Skip to main content
Springer Nature Link
Log in

Strongly Unforgeable Signatures and Hierarchical Identity-Based Signatures from Lattices without Random Oracles

  • Conference paper
Post-Quantum Cryptography (PQCrypto 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6061))

Included in the following conference series:

  • 1996 Accesses

Abstract

We propose a variant of the “bonsai tree” signature scheme, a lattice-based existentially unforgeable signature scheme in the standard model. Our construction offers the same efficiency as the “bonsai tree” scheme but supports the stronger notion of strong unforgeability. Strong unforgeability demands that the adversary is unable to produce a new message-signature pair (m, s), even if he or she is allowed to see a different signature s ′ for m.

In particular, we provide the first treeless signature scheme that supports strong unforgeability for the post-quantum era in the standard model. Moreover, we show how to directly implement identity-based, and even hierarchical identity-based, signatures (IBS) in the same strong security model without random oracles. An additional advantage of this direct approach over the usual generic conversion of hierarchical identity-based encryption to IBS is that we can exploit the efficiency of ideal lattices without significantly harming security.

We equip all constructions with strong security proofs based on mild worst-case assumptions on lattices and we also propose concrete security parameters.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agrawal, S., Boyen, X.: Identity-based encryption from lattices in the standard model (July 2009) (manuscript), http://www.cs.stanford.edu/~xb/ab09/

  2. Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: STOC, pp. 99–108. ACM, New York (1996)

    Google Scholar 

  3. Ajtai, M., Kumar, R., Sivakumar, D.: A sieve algorithm for the shortest lattice vector problem. In: STOC, pp. 601–610. ACM, New York (2001)

    Google Scholar 

  4. Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. Cryptology ePrint Archive, Report 2008/521 (2008), http://eprint.iacr.org/

  5. Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: Albers, S., Marion, J.-Y. (eds.) STACS. Dagstuhl Seminar Proceedings, vol. 09001, pp. 75–86. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany (2009)

    Google Scholar 

  6. Bellare, M., Shoup, S.: Two-tier signatures, strongly unforgeable signatures, and fiat-shamir without random oracles. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 201–216. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Bernstein, D.J., Buchmann, J.A., Dahmen, E. (eds.): Post-Quantum Cryptography. Springer, Heidelberg (2008)

    Google Scholar 

  8. Boneh, D., Boyen, X.: Efficient selective-id secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)

    Google Scholar 

  9. Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007)

    Article  MathSciNet  Google Scholar 

  10. Boneh, D., Shen, E., Waters, B.: Strongly unforgeable signatures based on computational diffie-hellman. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 229–240. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)

    Article  MathSciNet  Google Scholar 

  12. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: EUROCRYPT 2010 (to appear, 2010)

    Google Scholar 

  13. Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Galindo, D., Herranz, J., Kiltz, E.: On the generic construction of identity-based signatures with additional properties. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 178–193. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Gama, N., Nguyen, P.Q.: Predicting lattice reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 31–51. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Ladner, R.E., Dwork, C. (eds.) STOC, pp. 197–206. ACM, New York (2008)

    Google Scholar 

  17. Gentry, C., Silverberg, A.: Hierarchical id-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Halevi, S. (ed.): CRYPTO 2009. LNCS, vol. 5677. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  19. Hohenberger, S., Waters, B.: Short and stateless signatures from the rsa assumption. In: Halevi (ed.) [18], pp. 654–670.

    Google Scholar 

  20. Kiltz, E., Mityagin, A., Panjwani, S., Raghavan, B.: Append-only signatures. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 434–445. Springer, Heidelberg (2005)

    Google Scholar 

  21. Kiltz, E., Neven, G.: Identity-based signatures. In: Joye, M., Neven, G. (eds.) Cryptology and Information Security Series, vol. 2, pp. 31–44. IOS Press, Amsterdam (2008)

    Google Scholar 

  22. Krawczyk, H., Rabin, T.: Chameleon hashing and signatures. Cryptology ePrint Archive, Report 1998/010 (1998), http://eprint.iacr.org/

  23. Krawczyk, H., Rabin, T.: Chameleon signatures. In: NDSS. The Internet Society (2000)

    Google Scholar 

  24. Leurent, G., Nguyen, P.Q.: How risky is the random-oracle model? In: Halevi (ed.) [18], pp. 445–464

    Google Scholar 

  25. Libert, B., Quisquater, J.-J.: The exact security of an identity based signature and its applications. Cryptology ePrint Archive, Report 2004/102 (2004), http://eprint.iacr.org/

  26. Lyubashevsky, V.: Fiat-shamir with aborts: Applications to lattice and factoring-based signatures. In: Matsui (ed.) [28], pp. 598–616

    Google Scholar 

  27. Lyubashevsky, V., Micciancio, D.: Asymptotically efficient lattice-based digital signatures. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 37–54. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Matsui, M. (ed.): ASIACRYPT 2009. LNCS, vol. 5912. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  29. Merkle, R.C.: A certified digital signature. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 218–238. Springer, Heidelberg (1990)

    Google Scholar 

  30. Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. Computational Complexity 16(4), 365–411 (2007); Prelim. in FOCS 2002 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  31. Micciancio, D., Regev, O.: Lattice-based cryptography. In: Bernstein, et al. (eds.) [7], pp. 147–191

    Google Scholar 

  32. Peikert, C., Rosen, A.: Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 145–166. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  33. Rückert, M.: Strongly unforgeable signatures and hierarchical identity-based signatures from lattices without random oracles. Cryptology ePrint Archive, Report 2010/070 (2010), http://eprint.iacr.org/

  34. Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  35. Stehlé, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient public key encryption based on ideal lattices. In: Matsui (ed.) [28], pp. 617–635

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cryptography and Computeralgebra, Department of Computer Science, TU Darmstadt,  

    Markus Rückert

Authors
  1. Markus Rückert
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Projet Team SECRET, Centre de Recherche INRIA Paris-Rocquencourt,, B.P. 105, 78153, Le Chesnay Cedex, France

    Nicolas Sendrier

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rückert, M. (2010). Strongly Unforgeable Signatures and Hierarchical Identity-Based Signatures from Lattices without Random Oracles. In: Sendrier, N. (eds) Post-Quantum Cryptography. PQCrypto 2010. Lecture Notes in Computer Science, vol 6061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12929-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12929-2_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12928-5

  • Online ISBN: 978-3-642-12929-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics