Skip to main content
SpringerLink
Log in

Non-zero Inner Product Encryption with Short Ciphertexts and Private Keys

  • Conference paper
  • First Online:
Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

Included in the following conference series:

Abstract

We describe two constructions of non-zero inner product encryption (NIPE) systems in the public index setting, both having ciphertexts and secret keys of constant size. Both schemes are obtained by tweaking the Boneh-Gentry-Waters broadcast encryption system (Crypto 2005) and are proved selectively secure under previously considered assumptions in groups with a bilinear map. Our first realization builds on prime-order bilinear groups and is proved secure under the Decisional Bilinear Diffie-Hellman Exponent assumption, which is parameterized by the length n of vectors over which the inner product is defined. By moving to composite order bilinear groups, we are able to obtain security under static subgroup decision assumptions following the Déjà Q framework of Chase and Meiklejohn (Eurocrypt 2014) and its extension by Wee (TCC 2016). Our schemes are the first NIPE systems to achieve such parameters, even in the selective security setting. Moreover, they are the first proposals to feature optimally short private keys, which only consist of one group element. Our prime-order-group realization is also the first one with a deterministic key generation mechanism.

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

Access this chapter

Log in via an institution
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 EPUB and 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

Institutional subscriptions

Notes

  1. 1.

    One may object saying the linear-length vector \(\varvec{x}\) still has to be appended to the ciphertext. Nevertheless, in many applications the description of \(\varvec{x}\) can be very short. For example, in an ordinary (i.e., non-identity-based) broadcast encryption scheme for n users, \(\varvec{x}\) is uniquely determined by the n-bit word that specifies which users are in the revoked set. In this case, our ciphertexts reduce the communication overhead from \(O(n \lambda )\) to \(O(n+\lambda )\) bits if \(\lambda \) is the security parameter.

References

  1. Abdalla, M., Bourse, F., De Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 733–751. Springer, Heidelberg (2015)

    Google Scholar 

  2. Agrawal, S., Freeman, D.M., Vaikuntanathan, V.: Functional encryption for inner product predicates from learning with errors. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 21–40. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Agrawal, S., Libert, B., Stehlé, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 333–362. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53015-3_12. Cryptology ePrint Archive: Report 2015/608

    Chapter  Google Scholar 

  4. Attrapadung, N., Libert, B.: Functional encryption for inner product: achieving constant-size ciphertexts with adaptive security or support for negation. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 384–402. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Attrapadung, N., Libert, B., de Panafieu, E.: Expressive key-policy attribute-based encryption with constant-size ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 90–108. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Bishop, A., Jain, A., Kowalczyk, L.: Function-hiding inner product encryption. In: Iwata, T., et al. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 470–491. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48797-6_20

    Chapter  Google Scholar 

  7. 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)

    Chapter  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)

    Chapter  Google Scholar 

  9. Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Boneh, D., Gentry, C., Waters, B.: Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 258–275. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Camenisch, J., Kohlweiss, M., Soriente, C.: An accumulator based on Bilinear maps and efficient revocation for anonymous credentials. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 481–500. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Catalano, D., Fiore, D.: Concise vector commitments and their applications to zero-knowledge elementary databases. In: Cryptology ePrint Archive: Report 2011/495 (2011)

    Google Scholar 

  15. Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015)

    Google Scholar 

  16. Chase, M., Meiklejohn, S.: Déjà Q: using dual systems to revisit q-type assumptions. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 622–639. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  17. Cheon, J.H.: Security analysis of the strong Diffie-Hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Delerablée, C.: Identity-based broadcast encryption with constant size ciphertexts and private keys. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 200–215. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Dodis, Y., Yampolskiy, A.: A verifiable random function with short proofs and keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM CCS 2006, pp. 89–98 (2006)

    Google Scholar 

  21. Izabachène, M., Libert, B., Vergnaud, D.: Block-wise P-signatures and non-interactive anonymous credentials with efficient attributes. In: Chen, L. (ed.) IMACC 2011. LNCS, vol. 7089, pp. 431–450. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  22. Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Lewko, A., Sahai, A., Waters, B.: Revocation systems with very small private keys. In: IEEE Symposium on Security and Privacy 2010, pp. 273–285. IEEE Computer Society (2010)

    Google Scholar 

  24. 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)

    Chapter  Google Scholar 

  25. Lewko, A., Waters, B.: New techniques for dual system encryption and fully secure HIBE with short ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  26. Libert, B., Ramanna, S.C., Yung, M.: Functional commitment schemes: from polynomial commitments to pairing-based accumulators from simple assumptions. In: ICALP 2016 (2016, to appear)

    Google Scholar 

  27. Libert, B., Yung, M.: Concise mercurial vector commitments and independent zero-knowledge sets with short proofs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 499–517. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  28. Naor, M.: On cryptographic assumptions and challenges. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 96–109. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  29. Naor, M., Pinkas, B.: Efficient trace and revoke schemes. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 1–20. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  30. Okamoto, T., Takashima, K.: Hierarchical predicate encryption for inner-products. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 214–231. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  31. Okamoto, T., Takashima, K.: Fully secure functional encryption with general relations from the decisional linear assumption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 191–208. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  32. Okamoto, T., Takashima, K.: Adaptively attribute-hiding (Hierarchical) inner product encryption. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 591–608. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  33. Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349–366. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  34. Okamoto, T., Takashima, K.: Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption. Des. Codes Crypt. 77(2–3), 725–771 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  35. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  36. Shen, E., Shi, E., Waters, B.: Predicate privacy in encryption systems. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 457–473. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  37. Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  38. Wee, H.: Threshold and revocation cryptosystems via extractable hash proofs. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 589–609. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  39. Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  40. Wee, H.: Déjà Q: encore! Un Petit IBE. In: Kushilevitz, E., et al. (eds.) TCC 2016-A. LNCS, vol. 9563, pp. 237–258. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49099-0_9

    Chapter  Google Scholar 

  41. Yamada, S., Attrapadung, N., Hanaoka, G., Kunihiro, N.: A framework and compact constructions for non-monotonic attribute-based encryption. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 275–292. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

Download references

Acknowledgements

The authors were funded by the “Programme Avenir Lyon Saint-Etienne de l’Université de Lyon” in the framework of the programme “Investissements d’Avenir” (ANR-11-IDEX-0007). Jie Chen was also supported in part by the National Natural Science Foundation of China (Grant No. 61472142).

Author information

Authors and Affiliations

  1. Laboratoire LIP, École Normale Supérieure de Lyon, Lyon, France

    Jie Chen, Benoît Libert & Somindu C. Ramanna

  2. East China Normal University, Shanghai, China

    Jie Chen

Authors
  1. Jie Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benoît Libert
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Somindu C. Ramanna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jie Chen , Benoît Libert or Somindu C. Ramanna .

Editor information

Editors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Chen, J., Libert, B., Ramanna, S.C. (2016). Non-zero Inner Product Encryption with Short Ciphertexts and Private Keys. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-44618-9_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44617-2

  • Online ISBN: 978-3-319-44618-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation