Abstract
With Attribute-based Signatures (ABS) users can simultaneously sign messages and prove compliance of their attributes, issued by designated attribute authorities, with some verification policy. Neither signer’s identity nor possessed attributes are leaked during the verification process, making ABS schemes a handy tool for applications requiring privacy-preserving authentication. Earlier ABS schemes lacked support for hierarchical delegation of attributes (across tiers of attribute authorities down to the signers), a distinct property that has made traditional PKIs more scalable and widely adoptable.
This changed recently with the introduction of Hierarchical ABS (HABS) schemes, where support for attribute delegation was proposed in combination with stronger privacy guarantees for the delegation paths (path anonymity) and new accountability mechanisms allowing a dedicated tracing authority to identify these paths (path traceability) and the signer, along with delegated attributes, if needed. Yet, current HABS construction is generic with inefficient delegation process resulting in sub-optimal signature lengths of order \(O(k^{2}|\varPsi |)\) where \(\varPsi \) is the policy size and k the height of the hierarchy.
This paper proposes a direct HABS construction in bilinear groups that significantly improves on these bounds and satisfies the original security and privacy requirements. At the core of our HABS scheme is a new delegation process based on the length-reducing homomorphic trapdoor commitments to group elements for which we introduce a new delegation technique allowing step-wise commitments to additional elements without changing the length of the original commitment and its opening. While also being of independent interest, this technique results in shorter HABS keys and achieves the signature-length growth of \(O(k|\varPsi |)\) which is optimal due to the path-traceability requirement.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abe, M., Chase, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Constant-size structure-preserving signatures: generic constructions and simple assumptions. J. Cryptol. 29, 833–878 (2016)
Abe, M., Haralambiev, K., Ohkubo, M.: Signing on elements in bilinear groups for modular protocol design. IACR Cryptology ePrint Archive, p. 133 (2010)
Backes, M., Meiser, S., Schröder, D.: Delegatable functional signatures. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 357–386. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49384-7_14
Belenkiy, M., Camenisch, J., Chase, M., Kohlweiss, M., Lysyanskaya, A., Shacham, H.: Randomizable proofs and delegatable anonymous credentials. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 108–125. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_7
Bellare, M., Fuchsbauer, G.: Policy-based signatures. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 520–537. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_30
Blazy, O., Fuchsbauer, G., Izabachène, M., Jambert, A., Sibert, H., Vergnaud, D.: Batch Groth–Sahai. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 218–235. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13708-2_14
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
Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_29
Camenisch, J., Lysyanskaya, A.: A signature scheme with efficient protocols. In: Cimato, S., Persiano, G., Galdi, C. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36413-7_20
Chaum, D.: Security without identification: transaction systems to make big brother obsolete. Commun. ACM 28(10), 1030–1044 (1985)
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
Drǎgan, C.-C., Gardham, D., Manulis, M.: Hierarchical attribute-based signatures. In: Camenisch, J., Papadimitratos, P. (eds.) CANS 2018. LNCS, vol. 11124, pp. 213–234. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00434-7_11
El Kaafarani, A., Ghadafi, E.: Attribute-based signatures with user-controlled linkability without random oracles. In: O’Neill, M. (ed.) IMACC 2017. LNCS, vol. 10655, pp. 161–184. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71045-7_9
El Kaafarani, A., Ghadafi, E., Khader, D.: Decentralized traceable attribute-based signatures. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 327–348. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04852-9_17
El Kaafarani, A., Katsumata, S.: Attribute-based signatures for unbounded circuits in the ROM and efficient instantiations from lattices. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10770, pp. 89–119. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_4
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
Fuchsbauer, G., Pointcheval, D.: Anonymous proxy signatures. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 201–217. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85855-3_14
Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008)
Gardham, D., Manulis, M.: Hierarchical attribute-based signatures: short keys and optimal signature length. Cryptology ePrint Archive, Report 2019/382 (2019). https://eprint.iacr.org/2019/382
Ghadafi, E.: Stronger security notions for decentralized traceable attribute-based signatures and more efficient constructions. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 391–409. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16715-2_21
Groth, J.: Homomorphic Trapdoor Commitments to Group Elements. Cryptology ePrint Archive, Report 2009/007 (2009)
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
Herranz, J.: Attribute-based signatures from RSA. TCS 527, 73–82 (2014)
Jager, T., Rupp, A.: The semi-generic group model and applications to pairing-based cryptography. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 539–556. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_31
Kaaniche, N., Laurent, M., Rocher, P.-O., Kiennert, C., Garcia-Alfaro, J.: PCS, a privacy-preserving certification scheme. In: Data Privacy Management, Cryptocurrencies and Blockchain Technology, pp. 239–256 (2017)
Kakvi, S.A.: Efficient fully anonymous group signatures based on the Groth group signature scheme. Master’s thesis, University College London (2010)
Khader, D., Chen, L., Davenport, J.H.: Certificate-free attribute authentication. In: Parker, M.G. (ed.) IMACC 2009. LNCS, vol. 5921, pp. 301–325. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10868-6_18
Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_30
Krzywiecki, Ł., Sulkowska, M., Zagórski, F.: Hierarchical ring signatures revisited – unconditionally and perfectly anonymous schnorr version. In: Chakraborty, R.S., Schwabe, P., Solworth, J. (eds.) SPACE 2015. LNCS, vol. 9354, pp. 329–346. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24126-5_19
Li, J., Au, M.H., Susilo, W., Xie, D., Ren, K.: Attribute-based signature and its applications. In: ACM ASIACCS 2010, pp. 60–69. ACM (2010)
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
Okamoto, T., Takashima, K.: Decentralized attribute-based signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 125–142. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_9
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
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
Sakai, Y.: Practical attribute-based signature schemes for circuits from bilinear map. IET Inf. Secur. 12, 184–193 (2018)
Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_18
Trolin, M., Wikström, D.: Hierarchical group signatures. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 446–458. Springer, Heidelberg (2005). https://doi.org/10.1007/11523468_37
Tsabary, R.: An equivalence between attribute-based signatures and homomorphic signatures, and new constructions for both. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 489–518. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_16
Acknowledgements
Daniel Gardham was supported by the UK Government PhD studentship scheme. Mark Manulis was supported by the EPSRC project TAPESTRY (EP/N02799X). The authors thank the anonymous reviewers of ACNS 2019 for their valuable comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Gardham, D., Manulis, M. (2019). Hierarchical Attribute-Based Signatures: Short Keys and Optimal Signature Length. In: Deng, R., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2019. Lecture Notes in Computer Science(), vol 11464. Springer, Cham. https://doi.org/10.1007/978-3-030-21568-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-21568-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21567-5
Online ISBN: 978-3-030-21568-2
eBook Packages: Computer ScienceComputer Science (R0)