Partitioning via Non-linear Polynomial Functions: More Compact IBEs from Ideal Lattices and Bilinear Maps

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10032)

Abstract

In this paper, we present new adaptively secure identity-based encryption (IBE) schemes. One of the distinguishing properties of the schemes is that it achieves shorter public parameters than previous schemes. Both of our schemes follow the general framework presented in the recent IBE scheme of Yamada (Eurocrypt 2016), employed with novel techniques tailored to meet the underlying algebraic structure to overcome the difficulties arising in our specific setting. Specifically, we obtain the following:

- Our first scheme is proven secure under the ring learning with errors (RLWE) assumption and achieves the best asymptotic space efficiency among existing schemes from the same assumption. The main technical contribution is in our new security proof that exploits the ring structure in a crucial way. Our technique allows us to greatly weaken the underlying hardness assumption (e.g., we assume the hardness of RLWE with a fixed polynomial approximation factor whereas Yamada’s scheme requires a super-polynomial approximation factor) while improving the overall efficiency.

- Our second IBE scheme is constructed on bilinear maps and is secure under the 3-computational bilinear Diffie-Hellman exponent assumption. This is the first IBE scheme based on the hardness of a computational/search problem, rather than a decisional problem such as DDH and DLIN on bilinear maps with sub-linear public parameter size.

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). doi:10.1007/978-3-642-13190-5_28 CrossRefGoogle Scholar
  2. [ACPS09]
    Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03356-8_35 CrossRefGoogle Scholar
  3. [Alp15]
    Alperin-Sheriff, J.: Short signatures with short public keys from homomorphic trapdoor functions. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 236–255. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46447-2_11 Google Scholar
  4. [AFL16]
    Apon, D., Fan, X., Liu, F.: Fully-secure lattice-based IBE as compact as PKE. In: IACR Cryptology ePrint Archive 2016, p. 125 (2016)Google Scholar
  5. [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). doi:10.1007/978-3-540-24676-3_14 CrossRefGoogle Scholar
  6. [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). doi:10.1007/978-3-540-28628-8_27 CrossRefGoogle Scholar
  7. [BBG05]
    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). doi:10.1007/11426639_26 CrossRefGoogle Scholar
  8. [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). doi:10.1007/3-540-44647-8_13 CrossRefGoogle Scholar
  9. [BGG+14]
    Boneh, D., Gentry, C., Gorbunov, S., Halevi, S., Nikolaenko, V., Segev, G., Vaikuntanathan, V., Vinayagamurthy, D.: 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). doi:10.1007/978-3-642-55220-5_30 CrossRefGoogle Scholar
  10. [BGH07]
    Boneh, D., Gentry, C., Hamburg, M.: Space-efficient identity based encryption without pairings. In: FOCS, pp. 647–657 (2007)Google Scholar
  11. [BGW05]
    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). doi:10.1007/11535218_16 CrossRefGoogle Scholar
  12. [BH08]
    Boneh, D., Hamburg, M.: Generalized identity based and broadcast encryption schemes. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 455–470. Springer, Heidelberg (2008). doi:10.1007/978-3-540-89255-7_28 CrossRefGoogle Scholar
  13. [Boy10]
    Boyen, X.: Lattice Mixing and Vanishing Trapdoors: a framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13013-7_29 CrossRefGoogle Scholar
  14. [BR09]
    Bellare, M., Ristenpart, T.: Simulation without the Artificial Abort: simplified proof and improved concrete security for Waters’ IBE scheme. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 407–424. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01001-9_24 CrossRefGoogle Scholar
  15. [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). doi:10.1007/978-3-642-13190-5_27 CrossRefGoogle Scholar
  16. [CCZ11]
    Chen, Y., Chen, L., Zhang, Z.: CCA secure IB-KEM from the computational bilinear Diffie-Hellman assumption in the standard model. In: Kim, H. (ed.) ICISC 2011. LNCS, vol. 7259, pp. 275–301. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31912-9_19 CrossRefGoogle Scholar
  17. [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). doi:10.1007/3-540-45325-3_32 CrossRefGoogle Scholar
  18. [CW13]
    Chen, J., Wee, H.: Fully, (almost) tightly secure IBE and dual system groups. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 435–460. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40084-1_25 CrossRefGoogle Scholar
  19. [DM14]
    Ducas, L., Micciancio, D.: Improved short lattice signatures in the standard model. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 335–352. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44371-2_19 CrossRefGoogle Scholar
  20. [DLP14]
    Ducas, L., Lyubashevsky, V., Prest, T.: Efficient identity-based encryption over NTRU lattices. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 22–41. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45608-8_2 Google Scholar
  21. [DM15]
    Ducas, L., Micciancio, D.: FHEW: bootstrapping homomorphic encryption in less than a second. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 617–640. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46800-5_24 Google Scholar
  22. [Gal10]
    Galindo, D.: Chosen-ciphertext secure identity-based encryption from computational bilinear Diffie-Hellman. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 367–376. Springer, Heidelberg (2010). doi:10.1007/978-3-642-17455-1_23 CrossRefGoogle Scholar
  23. [Gen06]
    Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006). doi:10.1007/11761679_27 CrossRefGoogle Scholar
  24. [GL89]
    Goldreich, O., Levin, L.: A hard-core predicate for all one-way functions. In: STOC, pp. 25–32 (1989)Google Scholar
  25. [GPV08]
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197–206 (2008)Google Scholar
  26. [JR13]
    Jutla, C.S., Roy, A.: Shorter Quasi-Adaptive NIZK proofs for linear subspaces. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8269, pp. 1–20. Springer, Heidelberg (2013). doi:10.1007/978-3-642-42033-7_1 CrossRefGoogle Scholar
  27. [LOS+10]
    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). doi:10.1007/978-3-642-13190-5_4 CrossRefGoogle Scholar
  28. [LPR10]
    Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13190-5_1 CrossRefGoogle Scholar
  29. [LPR13]
    Lyubashevsky, V., Peikert, C., Regev, O.: A toolkit for ring-LWE cryptography. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 35–54. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38348-9_3 CrossRefGoogle Scholar
  30. [LS15]
    Langlois, A., Stehlé, D.: Worst-case to average-case reductions for module lattices. DES 75(3), 565–599 (2015)MathSciNetMATHGoogle Scholar
  31. [LW10]
    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). doi:10.1007/978-3-642-11799-2_27 CrossRefGoogle Scholar
  32. [MP12]
    Micciancio, D., Peikert, C.: Trapdoors for Lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29011-4_41 CrossRefGoogle Scholar
  33. [Nac07]
    Naccache, D.: Secure and practical identity-based encryption. IET Inf. Sec. 1(2), 59–64 (2007)CrossRefGoogle Scholar
  34. [Reg05]
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93. ACM Press (2005)Google Scholar
  35. [Sha85]
    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). doi:10.1007/3-540-39568-7_5 CrossRefGoogle Scholar
  36. [SOK00]
    Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairings. In: SCIS (2000). (In Japanese)Google Scholar
  37. [SRB12]
    Singh, K., Pandu Rangan, C., Banerjee, A.K.: Adaptively secure efficient Lattice (H)IBE in standard model with short public parameters. In: Bogdanov, A., Sanadhya, S. (eds.) SPACE 2012. LNCS, vol. 7644, pp. 153–172. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34416-9_11 CrossRefGoogle 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). doi:10.1007/11426639_7 CrossRefGoogle 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). doi:10.1007/978-3-642-03356-8_36 CrossRefGoogle Scholar
  40. [Xag13]
    Xagawa, K.: Improved (hierarchical) inner-product encryption from lattices. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 235–252. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36362-7_15 CrossRefGoogle Scholar
  41. [Yam16]
    Yamada, S.: Adaptively secure identity-based encryption from lattices with asymptotically shorter public parameters. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 32–62. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49896-5_2 CrossRefGoogle Scholar
  42. [ZCZ16]
    Zhang, J., Chen, Y., Zhang, Z.: Programmable Hash Functions from Lattices: short signatures and IBEs with small key sizes. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 303–332. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53015-3_11 CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.The University of TokyoTokyoJapan
  2. 2.National Institute of Advanced Industrial Science and Technology (AIST)TokyoJapan

Personalised recommendations