Efficient RKA-Secure KEM and IBE Schemes Against Invertible Functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9230)

Abstract

We propose efficient KEM and IBE schemes secure under the related-key attacks (RKAs) against almost all invertible related-key derivation (RKD) functions under the DBDH assumption. The class of RKD functions we consider is broader than the best known RKD function class: For example, the class contains polynomial functions of (bounded) polynomial degrees and the XOR functions simultaneously.

Keywords

Related-key attack security Invertible related-key derivation functions 

References

  1. 1.
    Abdalla, M., Benhamouda, F., Passelègue, A., Paterson, K.G.: Related-key security for pseudorandom functions beyond the linear barrier. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 77–94. Springer, Heidelberg (2014). https://eprint.iacr.org/2014/488 Google Scholar
  2. 2.
    Aggarwal, D., Dodis, Y., Lovett, S.: Non-malleable codes from additive combinatorics. In: Shmoys, D.B. (ed.) STOC 2013, pp. 774–783. ACM (2014). https://eprint.iacr.org/2013/201
  3. 3.
    Applebaum, B., Harnik, D., Ishai, Y.: Semantic security under related-key attacks and applications. In: Chazelle, B. (ed.) ICS 2011, pp. 45–60. Tsinghua University Press (2011). https://eprint.iacr.org/2010/544
  4. 4.
    Bellare, M., Cash, D.: Pseudorandom functions and permutations provably secure against related-key attacks. In: Rabin [30], pp. 666–684. https://eprint.iacr.org/2010/397
  5. 5.
    Bellare, M., Cash, D., Miller, R.: Cryptography secure against related-key attacks and tampering. In: Lee and Wang [25], pp. 486–503. https://eprint.iacr.org/2011/252
  6. 6.
    Bellare, M., Kohno, T.: A theoretical treatment of related-key attacks: RKA-PRPs, RKA-PRFs, and applications. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 491–506. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Bellare, M., Paterson, K.G., Thomson, S.: RKA Security beyond the linear barrier: IBE, encryption and signatures. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 331–348. Springer, Heidelberg (2012). https://eprint.iacr.org/2012/514 CrossRefGoogle Scholar
  8. 8.
    Biham, E.: New types of cryptanalytic attacks using related keys. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 398–409. Springer, Heidelberg (1994)Google Scholar
  9. 9.
    Biham, E.: New types of cryptanalytic attacks using related keys. J. Cryptol. 7(4), 229–246 (1994). A preliminary version appeared in EUROCRYPT 1993 (1993)CrossRefGoogle Scholar
  10. 10.
    Boneh, D., Boyen, X.: Efficient selective identity-based encryption without random oracles. J. Cryptol. 24(4), 659–693 (2011). A preliminary version appeared in EUROCRYPT 2004, 2004MathSciNetCrossRefGoogle Scholar
  11. 11.
    Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Boneh, D., DeMillo, R.A., Lipton, R.J.: On the importance of eliminating errors in cryptographic computations. J. Cryptol. 14(2), 101–119 (2001). A preliminary version appeared in EUROCRYPT 1997 (1997)MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Boyen, X., Mei, Q., Waters, B.: Direct chosen ciphertext security from identity-based techniques. In: Atluri, V., Meadows, C., Juels, A. (eds.) CCS 2005, pp. 320–329. ACM (2005). https://eprint.iacr.org/2005/288
  14. 14.
    Choi, S.G., Kiayias, A., Malkin, T.: BiTR: built-in tamper resilience. In: Lee and Wang [25], pp. 740–758. https://eprint.iacr.org/2010/503
  15. 15.
    Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: Yao, A.C.-C. (ed.) ICS 2010, pp. 434–452. Tsinghua University Press (2010). https://eprint.iacr.org/2009/608
  16. 16.
    Faust, S., Mukherjee, P., Venturi, D., Wichs, D.: Efficient non-malleable codes and key-derivation for poly-size tampering circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 111–128. Springer, Heidelberg (2014). https://eprint.iacr.org/2013/702 CrossRefGoogle Scholar
  17. 17.
    Gennaro, R., Lysyanskaya, A., Malkin, T., Micali, S., Rabin, T.: Algorithmic tamper-proof (ATP) security: theoretical foundations for security against hardware tampering. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 258–277. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Goyal, V., O’Neill, A., Rao, V.: Correlated-input secure hash functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 182–200. Springer, Heidelberg (2011). https://eprint.iacr.org/2011/233 CrossRefGoogle Scholar
  19. 19.
    Jafargholi, Z., Wichs, D.: Tamper detection and continuous non-malleable codes. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part I. LNCS, vol. 9014, pp. 451–480. Springer, Heidelberg (2015). https://eprint.iacr.org/2014/956 Google Scholar
  20. 20.
    Jia, D., Li, B., Lu, X., Mei, Q.: Related key secure PKE from hash proof systems. In: Yoshida, M., Mouri, K. (eds.) IWSEC 2014. LNCS, vol. 8639, pp. 250–265. Springer, Heidelberg (2014) Google Scholar
  21. 21.
    Jia, D., Lu, X., Li, B., Mei, Q.: RKA secure PKE based on the DDH and HR assumptions. In: Susilo, W., Reyhanitabar, R. (eds.) ProvSec 2013. LNCS, vol. 8209, pp. 271–287. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  22. 22.
    Kalai, Y.T., Kanukurthi, B., Sahai, A.: Cryptography with tamperable and leaky memory. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 373–390. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  23. 23.
    Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  24. 24.
    Knudsen, L.R.: Cryptanalysis of LOKI91. In: Seberry, J., Zheng, Y. (eds.) AUSCRYPT ’92. LNCS, vol. 718, pp. 196–208. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  25. 25.
    Lee, D.H., Wang, X. (eds.): ASIACRYPT 2011. LNCS, vol. 7073. Springer, Heidelberg (2011)MATHGoogle Scholar
  26. 26.
    Lewi, K., Montgomery, H., Raghunathan, A.: Improved constructions of PRFs secure against related-key attacks. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 44–61. Springer, Heidelberg (2014) Google Scholar
  27. 27.
    Liu, F.-H., Lysyanskaya, A.: Tamper and leakage resilience in the split-state model. Manuscript, February 2012. Available at the authors’ citeGoogle Scholar
  28. 28.
    Paterson, K.G., Schuldt, J.C.N., Stam, M., Thomson, S.: On the joint security of encryption and signature, revisited. In: Lee and Wang [25], pp. 161–178. https://eprint.iacr.org/2011/486
  29. 29.
    Qin, B., Liu, S., Yuen, T.H., Deng, R.H., Chen, K.: Continuous non-malleable key derivation and its application to related-key security. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 557–578. Springer, Heidelberg (2015). https://eprint.iacr.org/2015/003 Google Scholar
  30. 30.
    Rabin, T. (ed.): CRYPTO 2010. LNCS, vol. 6223. Springer, Heidelberg (2010) MATHGoogle Scholar
  31. 31.
    von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 3rd edn. Cambridge University Press, Cambridge (2013) MATHCrossRefGoogle Scholar
  32. 32.
    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://eprint.iacr.org/2004/180 CrossRefGoogle Scholar
  33. 33.
    Wee, H.: Efficient chosen-ciphertext security via extractable hash proofs. In: Rabin [30], pp. 314–332Google Scholar
  34. 34.
    Wee, H.: Public key encryption against related key attacks. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 262–279. Springer, Heidelberg (2012) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.NTT Secure Platform LaboratoriesTokyoJapan

Personalised recommendations