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Bootstrappable Identity-Based Fully Homomorphic Encryption

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Cryptology and Network Security (CANS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8813))

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Abstract

It has been an open problem for a number of years to construct an identity-based fully homomorphic encryption (IBFHE) scheme (first mentioned by Naccache at CHES/CRYPTO 2010). At CRYPTO 2013, Gentry, Sahai and Waters largely settled the problem by presenting leveled IBFHE constructions based on the Learning With Errors problem. However their constructions are not bootstrappable, and as a result, are not “pure” IBFHE schemes. The major challenge with bootstrapping in the identity-based setting is that it must be possible to non-interactively derive from the public parameters an “encryption” of the secret key for an arbitrary identity. All presently-known leveled IBFHE schemes only allow bootstrapping if such an “encryption” of the secret key is supplied out-of-band. In this work, we present a “pure” IBFHE scheme from indistinguishability obfuscation, and extend the result to the attribute-based setting. Our attribute-based scheme is the first to support homomorphic evaluation on ciphertexts with different attributes. Finally, we characterize presently-known leveled IBFHE schemes with a view to developing a “compiler” from a leveled IBFHE scheme to a bootstrappable IBFHE scheme, and sufficient conditions are identified.

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References

  1. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st annual ACM Symposium on Theory of Computing STOC 2009, p. 169 (September 2009)

    Google Scholar 

  2. Smart, N., Vercauteren, F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420–443. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Brakerski, Z., Vaikuntanathan, V.: Efficient Fully Homomorphic Encryption from (Standard) LWE. Cryptology ePrint Archive, Report 2011/344 (2011), http://eprint.iacr.org/

  6. Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 360–363. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Naccache, D.: Is theoretical cryptography any good in practice (2010); Talk given at CHES 2010 and Crypto 2010

    Google Scholar 

  10. Brakerski, Z., Vaikuntanathan, V.: Efficient Fully Homomorphic Encryption from (Standard) LWE. Cryptology ePrint Archive, Report 2011/344 Version: 20110627:080002 (2011), http://eprint.iacr.org/

  11. Clear, M., Hughes, A., Tewari, H.: Homomorphic encryption with access policies: Characterization and new constructions. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 2013. LNCS, vol. 7918, pp. 61–87. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 197–206. ACM, New York (2008)

    Google Scholar 

  13. 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 

  14. Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical ibe. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98–115. Springer, Heidelberg (2010)

    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. Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more. IACR Cryptology ePrint Archive 2013, 454 (2013)

    Google Scholar 

  17. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS, pp. 40–49. IEEE Computer Society (2013)

    Google Scholar 

  18. Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 280–300. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: ACM Conference on Computer and Communications Security, pp. 669–684. ACM (2013)

    Google Scholar 

  21. 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 

  22. Bethencourt, J., Sahai, A., Waters, B.: Ciphertext-policy attribute-based encryption. In: Proceedings of the 2007 IEEE Symposium on Security and Privacy, SP 2007, pp. 321–334. IEEE Computer Society, Washington, DC (2007)

    Google Scholar 

  23. López-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the 44th Symposium on Theory of Computing, STOC 2012, pp. 1219–1234. ACM Press, New York (2012)

    Google Scholar 

  24. Goldwasser, S., Goyal, V., Jain, A., Sahai, A.: Multi-input functional encryption. Cryptology ePrint Archive, Report 2013/727 (2013), http://eprint.iacr.org/

  25. Boneh, D., Boyen, X.: Efficient selective-id secure identity based encryption without random oracles. IACR Cryptology ePrint Archive 2004, 172 (2004)

    Google Scholar 

  26. Clear, M., McGoldrick, C.: Policy-Based Non-interactive Outsourcing of Computation using multikey FHE and CP-ABE. In: Proceedings of the 10th Internation Conference on Security and Cryptography, SECRYPT 2013 (2013)

    Google Scholar 

  27. Clear, M., McGoldrick, C.: Bootstrappable identity-based fully homomorphic encryption. Cryptology ePrint Archive, Report 2014/491 (2014), http://eprint.iacr.org/

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Author information

Authors and Affiliations

  1. School of Computer Science and Statistics, Trinity College Dublin, Ireland

    Michael Clear & Ciarán McGoldrick

Authors
  1. Michael Clear
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  2. Ciarán McGoldrick
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Editor information

Editors and Affiliations

  1. Department of Informatics, Athens University of Economics & Business, 76, Patission Str., 10434, Athens, Greece

    Dimitris Gritzalis

  2. Department of Informatics and Telecommunications, Panepistimiopolis, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Aggelos Kiayias

  3. FORTH-ICS, Vassilika Vouton, P.O. Box 1385, 711 10, Heraklion, Crete, Greece

    Ioannis Askoxylakis

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Clear, M., McGoldrick, C. (2014). Bootstrappable Identity-Based Fully Homomorphic Encryption. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds) Cryptology and Network Security. CANS 2014. Lecture Notes in Computer Science, vol 8813. Springer, Cham. https://doi.org/10.1007/978-3-319-12280-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-12280-9_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12279-3

  • Online ISBN: 978-3-319-12280-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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