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Shorter IBE and Signatures via Asymmetric Pairings

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Pairing-Based Cryptography – Pairing 2012 (Pairing 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7708))

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Abstract

We present efficient Identity-Based Encryption (IBE) and signature schemes under the Symmetric External Diffie-Hellman (SXDH) assumption in bilinear groups. In both the IBE and the signature schemes, all parameters have constant numbers of group elements, and are shorter than those of previous constructions based on Decisional Linear (DLIN) assumption. Our constructions use both dual system encryption (Waters, Crypto ’09) and dual pairing vector spaces (Okamoto and Takashima, Pairing ’08, Asiacrypt ’09). Specifically, we show how to adapt the recent DLIN-based instantiations of Lewko (Eurocrypt ’12) to the SXDH assumption. To our knowledge, this is the first work to instantiate either dual system encryption or dual pairing vector spaces under the SXDH assumption.

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References

  1. Abdalla, M., Bellare, M., Catalano, D., Kiltz, E., Kohno, T., Lange, T., Malone-Lee, J., Neven, G., Paillier, P., Shi, H.: Searchable encryption revisited: Consistency properties, relation to anonymous IBE, and extensions. J. Cryptology 21(3), 350–391 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agrawal, S., Boneh, D., Boyen, X.: Efficient Lattice (H)IBE in the Standard Model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Ateniese, G., Kirsch, J., Blanton, M.: Secret handshakes with dynamic and fuzzy matching. In: NDSS (2007)

    Google Scholar 

  4. Ballard, L., Green, M., de Medeiros, B., Monrose, F.: Correlation-resistant storage via keyword-searchable encryption. IACR Cryptology ePrint Archive, Report 2005/417 (2005)

    Google Scholar 

  5. Barker, E., Barker, W., Burr, W., Polk, W., Smid, M.: Recommendation for key management—part 1: General (revised). NIST Special Pub., 800-57 (2007)

    Google Scholar 

  6. Barreto, P.S.L.M., Naehrig, M.: Pairing-Friendly Elliptic Curves of Prime Order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319–331. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Boneh, D., Boyen, X.: Secure Identity Based Encryption Without Random Oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Boneh, D., Franklin, M.K.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. 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 

  11. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. J. Cryptology 17(4), 297–319 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Brakerski, Z., Kalai, Y.T., Katz, J., Vaikuntanathan, V.: Overcoming the hole in the bucket: Public-key cryptography resilient to continual memory leakage. In: FOCS, pp. 501–510 (2010)

    Google Scholar 

  13. Brezing, F., Weng, A.: Elliptic curves suitable for pairing based cryptography. Des. Codes Cryptography 37(1), 133–141 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Canetti, R., Halevi, S., Katz, J.: A Forward-Secure Public-Key Encryption Scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. 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 

  16. Cocks, C.: An identity based encryption scheme based on quadratic residues. In: IMA Int. Conf., pp. 360–363 (2001)

    Google Scholar 

  17. Ducas, L.: Anonymity from Asymmetry: New Constructions for Anonymous HIBE. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 148–164. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. J. Cryptology 23(2), 224–280 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Freeman, D.M.: Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 44–61. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  20. Galbraith, S.D., Rotger, V.: Easy decision Diffie-Hellman groups. IACR Cryptology ePrint Archive, Report 2004/070 (2004)

    Google Scholar 

  21. Gentry, C.: Practical Identity-Based Encryption Without Random Oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197–206 (2008)

    Google Scholar 

  23. Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  24. Groth, J., Sahai, A.: Efficient Non-interactive Proof Systems for Bilinear Groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Lewko, A.: Tools for Simulating Features of Composite Order Bilinear Groups in the Prime Order Setting. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 318–335. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  26. 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 

  27. 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 

  28. Miyaji, A., Nakabayashi, M., Takano, S.: Characterization of Elliptic Curve Traces under FR-Reduction. In: Won, D. (ed.) ICISC 2000. LNCS, vol. 2015, pp. 90–108. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  29. Okamoto, T., Takashima, K.: Homomorphic Encryption and Signatures from Vector Decomposition. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 57–74. Springer, Heidelberg (2008)

    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.: Fully secure functional encryption with general relations from the decisional linear assumption. Cryptology ePrint Archive, Report 2010/563 (2010)

    Google Scholar 

  33. Ramanna, S.C., Chatterjee, S., Sarkar, P.: Variants of waters’ dual-system primitives using asymmetric pairings. IACR Cryptology ePrint Archive, Report 2012/024 (2012)

    Google Scholar 

  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. Verheul, E.R.: Evidence that XTR is more secure than Supersingular Elliptic Curve cryptosystems. Journal of Cryptology 17(4), 277–296 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  36. Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)

    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 

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore

    Jie Chen, Hoon Wei Lim, San Ling, Huaxiong Wang & Hoeteck Wee

  2. Department of Computer Science, George Washington University, USA

    Hoeteck Wee

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  1. Jie Chen
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  3. San Ling
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  4. Huaxiong Wang
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Editors and Affiliations

  1. Départment d’Informatique, École Normale Supérieure and CNRS, 45 rue d’Ulm, 75005, Paris, France

    Michel Abdalla

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Tanja Lange

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Chen, J., Lim, H.W., Ling, S., Wang, H., Wee, H. (2013). Shorter IBE and Signatures via Asymmetric Pairings. In: Abdalla, M., Lange, T. (eds) Pairing-Based Cryptography – Pairing 2012. Pairing 2012. Lecture Notes in Computer Science, vol 7708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36334-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-36334-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36333-7

  • Online ISBN: 978-3-642-36334-4

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