Attribute-Based Signatures for Unbounded Languages from Standard Assumptions

  • Yusuke SakaiEmail author
  • Shuichi Katsumata
  • Nuttapong Attrapadung
  • Goichiro Hanaoka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11273)


Attribute-based signature (ABS) schemes are advanced signature schemes that simultaneously provide fine-grained authentication while protecting privacy of the signer. Previously known expressive ABS schemes support either the class of deterministic finite automata and circuits from standard assumptions or Turing machines from the existence of indistinguishability obfuscations.

In this paper, we propose the first ABS scheme for a very general policy class, all deterministic Turing machines, from a standard assumption, namely, the Symmetric External Diffie-Hellman (SXDH) assumption. We also propose the first ABS scheme that allows nondeterministic finite automata (NFA) to be used as policies. Although the expressiveness of NFAs are more restricted than Turing machines, this is the first scheme that supports nondeterministic computations as policies.

Our main idea lies in abstracting ABS constructions and presenting the concept of history of computations; this allows a signer to prove possession of a policy that accepts the string associated to a message in zero-knowledge while also hiding the policy, regardless of the computational model being used. With this abstraction in hand, we are able to construct ABS for Turing machines and NFAs using a surprisingly weak NIZK proof system. Essentially we only require a NIZK proof system for proving that a (normal) signature is valid. Such a NIZK proof system together with a base signature scheme are, in turn, possible from bilinear groups under the SXDH assumption, and hence so are our ABS schemes.


Attribute-based signatures Groth-Sahai proofs Structure-preserving signatures Turing machines Nondeterministic Finite Automata 



The first author is supported by JSPS KAKENHI Grant Number 18K18055. The second author was partially supported by JST CREST Grant Number JPMJCR1302 and JSPS KAKENHI Grant Number 17J05603. The first, third, and fourth authors are partially supported by JST CREST Grant Number JPMJCR1688.


  1. [AS16]
    Ananth, P., Sahai, A.: Functional encryption for turing machines. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 125–153. Springer, Heidelberg (2016). Scholar
  2. [BF14]
    Bellare, M., Fuchsbauer, G.: Policy-based signatures. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 520–537. Springer, Heidelberg (2014). Scholar
  3. [BGI14]
    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). Scholar
  4. [DDM17]
    Datta, P., Dutta, R., Mukhopadhyay, S.: Attribute-based signatures for Turing machines. Cryptology ePrint Archive, Report 2017/801 (2017).
  5. [GKP+13]
    Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: How to run turing machines on encrypted data. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 536–553. Springer, Heidelberg (2013). Scholar
  6. [GS12]
    Groth, J., Sahai, A.: Efficient noninteractive proof systems for bilinear groups. SIAM J. Comput. 41(5), 1193–1232 (2012)MathSciNetCrossRefGoogle Scholar
  7. [KPW15]
    Kiltz, E., Pan, J., Wee, H.: Structure-preserving signatures from standard assumptions, revisited. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 275–295. Springer, Heidelberg (2015). Scholar
  8. [MPR11]
    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). Scholar
  9. [NP15]
    Nandi, M., Pandit, T.: On the power of pair encodings: Frameworks for predicate cryptographic primitives. Cryptology ePrint Archive, Report 2015/955 (2015).
  10. [OT11]
    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). Scholar
  11. [SAH16]
    Sakai, Y., Attrapadung, N., Hanaoka, G.: Attribute-based signatures for circuits from bilinear map. In: Cheng, C.-M., Chung, K.-M., Persiano, G., Yang, B.-Y. (eds.) PKC 2016. LNCS, vol. 9614, pp. 283–300. Springer, Heidelberg (2016). Scholar
  12. [Sip96]
    Sipser, M.: Introduction to the Theory of Computation, 1st edn. International Thomson Publishing, Stamford (1996)zbMATHGoogle Scholar
  13. [SSN09]
    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). Scholar
  14. [TLL14]
    Tang, F., Li, H., Liang, B.: Attribute-Based Signatures for Circuits from Multilinear Maps. In: Chow, S.S.M., Camenisch, J., Hui, L.C.K., Yiu, S.M. (eds.) ISC 2014. LNCS, vol. 8783, pp. 54–71. Springer, Cham (2014). Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Yusuke Sakai
    • 1
    Email author
  • Shuichi Katsumata
    • 1
    • 2
  • Nuttapong Attrapadung
    • 1
  • Goichiro Hanaoka
    • 1
  1. 1.AISTTokyoJapan
  2. 2.The University of TokyoTokyoJapan

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