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On New Zero-Knowledge Arguments for Attribute-Based Group Signatures from Lattices

  • Veronika Kuchta
  • Rajeev Anand Sahu
  • Gaurav Sharma
  • Olivier Markowitch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10779)

Abstract

Due to its emerging security and computational properties, lattice-based constructions are of prime concerns in recent research. Zero-knowledge evidences serve strongest security guarantees to cryptographic primitives. In this paper we formalize a new zero-knowledge argument (ZKA) suitable for lattice-based construction and employ it to security assurance of the proposed structure of attribute-based group signature on lattice assumption. To the best of our knowledge this paper proposes the first such construction.

References

  1. 1.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13190-5_28 CrossRefGoogle Scholar
  2. 2.
    Ali, S.T., Amberker, B.: Attribute-based group signature without random oracles with attribute anonymity. Int. J. Inf. Comput. Secur. 6(2), 109–132 (2014)Google Scholar
  3. 3.
    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 CrossRefGoogle Scholar
  4. 4.
    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 CrossRefGoogle Scholar
  5. 5.
    Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24676-3_4 CrossRefGoogle Scholar
  6. 6.
    Boyen, X.: Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13013-7_29 CrossRefGoogle Scholar
  7. 7.
    Boyen, X., Waters, B.: Full-domain subgroup hiding and constant-size group signatures. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 1–15. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-71677-8_1 CrossRefGoogle Scholar
  8. 8.
    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 Google Scholar
  9. 9.
    El Bansarkhani, R., El Kaafarani, A.: Post-quantum attribute-based signatures from lattice assumptions. IACR Cryptology ePrint Archive, 2016, p. 823 (2016)Google Scholar
  10. 10.
    Emura, K., Miyaji, A., Omote, K.: A dynamic attribute-based group signature scheme and its application in an anonymous survey for the collection of attribute statistics. Inf. Media Technol. 4(4), 1060–1075 (2009)Google Scholar
  11. 11.
    Escala, A., Herranz, J., Morillo, P.: Revocable attribute-based signatures with adaptive security in the standard model. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 224–241. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-21969-6_14 CrossRefGoogle Scholar
  12. 12.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 197–206. ACM (2008)Google Scholar
  13. 13.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008, pp. 197–206. ACM (2008)Google Scholar
  14. 14.
    Gordon, S.D., Katz, J., Vaikuntanathan, V.: A group signature scheme from lattice assumptions. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 395–412. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    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 CrossRefGoogle Scholar
  16. 16.
    Herranz, J., Laguillaumie, F., Libert, B., Ràfols, C.: Short attribute-based signatures for threshold predicates. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 51–67. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-27954-6_4 CrossRefGoogle Scholar
  17. 17.
    Jia, X., Yupu, H., Juntao, G., Wen, G., Xuelian, L.: Attribute-based signatures on lattices. J. China Univ. Posts Telecommun. 23(4), 83–90 (2016)CrossRefGoogle Scholar
  18. 18.
    Khader, D.: Attribute based group signature with revocation. IACR Cryptology ePrint Archive 2007, p. 241 (2007)Google Scholar
  19. 19.
    Khader, D.: Attribute based group signatures. IACR Cryptology ePrint Archive 2007, p. 159 (2007)Google Scholar
  20. 20.
    Laguillaumie, F., Langlois, A., Libert, B., Stehlé, D.: Lattice-based group signatures with logarithmic signature size. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 41–61. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-42045-0_3 CrossRefGoogle Scholar
  21. 21.
    Langlois, A., Ling, S., Nguyen, K., Wang, H.: Lattice-based group signature scheme with verifier-local revocation. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 345–361. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54631-0_20 CrossRefGoogle Scholar
  22. 22.
    Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13190-5_4 CrossRefGoogle Scholar
  23. 23.
    Li, J., Kim, K.: Attribute-based ring signatures. IACR Cryptology EPrint Archive 2008, p. 394 (2008)Google Scholar
  24. 24.
    Liang, X., Cao, Z., Shao, J., Lin, H.: Short group signature without random oracles. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 69–82. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-77048-0_6 CrossRefGoogle Scholar
  25. 25.
    Libert, B., Ling, S., Mouhartem, F., Nguyen, K., Wang, H.: Signature schemes with efficient protocols and dynamic group signatures from lattice assumptions. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 373–403. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53890-6_13 CrossRefGoogle Scholar
  26. 26.
    Libert, B., Ling, S., Nguyen, K., Wang, H.: Zero-knowledge arguments for lattice-based accumulators: logarithmic-size ring signatures and group signatures without trapdoors. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 1–31. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49896-5_1 CrossRefGoogle Scholar
  27. 27.
    Ling, S., Nguyen, K., Stehlé, D., Wang, H.: Improved zero-knowledge proofs of knowledge for the ISIS problem, and applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 107–124. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36362-7_8 CrossRefGoogle Scholar
  28. 28.
    Maji, H.K., Prabhakaran, M., Rosulek, M.: Attribute-based signatures: achieving attribute-privacy and collusion-resistance. IACR Cryptology ePrint Archive 2008, p. 328 (2008)Google Scholar
  29. 29.
    Maji, H.K., Prabhakaran, M., Rosulek, M.: Attribute-based signatures. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 376–392. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-19074-2_24 CrossRefGoogle Scholar
  30. 30.
    Mao, X.-P., Chen, K.-F., Long, Y., Wang, L.-L.: Attribute-based signature on lattices. J. Shanghai Jiaotong Univ. (Sci.) 19(4), 406–411 (2014)CrossRefGoogle Scholar
  31. 31.
    Micciancio, D., Vadhan, S.P.: Statistical zero-knowledge proofs with efficient provers: lattice problems and more. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 282–298. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-540-45146-4_17 CrossRefGoogle Scholar
  32. 32.
    Nguyen, P.Q., Zhang, J., Zhang, Z.: Simpler efficient group signatures from lattices. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 401–426. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46447-2_18 Google Scholar
  33. 33.
    Okamoto, T., Takashima, K.: Efficient attribute-based signatures for non-monotone predicates in the standard model. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 35–52. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-19379-8_3 CrossRefGoogle Scholar
  34. 34.
    Patel, B.K., Jinwala, D.: Anonymity in attribute-based group signatures. In: Thilagam, P.S., Pais, A.R., Chandrasekaran, K., Balakrishnan, N. (eds.) ADCONS 2011. LNCS, vol. 7135, pp. 495–504. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29280-4_58 CrossRefGoogle Scholar
  35. 35.
    Regev, O.: On lattices, learning with errors, random linear codes and cryptography. In: STOC 2005, pp. 84–93. ACM (2005)Google Scholar
  36. 36.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 34 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45682-1_32 CrossRefGoogle Scholar
  38. 38.
    Shahandashti, S.F., Safavi-Naini, R.: Threshold attribute-based signatures and their application to anonymous credential systems. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 198–216. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-02384-2_13 CrossRefGoogle Scholar
  39. 39.
    Zhang, Y., Hu, Y., Jiang, M.: An attribute-based signature scheme from lattice assumption. Wuhan Univ. J. Nat. Sci. 20(3), 207–213 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Veronika Kuchta
    • 1
  • Rajeev Anand Sahu
    • 1
  • Gaurav Sharma
    • 1
  • Olivier Markowitch
    • 1
  1. 1.Université libre de BruxellesBrusselsBelgium

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