Skip to main content

Efficient Threshold Encryption from Lossy Trapdoor Functions

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7071))

Abstract

This paper discusses the problem of building secure threshold public key encryption (TPKE) schemes from lossy trapdoor functions, which can in turn be built from a number of assumptions, e.g. lattices. Our methodology is generic and our concrete instantiation is more efficient than previous construction.

This work is partially supported by the Fund of the National Natural Science Foundation of China under Grants No. 60873260 and the National High Technology Research and Development Program of China under Grant No. 2009AA01Z414.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arita, S., Tsurudome, K.: Construction of Threshold Public-Key Encryptions Through Tag-Based Encryptions. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 186–200. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Bendlin, R., Damgård, I.: Threshold Decryption and Zero-Knowledge Proofs for Lattice-Based Cryptosystems. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 201–218. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Boneh, D., Boyen, X., Halevi, S.: Chosen Ciphertext Secure Public Key Threshold Encryption without Random Oracles. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 226–243. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Canetti, R., Goldwasser, S.: An Efficient threshold Public Key Cryptosystem Secure Against Adaptive Chosen Ciphertext Attack (Extended Abstract). In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 90–106. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai Trees, or How to Delegate a Lattice Basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Chaum, D.L.: Untraceable electronic mail, return addresses, and digital pseudonyms. Communications of the ACM 24(2), 84–90 (1981)

    Article  Google Scholar 

  7. Damgård, I., Hofheinz, D., Kiltz, E., Thorbek, R.: Public-Key Encryption with Non-Interactive Opening. In: Malkin, T. (ed.) CT-RSA 2008. LNCS, vol. 4964, pp. 239–255. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Desmedt, Y.G.: Society and Group Oriented Cryptography: A New Concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988)

    Google Scholar 

  9. Desmedt, Y., Frankel, Y.: Threshold Cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)

    Google Scholar 

  10. Dodis, Y., Katz, J.: Chosen-Ciphertext Security of Multiple Encryption. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 188–209. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Dodis, Y., Reyzin, L., Smith, A.: Fuzzy Extractors: How to Generate Strong Keys from Biometrics and other Noisy Data. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 523–540. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, pp. 542–552. ACM (1991)

    Google Scholar 

  13. Frankel, Y.: A Practical Protocol for Large Group Oriented Networks. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 56–61. Springer, Heidelberg (1990)

    Google Scholar 

  14. Freeman, D.M., Goldreich, O., Kiltz, E., Rosen, A., Segev, G.: More Constructions of Lossy and Correlation-Secure Trapdoor Functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 279–295. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Galindo, D.: Breaking and Repairing Damgård et al. Public Key Encryption Scheme with Non-interactive Opening. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 389–398. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Galindo, D., Libert, B., Fischlin, M., Fuchsbauer, G., Lehmann, A., Manulis, M., Schröder, D.: Public-Key Encryption with Non-Interactive Opening: New Constructions and Stronger Definitions. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 333–350. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Gemmell, P.: An introduction to threshold cryptography. RSA CryptoBytes 2(3), 7–12 (1997)

    Google Scholar 

  18. Kawachi, A., Tanaka, K., Xagawa, K.: Concurrently Secure Identification Schemes Based on the Worst-Case Hardness of Lattice Problems. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 372–389. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Mohassel, P.: One-Time Signatures and Chameleon Hash Functions. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 302–319. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  21. Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, pp. 427–437. ACM (1990)

    Google Scholar 

  22. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, pp. 333–342. ACM (2009)

    Google Scholar 

  23. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 187–196. ACM (2008)

    Google Scholar 

  24. Rackoff, C., Simon, D.: Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)

    Google Scholar 

  25. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 84–93. ACM (2005)

    Google Scholar 

  26. Rosen, A., Segev, G.: Efficient lossy trapdoor functions based on the composite residuosity assumption. IACR ePrint Archive (2008)

    Google Scholar 

  27. Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  28. Shoup, V.: A proposal for an ISO standard for public key encryption. Manuscript 100, 101–103 (2001)

    Google Scholar 

  29. Shoup, V., Gennaro, R.: Securing Threshold Cryptosystems Against Chosen Ciphertext Attack. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 1–16. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  30. Wegman, M.N., Carter, J.L.: New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences 22(3), 265–279 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhang, R., Hanaoka, G., Shikata, J., Imai, H.: On the Security of Multiple Encryption or CCA-Security+ CCA-Security= CCA-Security? In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 360–374. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xie, X., Xue, R., Zhang, R. (2011). Efficient Threshold Encryption from Lossy Trapdoor Functions. In: Yang, BY. (eds) Post-Quantum Cryptography. PQCrypto 2011. Lecture Notes in Computer Science, vol 7071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25405-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25405-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25404-8

  • Online ISBN: 978-3-642-25405-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics