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Identity-Based Encryption Resilient to Auxiliary Leakage under the Decisional Linear Assumption

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Cryptology and Network Security (CANS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11124))

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Abstract

Leakage-resilience guarantees that even if some information about the secret key is partially leaked, the security is maintained. Several security models considering leakage-resilience have been proposed. Among them, auxiliary leakage model proposed by Dodis et al. in STOC’09 is especially important, since it can deal with a leakage caused by a function which information-theoretically reveals the secret key, e.g., one-way permutation.

Contribution of this work is two-fold. Firstly, we propose an identity-based encryption (IBE) scheme and prove that it is fully secure and resilient to the auxiliary leakage under the decisional linear assumption in the standard model. Secondly, although the IBE scheme proposed by Yuen et al. in Eurocrypt’12 has been considered to be the only IBE scheme resilient to auxiliary leakage, we prove that the security proof for the IBE scheme is defective. We insist that our IBE scheme is the only IBE scheme resilient to auxiliary leakage.

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Notes

  1. 1.

    Secret denotes the secret information. |Secret| denotes the bit-length of Secret.

  2. 2.

    k denotes the minimum entropy of the secret key \(\mathrm{sk}\). If the secret-key is generated uniformly at random, k is equivalent to the bit-length of the secret-key \(|\mathrm{sk}|\).

  3. 3.

    Note that each one of our counterexamples indicates that their current proof is wrong, but not that their scheme cannot be proven to be secure in their security model. Thus, it is possible that their scheme is proven to be secure if the proof is done in another manner.

  4. 4.

    It obviously holds that \(\begin{bmatrix} \mathbf {I}_m|(r_0+\varSigma _{i=1}^{n} ID[i]r_i)\mathbf {I}_m \end{bmatrix} \mathbf {v}= \mathbf {E}\). Note that by pre-multiplying this equation by \(\mathbf {A}_0\), we obtain \(\mathbf {F}(ID)\mathbf {v}= \mathbf {D}\).

References

  1. 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_28

    Chapter  MATH  Google Scholar 

  2. Alwen, J., Dodis, Y., Wichs, D.: Leakage-resilient public-key cryptography in the bounded-retrieval model. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 36–54. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_3

    Chapter  MATH  Google Scholar 

  3. Akavia, A., Goldwasser, S., Vaikuntanathan, V.: Simultaneous hardcore bits and cryptography against memory attacks. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 474–495. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00457-5_28

    Chapter  MATH  Google Scholar 

  4. 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_14

    Chapter  Google Scholar 

  5. 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_27

    Chapter  Google Scholar 

  6. Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_3

    Chapter  Google Scholar 

  7. 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_13

    Chapter  Google Scholar 

  8. Brakerski, Z., Goldwasser, S.: Circular and leakage resilient public-key encryption under subgroup indistinguishability. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_1

    Chapter  Google Scholar 

  9. 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_30

    Chapter  Google Scholar 

  10. 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 2010, pp. 501–510 (2010)

    Google Scholar 

  11. Bellare, M., O’Neill, A., Stepanovs, I.: Forward-security under continual leakage. Cryptology ePrint Archive: Report 2017/476 (2017)

    Google Scholar 

  12. Boyle, E., Segev, G., Wichs, D.: Fully leakage-resilient signatures. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 89–108. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_7

    Chapter  Google Scholar 

  13. 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_32

    Chapter  Google Scholar 

  14. Chow, S.S.M., Dodis, Y., Rouselakis, Y., Waters, B.: Practical leakage-resilient identity-based encryption from simple assumptions. In: ACMCCS 2010, pp. 152–161 (2010)

    Google Scholar 

  15. 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). https://doi.org/10.1007/3-540-39200-9_16

    Chapter  Google Scholar 

  16. Dodis, Y., Goldwasser, S., Tauman Kalai, Y., Peikert, C., Vaikuntanathan, V.: Public-key encryption schemes with auxiliary inputs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 361–381. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_22

    Chapter  Google Scholar 

  17. Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Cryptography against continuous memory attacks. In: FOCS 2010, pp. 511–520 (2010)

    Google Scholar 

  18. Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Efficient public-key cryptography in the presence of key leakage. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 613–631. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_35

    Chapter  MATH  Google Scholar 

  19. Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Efficient public-key cryptography in the presence of key leakage. Cryptology ePrint Archive: Report 2010/154 (2010)

    Google Scholar 

  20. Dodis, Y., Kalai, Y.T., Lovett, S.: On cryptography with auxiliary input. In: STOC 2009, pp. 621–630 (2009)

    Google Scholar 

  21. Faust, S., Hazay, C., Nielsen, J.B., Nordholt, P.S., Zottarel, A.: Signature schemes secure against hard-to-invert leakage. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 98–115. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_8

    Chapter  Google Scholar 

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

    Google Scholar 

  23. Halderman, J.A., et al.: Lest we remember: cold boot attacks on encryption keys. In: USENIX Security Symposium, pp. 45–60 (2008)

    Google Scholar 

  24. Kurosawa, K., Trieu Phong, L.: Leakage resilient IBE and IPE under the DLIN assumption. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 487–501. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38980-1_31

    Chapter  MATH  Google Scholar 

  25. Lewko, A., Lewko, M., Waters, B.: How to leak on key updates. Cryptology ePrint Archive: Report 2010/562 (2010)

    Google Scholar 

  26. Lewko, A., Lewko, M., Waters, B.: How to leak on key updates. In: STOC 2011, pp. 725–734 (2011)

    Google Scholar 

  27. Lewko, A., Rouselakis, Y., Waters, B.: Achieving leakage resilience through dual system encryption. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 70–88. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_6

    Chapter  Google Scholar 

  28. 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). https://doi.org/10.1007/978-3-642-13190-5_4

    Chapter  Google Scholar 

  29. 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). https://doi.org/10.1007/978-3-642-11799-2_27

    Chapter  Google Scholar 

  30. Naor, M., Segev, G.: Public-key cryptosystems resilient to key leakage. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 18–35. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_2

    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). https://doi.org/10.1007/978-3-642-14623-7_11

    Chapter  Google Scholar 

  32. 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_5

    Chapter  Google Scholar 

  33. 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_7

    Chapter  Google Scholar 

  34. 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_36

    Chapter  Google Scholar 

  35. Wang, Z., Yiu, S.M.: Attribute-based encryption resilient to auxiliary input. In: Au, M.-H., Miyaji, A. (eds.) ProvSec 2015. LNCS, vol. 9451, pp. 371–390. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26059-4_21

    Chapter  Google Scholar 

  36. Yuen, T.H., Chow, S.S.M., Zhang, Y., Yiu, S.M.: Identity-based encryption resilient to continual auxiliary leakage. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 117–134. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_9

    Chapter  Google Scholar 

  37. Zhang, M.: New model and construction of ABE: achieving key resilient-leakage and attribute direct-revocation. In: Susilo, W., Mu, Y. (eds.) ACISP 2014. LNCS, vol. 8544, pp. 192–208. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08344-5_13

    Chapter  Google Scholar 

  38. Zhang, M., Wang, C., Takagi, T., Mu, Y.: Functional encryption resilient to hard-to-invert leakage. Comput. J. (2013). https://doi.org/10.1093/comjnl/bxt105

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Authors and Affiliations

  1. Institute of Industrial Science, The University of Tokyo, Tokyo, Japan

    Masahito Ishizaka & Kanta Matsuura

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  1. Masahito Ishizaka
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  2. Kanta Matsuura
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Correspondence to Masahito Ishizaka .

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  1. IBM Research - Zurich, Rüschlikon, Switzerland

    Jan Camenisch

  2. KTH Royal Institute of Technology, Stockholm, Sweden

    Panos Papadimitratos

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Ishizaka, M., Matsuura, K. (2018). Identity-Based Encryption Resilient to Auxiliary Leakage under the Decisional Linear Assumption. In: Camenisch, J., Papadimitratos, P. (eds) Cryptology and Network Security. CANS 2018. Lecture Notes in Computer Science(), vol 11124. Springer, Cham. https://doi.org/10.1007/978-3-030-00434-7_21

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  • DOI: https://doi.org/10.1007/978-3-030-00434-7_21

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