatures with revocation. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 609–627. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_36

    Chapter  Google Scholar 

  38. Sakai, Y., Emura, K., Hanaoka, G., Kawai, Y., Matsuda, T., Omote, K.: Group signatures with message-dependent opening. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 270–294. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36334-4_18

    Chapter  Google Scholar 

  39. Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 688–689. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-46885-4_68

    Chapter  Google Scholar 

  40. Slamanig, D., Spreitzer, R., Unterluggauer, T.: Adding controllable linkability to pairing-based group signatures for free. In: Chow, S.S.M., Camenisch, J., Hui, L.C.K., Yiu, S.M. (eds.) ISC 2014. LNCS, vol. 8783, pp. 388–400. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13257-0_23

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Surrey, Guildford, UK

    Ashley Fraser

  2. Royal Holloway, University of London, Egham, UK

    Lydia Garms

  3. IMDEA Software Institute, Madrid, Spain

    Lydia Garms

  4. Hasso-Plattner-Institute, University of Potsdam, Potsdam, Germany

    Anja Lehmann

Authors
  1. Ashley Fraser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lydia Garms
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anja Lehmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lydia Garms .

Editor information

Editors and Affiliations

  1. University of Padua, Padua, Italy

    Mauro Conti

  2. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

    Marc Stevens

  3. AIT Austrian Institute of Technology, Vienna, Austria

    Stephan Krenn

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Fraser, A., Garms, L., Lehmann, A. (2021). Selectively Linkable Group Signatures—Stronger Security and Preserved Verifiability. In: Conti, M., Stevens, M., Krenn, S. (eds) Cryptology and Network Security. CANS 2021. Lecture Notes in Computer Science(), vol 13099. Springer, Cham. https://doi.org/10.1007/978-3-030-92548-2_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-92548-2_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92547-5

  • Online ISBN: 978-3-030-92548-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation