Leakage-Resilient Identity-Based Encryption in Bounded Retrieval Model with Nearly Optimal Leakage-Ratio

  • Ryo Nishimaki
  • Takashi YamakawaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11442)


We propose new constructions of leakage-resilient public-key encryption (PKE) and identity-based encryption (IBE) schemes in the bounded retrieval model (BRM). In the BRM, adversaries are allowed to obtain at most \(\ell \)-bit leakage from a secret key and we can increase \(\ell \) only by increasing the size of secret keys without losing efficiency in any other performance measure. We call \(\ell /|\mathsf {sk}|\) leakage-ratio where \(|\mathsf {sk}|\) denotes a bit-length of a secret key. Several PKE/IBE schemes in the BRM are known. However, none of these constructions achieve a constant leakage-ratio under a standard assumption in the standard model. Our PKE/IBE schemes are the first schemes in the BRM that achieve leakage-ratio \(1-\epsilon \) for any constant \(\epsilon >0\) under standard assumptions in the standard model.

As previous works, we use identity-based hash proof systems (IB-HPS) to construct IBE schemes in the BRM. It is known that a parameter for IB-HPS called the universality-ratio is translated into the leakage-ratio of the resulting IBE scheme in the BRM. We construct an IB-HPS with universality-ratio \(1-\epsilon \) for any constant \(\epsilon >0\) based on any inner-product predicate encryption (IPE) scheme with compact secret keys. Such IPE schemes exist under the d-linear, subgroup decision, learning with errors, or computational bilinear Diffie-Hellman assumptions. As a result, we obtain IBE schemes in the BRM with leakage-ratio \(1-\epsilon \) under any of these assumptions. Our PKE schemes are immediately obtained from our IBE schemes.



We thank Daniel Wichs for helpful comments on the presentation.


  1. [ADN+09]
    Alwen, J., Dodis, Y., Naor, M., Segev, G., Walfish, S., Wichs, D.: Public-key encryption in the bounded-retrieval model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 113–134. Springer, Heidelberg (2010). IACR Cryptology ePrint Archive, 2009:512, 2009. Version 20091028:202321CrossRefzbMATHGoogle Scholar
  2. [ADW09]
    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). Scholar
  3. [AFV11]
    Agrawal, S., Freeman, D.M., Vaikuntanathan, V.: Functional encryption for inner product predicates from learning with errors. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 21–40. Springer, Heidelberg (2011). Scholar
  4. [AGV09]
    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). Scholar
  5. [BB04]
    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). Scholar
  6. [BG10]
    Brakerski, Z., Goldwasser, S.: Circular and leakage resilient public-key encryption under subgroup indistinguishability - (or: Quadratic residuosity strikes back). In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010). Scholar
  7. [BKKV10]
    Brakerski, Z., Kalai, Y.T., Katz, J., Vaikuntanathan, V.: Overcoming the hole in the bucket: public-key cryptography resilient to continual memory leakage. In: 51st FOCS, pp. 501–510. IEEE Computer Society Press, October 2010Google Scholar
  8. [BLSV18]
    Brakerski, Z., Lombardi, A., Segev, G., Vaikuntanathan, V.: Anonymous IBE, leakage resilience and circular security from new assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part I. LNCS, vol. 10820, pp. 535–564. Springer, Cham (2018). Scholar
  9. [BSW13]
    Boyle, E., Segev, G., Wichs, D.: Fully leakage-resilient signatures. J. Cryptol. 26(3), 513–558 (2013)MathSciNetCrossRefGoogle Scholar
  10. [CDRW10]
    Chow, S.S.M., Dodis, Y., Rouselakis, Y., Waters, B.: Practical leakage-resilient identity-based encryption from simple assumptions. In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) ACM CCS 2010, pp. 152–161. ACM Press, October 2010Google Scholar
  11. [CGW15]
    Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015). Scholar
  12. [CS02]
    Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). Scholar
  13. [CZLC16]
    Chen, Y., Zhang, Z., Lin, D., Cao, Z.: Generalized (identity-based) hash proof system and its applications. Secur. Commun. Netw. 9(12), 1698–1716 (2016)CrossRefGoogle Scholar
  14. [DGK+10]
    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). Scholar
  15. [DHLW10a]
    Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Cryptography against continuous memory attacks. In: 51st FOCS, pp. 511–520. IEEE Computer Society Press, October 2010Google Scholar
  16. [DHLW10b]
    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). Scholar
  17. [DKL09]
    Dodis, Y., Kalai, Y.T., Lovett, S.: On cryptography with auxiliary input. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 621–630. ACM Press, May/June 2009Google Scholar
  18. [DLW06]
    Di Crescenzo, G., Lipton, R., Walfish, S.: Perfectly secure password protocols in the bounded retrieval model. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 225–244. Springer, Heidelberg (2006). Scholar
  19. [Dzi06]
    Dziembowski, S.: Intrusion-resilience via the bounded-storage model. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 207–224. Springer, Heidelberg (2006). Scholar
  20. [GJS11]
    Garg, S., Jain, A., Sahai, A.: Leakage-resilient zero knowledge. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 297–315. Springer, Heidelberg (2011). Scholar
  21. [GL89]
    Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: 21st ACM STOC, pp. 25–32. ACM Press, May 1989Google Scholar
  22. [HLWW16]
    Hazay, C., López-Alt, A., Wee, H., Wichs, D.: Leakage-resilient cryptography from minimal assumptions. J. Cryptol. 29(3), 514–551 (2016)MathSciNetCrossRefGoogle Scholar
  23. [KP17]
    Kurosawa, K., Phong, L.T.: Anonymous and leakage resilient IBE and IPE. Des. Codes Crypt. 85(2), 273–298 (2017)MathSciNetCrossRefGoogle Scholar
  24. [KSW08]
    Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008). Scholar
  25. [KV09]
    Katz, J., Vaikuntanathan, V.: Signature schemes with bounded leakage resilience. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 703–720. Springer, Heidelberg (2009). Scholar
  26. [LRW11]
    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). Scholar
  27. [NS12]
    Naor, M., Segev, G.: Public-key cryptosystems resilient to key leakage. SIAM J. Comput. 41(4), 772–814 (2012)MathSciNetCrossRefGoogle Scholar
  28. [QL13]
    Qin, B., Liu, S.: Leakage-resilient chosen-ciphertext secure public-key encryption from hash proof system and one-time lossy filter. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 381–400. Springer, Heidelberg (2013). Scholar
  29. [QL14]
    Qin, B., Liu, S.: Leakage-flexible CCA-secure public-key encryption: simple construction and free of pairing. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 19–36. Springer, Heidelberg (2014). Scholar
  30. [Wee14]
    Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616–637. Springer, Heidelberg (2014). Scholar
  31. [YAX+16]
    Yu, Z., Au, M.H., Xu, Q., Yang, R., Han, J.: Leakage-resilient functional encryption via pair encodings. In: Liu, J.K.K., Steinfeld, R. (eds.) ACISP 2016, Part I. LNCS, vol. 9722, pp. 443–460. Springer, Cham (2016). Scholar
  32. [YCZY12]
    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). Scholar
  33. [ZCG+18]
    Zhang, J., Chen, J., Gong, J., Ge, A., Ma, C.: Leakage-resilient attribute based encryption in prime-order groups via predicate encodings. Des. Codes Crypt. 86(6), 1339–1366 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.NTT Secure Platform LaboratoriesTokyoJapan

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