Advertisement

Multi-identity IBFHE and Multi-attribute ABFHE in the Standard Model

  • Xuecheng Ma
  • Dongdai LinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11396)

Abstract

The notion of multi-identity IBFHE is an extension of identity based fully homomorphic (IBFHE) encryption. In 2015, Clear and McGoldrick (CRYPTO 2015) proposed a multi-identity IBFHE scheme that is selectively secure in the random oracle model under the hardness of Learning with Errors (LWE). At TCC 2016, Brakerski et al. presented multi-target ABFHE in the random oracle where the evaluator should know the target policy. In this paper, we present a multi-identity IBFHE scheme and a multi-attribute ABFHE scheme in the standard model. Our schemes can support evaluating circuits of unbounded depth but with one limitation: there is a bound N on the number of ciphertexts under the same identity or attribute involved in the computation. The bound N could be thought of as a bound on the number of independent senders. Our schemes allow N to be exponentially large so we do not think it is a limitation in practice. Our construction combines fully multi-key FHE and leveled single-identity IBFHE or single-attribute ABFHE, both of which have been realized from LWE, and therefore we can instantiate our construction that is secure under LWE. Moreover, our multi-attribute ABFHE is non-target where the public evaluator do not need to know the policy.

Keywords

Multi-identity Multi-attribute Homomorphic encryption Standard model 

References

  1. [ABB10]
    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).  https://doi.org/10.1007/978-3-642-13190-5_28CrossRefzbMATHGoogle Scholar
  2. [AP14]
    Alperin-Sheriff, J., Peikert, C.: Faster bootstrapping with polynomial error. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 297–314. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_17CrossRefGoogle Scholar
  3. [BB04a]
    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).  https://doi.org/10.1007/978-3-540-24676-3_14CrossRefGoogle Scholar
  4. [BB04b]
    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).  https://doi.org/10.1007/978-3-540-28628-8_27CrossRefGoogle Scholar
  5. [BCTW16]
    Brakerski, Z., Cash, D., Tsabary, R., Wee, H.: Targeted homomorphic attribute-based encryption. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 330–360. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_13CrossRefGoogle Scholar
  6. [BF01]
    Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_13CrossRefGoogle Scholar
  7. [BGG+14]
    Boneh, D., et al.: Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 533–556. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-55220-5_30CrossRefGoogle Scholar
  8. [BGH07]
    Boneh, D., Gentry, C., Hamburg, M.: Space-efficient identity based encryption without pairings. IACR Cryptology ePrint Archive, vol. 2007, no. 177 (2007)Google Scholar
  9. [BGV12]
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Innovations in Theoretical Computer Science 2012, Cambridge, MA, USA, 8–10 January 2012, pp. 309–325 (2012)Google Scholar
  10. [BHHO08]
    Boneh, D., Halevi, S., Hamburg, M., Ostrovsky, R.: Circular-secure encryption from decision Diffie-Hellman. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 108–125. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85174-5_7CrossRefGoogle Scholar
  11. [BP16]
    Brakerski, Z., Perlman, R.: Lattice-based fully dynamic multi-key FHE with short ciphertexts. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 190–213. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53018-4_8CrossRefGoogle Scholar
  12. [Bra12]
    Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_50CrossRefGoogle Scholar
  13. [BV11]
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, 22–25 October 2011, pp. 97–106 (2011)Google Scholar
  14. [CHKP10]
    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).  https://doi.org/10.1007/978-3-642-13190-5_27CrossRefGoogle Scholar
  15. [CM14]
    Clear, M., McGoldrick, C.: Bootstrappable identity-based fully homomorphic encryption. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds.) CANS 2014. LNCS, vol. 8813, pp. 1–19. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-12280-9_1CrossRefGoogle Scholar
  16. [CM15]
    Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 630–656. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-48000-7_31CrossRefGoogle Scholar
  17. [CM16]
    Clear, M., McGoldrick, C.: Attribute-based fully homomorphic encryption with a bounded number of inputs. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2016. LNCS, vol. 9646, pp. 307–324. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-31517-1_16CrossRefGoogle Scholar
  18. [Coc01]
    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).  https://doi.org/10.1007/3-540-45325-3_32CrossRefGoogle Scholar
  19. [CRRV17]
    Canetti, R., Raghuraman, S., Richelson, S., Vaikuntanathan, V.: Chosen-ciphertext secure fully homomorphic encryption. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10175, pp. 213–240. Springer, Heidelberg (2017).  https://doi.org/10.1007/978-3-662-54388-7_8CrossRefGoogle Scholar
  20. [CZW17]
    Chen, L., Zhang, Z., Wang, X.: Batched multi-hop multi-key FHE from ring-LWE with compact ciphertext extension. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 597–627. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70503-3_20CrossRefGoogle Scholar
  21. [DG17]
    Döttling, N., Garg, S.: Identity-based encryption from the Diffie-Hellman assumption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 537–569. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_18CrossRefGoogle Scholar
  22. [Gen09a]
    Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009). crypto.stanford.edu/craig
  23. [Gen09b]
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, Bethesda, MD, USA, 31 May–2 June 2009, pp. 169–178 (2009)Google Scholar
  24. [GPSW06]
    Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, CCS 2006, Alexandria, VA, USA, 30 October–3 November 2006, pp. 89–98 (2006)Google Scholar
  25. [GPV08]
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, 17–20 May 2008, pp. 197–206 (2008)Google Scholar
  26. [GSW13]
    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. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40041-4_5CrossRefGoogle Scholar
  27. [GVW13]
    Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: Symposium on Theory of Computing Conference, STOC 2013, Palo Alto, CA, USA, 1–4 June 2013, pp. 545–554 (2013)Google Scholar
  28. [HK17]
    Hiromasa, R., Kawai, Y.: Fully dynamic multi target homomorphic attribute-based encryption. IACR Cryptology ePrint Archive, vol. 2017, no. 373 (2017)Google Scholar
  29. [LTV12]
    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 Conference, STOC 2012, New York, NY, USA, 19–22 May 2012, pp. 1219–1234 (2012)Google Scholar
  30. [MW16]
    Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 735–763. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49896-5_26CrossRefGoogle Scholar
  31. [PS16]
    Peikert, C., Shiehian, S.: Multi-key FHE from LWE, revisited. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 217–238. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53644-5_9CrossRefGoogle Scholar
  32. [RAD78]
    Rivest, R.L., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. Found. Sec. Comput. 4, 169–179 (1978)MathSciNetGoogle Scholar
  33. [Reg05]
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, 22–24 May 2005, pp. 84–93 (2005)Google Scholar
  34. [Reg09]
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), 34:1–34:40 (2009)MathSciNetCrossRefGoogle Scholar
  35. [Sha84]
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985).  https://doi.org/10.1007/3-540-39568-7_5CrossRefGoogle Scholar
  36. [SOK00]
    Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystem based on pairings, 01 2000Google Scholar
  37. [SW05]
    Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_27CrossRefGoogle Scholar
  38. [Wat05]
    Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005).  https://doi.org/10.1007/11426639_7CrossRefGoogle Scholar
  39. [Wat09]
    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).  https://doi.org/10.1007/978-3-642-03356-8_36CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.School of Cyber SecurityUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations